###
post: Water in def2-SVP
agent: claude

Generated by `tools/hf_reference.py` from PySCF 2.5.0. Do not edit; rerun the
generator. Settings: conv_tol 1e-12, init_guess minao, symmetry off, and each
molecule built with cart=False and with cart=True. Every stored density is
then re-converged from itself at conv_tol_grad 1e-10 or tighter, and its
`_SELF_STEP` constant says how far one PySCF step moves it (below 1e-10).

Conventions:

- atoms[natm,4] = (Z, x, y, z) in Bohr; shells[nsh,8] = (atom, l, nprim, p0,
  cart0, sph0, ncart, nsph); prims[nprim,2] = (exponent, raw bas_ctr_coeff).
  General contractions are split into segmented shells, and primitives whose
  coefficient is exactly zero are dropped.
- `_unit` matrices are unit-Cartesian: PySCF's Cartesian integrals divided by
  F_i F_j, so every component has self-overlap 1. `_sph` matrices are PySCF's
  spherical ones, and `_m()` is M with X_sph = M^T X_unit M.
- Packed-8 ERIs in chemist's notation: ij = i(i+1)/2 + j for i >= j, and
  ijkl = ij(ij+1)/2 + kl for ij >= kl. Full when the basis has at most 19
  functions; otherwise the pair diagonal and 256 seeded samples. Both carry
  _SUMSQ = sum Gp^2 and _WSUM = sum w_k Gp_k, where w_k = s_k / (2^31 - 1),
  s_k = 16807 s_(k-1) mod (2^31 - 1) and s_0 = the module's _SEED_WSUM (20260923).
- Energies: `_E_<CFG>_DEFAULT` is the state PySCF reaches from the minao
  guess, `_E_<CFG>_STABLE` the lowest state reached by restarting from the
  stability-analysis orbitals until the energy stops dropping, and `_E_<CFG>`
  repeats the default. Densities (total for RHF, alpha and beta otherwise) are
  in the same basis convention as the matrices beside them: a unit-Cartesian
  density is F_i F_j times PySCF's. A `_stable_` density appears only when the
  stable state differs from the default.
- In a module with both bases, spherical names carry no suffix and Cartesian
  ones end in `_cart` / `_CART`.
###

# Seed of the LCG weights in every _WSUM checksum.
WATERSVP_SEED_WSUM = 20260923

# ---- helpers for the tests below ----

#| Reshape a flat row-major vector into r x c.
def watersvp_mat(v: Arr, r, c) -> Arr {
    a = zeros(r, c)
    for i to r {
        for j to c {
            a[i, j] = v[i * c + j]
        }
    }
    return a
}

def watersvp_eye(n) -> Arr {
    a = zeros(n, n)
    for i to n {
        a[i, i] = 1.0
    }
    return a
}

#| Largest |A_ij - A_ji| / (1 + |A_ij|): a kinetic entry near 100 carries
#| rounding of about 1e-14, so the gap is measured relative to the entry.
def watersvp_asym(a: Arr, n) {
    w = 0.0
    for i to n {
        for j to n {
            w = max(w, abs(a[i, j] - a[j, i]) / (1.0 + abs(a[i, j])))
        }
    }
    return w
}

#| Largest |A_ii - 1|.
def watersvp_diag_dev(a: Arr, n) {
    w = 0.0
    for i to n {
        w = max(w, abs(a[i, i] - 1.0))
    }
    return w
}

#| sum_ij A_ij B_ij: Tr(D S) is the electron count.
def watersvp_trace2(a: Arr, b: Arr, n) {
    t = 0.0
    for i to n {
        for j to n {
            t = t + a[i, j] * b[i, j]
        }
    }
    return t
}

#| pr[i, j] = the packed pair index of (i, j), in either order.
def watersvp_pair_table(n) -> Arr {
    pr = zeros(n, n)
    for i to n {
        for j to i + 1 {
            pr[i, j] = i * (i + 1) / 2 + j
            pr[j, i] = pr[i, j]
        }
    }
    return pr
}

#| One- plus two-electron energy from spin densities and packed (ij|kl):
#| sum Dt h + 1/2 sum (ij|kl) [Dt_ij Dt_kl - Da_ik Da_jl - Db_ik Db_jl].
#| For RHF pass Da = Db = D/2. Written over all n^4 quartets because it is
#| a check, not a J/K build.
def watersvp_e_elec(h: Arr, g: Arr, da: Arr, db: Arr, n) {
    pr = watersvp_pair_table(n)
    e = 0.0
    for i to n {
        for j to n {
            e = e + (da[i, j] + db[i, j]) * h[i, j]
        }
    }
    e2 = 0.0
    for i to n {
        for j to n {
            pij = pr[i, j]
            dij = da[i, j] + db[i, j]
            for k to n {
                for l to n {
                    pkl = pr[k, l]
                    a = max(pij, pkl)
                    b = min(pij, pkl)
                    x = g[a * (a + 1) / 2 + b]
                    e2 = e2 + x * (dij * (da[k, l] + db[k, l]) - da[i, k] * da[j, l] - db[i, k] * db[j, l])
                }
            }
        }
    }
    return e + 0.5 * e2
}

def watersvp_sumsq(g: Arr) {
    t = 0.0
    for k to len(g) {
        t = t + g[k] * g[k]
    }
    return t
}

#| sum_k w_k g_k with w_k = s_k / (2^31 - 1), s_k = 16807 s_(k-1) mod (2^31 - 1),
#| s_0 = seed. Every product stays below 2^53, so the weights are exact.
def watersvp_wsum(g: Arr, seed) {
    s = seed
    t = 0.0
    for k to len(g) {
        s = mod(16807.0 * s, 2147483647.0)
        t = t + s / 2147483647.0 * g[k]
    }
    return t
}

#| Largest (ij|kl)^2 - (ij|ij)(kl|kl) over the packed set, relative to the
#| bound. Cauchy-Schwarz says it is at most 0.
def watersvp_schwarz(g: Arr, n) {
    npair = n * (n + 1) / 2
    w = -1.0
    for a to npair {
        for b to a + 1 {
            x = g[a * (a + 1) / 2 + b]
            q = g[a * (a + 1) / 2 + a] * g[b * (b + 1) / 2 + b]
            w = max(w, (x * x - q) / (q + 1.0e-300))
        }
    }
    return w
}

#| The same bound on sampled entries, with the pair diagonal given.
def watersvp_sample_schwarz(idx: Arr, val: Arr, gd: Arr) {
    w = -1.0
    for k to len(idx) {
        a = floor((sqrt(8.0 * idx[k] + 1.0) - 1.0) / 2.0)
        if a * (a + 1) / 2 > idx[k] {
            a = a - 1
        }
        if (a + 1) * (a + 2) / 2 <= idx[k] {
            a = a + 1
        }
        b = idx[k] - a * (a + 1) / 2
        q = gd[a] * gd[b]
        w = max(w, (val[k] * val[k] - q) / (q + 1.0e-300))
    }
    return w
}

#| Largest |M^T X M - Y|.
def watersvp_mtxm_dev(m: Arr, x: Arr, y: Arr, nc, ns) {
    w = 0.0
    for a to ns {
        for b to ns {
            t = 0.0
            for i to nc {
                for j to nc {
                    t = t + m[i, a] * x[i, j] * m[j, b]
                }
            }
            w = max(w, abs(t - y[a, b]))
        }
    }
    return w
}

#| Count what is wrong with a shells pack: offsets that do not run on, a
#| component count that does not match l, a primitive range out of bounds.
def watersvp_pack_bad(sh: Arr, nsh, nprim, natm) {
    bad = 0
    p0 = 0
    c0 = 0
    s0 = 0
    for k to nsh {
        l = sh[k, 1]
        if sh[k, 0] < 0 or sh[k, 0] >= natm {
            bad = bad + 1
        }
        if sh[k, 3] != p0 or sh[k, 4] != c0 or sh[k, 5] != s0 {
            bad = bad + 1
        }
        if sh[k, 6] != (l + 1) * (l + 2) / 2 or sh[k, 7] != 2 * l + 1 {
            bad = bad + 1
        }
        p0 = p0 + sh[k, 2]
        c0 = c0 + sh[k, 6]
        s0 = s0 + sh[k, 7]
    }
    if p0 != nprim {
        bad = bad + 1
    }
    return bad
}

# ======== WATERSVP: def2-svp, spherical, and Cartesian with the _cart suffix ========

WATERSVP_NATOM = 3
WATERSVP_NSH = 12
WATERSVP_NPRIMTOT = 22
WATERSVP_NAO_CART = 25
WATERSVP_NAO_SPH = 24
WATERSVP_E_NUC = 9.188258417746113

#| (Z, x, y, z) in Bohr, one atom per row.
def watersvp_atoms_flat() -> Arr {
    return [8.0, 0.0, 0.0, 0.0,
        1.0, 0.0, -1.430522676295752, 1.1092692351196913,
        1.0, 0.0, 1.430522676295752, 1.1092692351196913]
}

def watersvp_atoms() -> Arr {
    return watersvp_mat(watersvp_atoms_flat(), 3, 4)
}

#| (atom, l, nprim, p0, cart0, sph0, ncart, nsph); general contractions split.
def watersvp_shells_flat() -> Arr {
    return [0, 0, 5, 0,
        0, 0, 1, 1,
        0, 0, 1, 5,
        1, 1, 1, 1,
        0, 0, 1, 6,
        2, 2, 1, 1,
        0, 1, 3, 7,
        3, 3, 3, 3,
        0, 1, 1, 10,
        6, 6, 3, 3,
        0, 2, 1, 11,
        9, 9, 6, 5,
        1, 0, 3, 12,
        15, 14, 1, 1,
        1, 0, 1, 15,
        16, 15, 1, 1,
        1, 1, 1, 16,
        17, 16, 3, 3,
        2, 0, 3, 17,
        20, 19, 1, 1,
        2, 0, 1, 20,
        21, 20, 1, 1,
        2, 1, 1, 21,
        22, 21, 3, 3]
}

def watersvp_shells() -> Arr {
    return watersvp_mat(watersvp_shells_flat(), 12, 8)
}

#| (exponent, raw bas_ctr_coeff).
def watersvp_prims_flat() -> Arr {
    return [2266.1767785, -0.005389350392174296, 340.87010191, -0.04023472138896016,
        77.363135167, -0.18008184205525826, 21.47964494, -0.46828857657650924,
        6.6589433124, -0.4469261716018729, 0.80975975668, 1.0000000000000002,
        0.25530772234, 1.0, 17.721504317, 0.06263024876316103,
        3.863550544, 0.3333113848235177, 1.0480920883, 0.7414863830812235,
        0.27641544411, 1.0000000000000002, 1.2, 1.0000000000000002,
        13.010701, 0.03348548481298865, 1.9622572, 0.23472187088124857,
        0.44453796, 0.8137702852595534, 0.12194962, 1.0,
        0.8, 1.0000000000000002, 13.010701, 0.03348548481298865,
        1.9622572, 0.23472187088124857, 0.44453796, 0.8137702852595534,
        0.12194962, 1.0, 0.8, 1.0000000000000002]
}

def watersvp_prims() -> Arr {
    return watersvp_mat(watersvp_prims_flat(), 22, 2)
}

#| F per Cartesian AO: PySCF-Cartesian = F x unit-Cartesian.
def watersvp_fc() -> Arr {
    return [1.0, 1.0, 1.0, 1.0,
        1.0, 1.0, 1.0, 1.0,
        1.0, 1.5853309190424043, 0.9152912328637689, 0.9152912328637689,
        1.5853309190424043, 0.9152912328637689, 1.5853309190424043, 1.0,
        1.0, 1.0, 1.0, 1.0,
        1.0, 1.0, 1.0, 1.0,
        1.0]
}

#| Overlap, spherical, [24,24].
def watersvp_s_sph_flat() -> Arr {
    return [0.9999999999999999, -0.3440165538027238, -0.15787004200514215, -0.0,
        -0.0, -0.0, -0.0, -0.0,
        -0.0, -0.0, -0.0, 0.0,
        -0.0, 0.0, -0.04785460032374623, -0.06252157963143691,
        -0.0, -0.07212249497292916, 0.05592589768706661, -0.04785460032374623,
        -0.06252157963143691, -0.0, 0.07212249497292916, 0.05592589768706661,
        -0.34401655380272383, 1.0000000000000002, 0.7889407941247987, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.32932204024788264, 0.3914645717081812,
        0.0, 0.3443105932745787, -0.26698853137672085, 0.32932204024788264,
        0.3914645717081812, 0.0, -0.3443105932745787, -0.26698853137672085,
        -0.15787004200514215, 0.7889407941247987, 1.0000000000000002, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.5110637904358923, 0.6903548488171068,
        0.0, 0.26026247518897516, -0.20181515579382875, 0.5110637904358923,
        0.6903548488171068, 0.0, -0.26026247518897516, -0.20181515579382875,
        -0.0, 0.0, 0.0, 1.0,
        0.0, 0.0, 0.5021408928230414, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.18318229508363296, 0.0, -0.0, 0.0,
        0.0, 0.18318229508363296, -0.0, -0.0,
        -0.0, 0.0, 0.0, 0.0,
        1.0, 0.0, 0.0, 0.5021408928230414,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, -0.22234476894334795, -0.0837029824736131,
        -0.0, -0.1736970385141288, 0.2767347012178153, 0.22234476894334795,
        0.0837029824736131, 0.0, -0.1736970385141288, -0.2767347012178153,
        -0.0, 0.0, 0.0, 0.0,
        0.0, 1.0, 0.0, 0.0,
        0.5021408928230414, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.17241265438539663, 0.06490574730780832,
        0.0, 0.27673470121781524, -0.031405907842202666, 0.17241265438539663,
        0.06490574730780832, 0.0, -0.27673470121781524, -0.031405907842202666,
        -0.0, 0.0, 0.0, 0.5021408928230416,
        0.0, 0.0, 1.0000000000000004, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.36398345112063346, 0.0, -0.0, 0.0,
        0.0, 0.36398345112063346, -0.0, -0.0,
        -0.0, 0.0, 0.0, 0.0,
        0.5021408928230416, 0.0, 0.0, 1.0000000000000004,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, -0.49180463764013643, -0.30882567073517864,
        -0.0, 0.05794675942438177, 0.23730982566142628, 0.49180463764013643,
        0.30882567073517864, 0.0, 0.05794675942438177, -0.23730982566142628,
        -0.0, 0.0, 0.0, 0.0,
        0.0, 0.5021408928230416, 0.0, 0.0,
        1.0000000000000004, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.3813597388305946, 0.23947248179861277,
        0.0, 0.2373098256614264, 0.17996645288647595, 0.3813597388305946,
        0.23947248179861277, 0.0, -0.2373098256614264, 0.17996645288647595,
        -0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 1.0000000000000007, 0.0, 0.0,
        0.0, 0.0, -0.0, -0.0,
        -0.24712287532498559, -0.0, 0.0, 0.0,
        0.0, 0.24712287532498559, -0.0, -0.0,
        -0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 1.0000000000000007, 0.0,
        0.0, 0.0, -0.19075773326005377, -0.019856741624293326,
        -0.0, -0.18483112538383964, 0.04479327158791809, 0.19075773326005377,
        0.019856741624293326, 0.0, -0.18483112538383964, -0.04479327158791809,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 1.0000000000000002,
        0.0, 0.0, 0.014386283671178335, 0.001497526275398453,
        0.0, 0.17106756795767766, 0.19925572151782525, 0.014386283671178335,
        0.001497526275398453, 0.0, -0.17106756795767766, 0.19925572151782525,
        -0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        1.0000000000000007, 0.0, 0.0, 0.0,
        0.19162632472360178, 0.0, -0.0, 0.0,
        0.0, 0.19162632472360178, -0.0, -0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 1.0000000000000009, -0.12300136633548614, -0.012803708185340767,
        0.0, 0.0043815723170357035, 0.18822872505372065, -0.12300136633548614,
        -0.012803708185340767, 0.0, -0.0043815723170357035, 0.18822872505372065,
        -0.04785460032374623, 0.32932204024788264, 0.5110637904358925, 0.0,
        -0.22234476894334804, 0.17241265438539666, 0.0, -0.49180463764013643,
        0.38135973883059454, -0.0, -0.190757733260054, 0.01438628367117828,
        0.0, -0.12300136633548625, 0.9999999999999997, 0.6847998247453728,
        0.0, 0.0, 0.0, 0.12116903885173679,
        0.30763577680074294, 0.0, -0.14171411608090512, 0.0,
        -0.06252157963143692, 0.39146457170818133, 0.690354848817107, 0.0,
        -0.08370298247361324, 0.06490574730780842, 0.0, -0.3088256707351786,
        0.23947248179861272, -0.0, -0.019856741624293354, 0.001497526275398453,
        0.0, -0.012803708185340767, 0.6847998247453728, 1.0,
        0.0, 0.0, 0.0, 0.30763577680074294,
        0.6070681526935895, 0.0, -0.1587920912149586, 0.0,
        -0.0, 0.0, 0.0, 0.18318229508363296,
        -0.0, 0.0, 0.36398345112063346, -0.0,
        0.0, -0.2471228753249856, -0.0, 0.0,
        0.1916263247236018, 0.0, 0.0, 0.0,
        1.0000000000000002, 0.0, 0.0, 0.0,
        0.0, 0.03784591602610543, -0.0, 0.0,
        -0.07212249497292919, 0.34431059327457875, 0.26026247518897516, 0.0,
        -0.17369703851412885, 0.27673470121781524, 0.0, 0.05794675942438186,
        0.23730982566142633, -0.0, -0.18483112538383967, 0.1710675679576777,
        0.0, 0.0043815723170357035, 0.0, 0.0,
        0.0, 1.0000000000000002, 0.0, 0.1417141160809051,
        0.15879209121495874, 0.0, -0.20998671804645133, 0.0,
        0.05592589768706662, -0.2669885313767209, -0.20181515579382883, -0.0,
        0.2767347012178153, -0.0314059078422026, -0.0, 0.23730982566142633,
        0.17996645288647595, 0.0, 0.04479327158791809, 0.19925572151782533,
        -0.0, 0.18822872505372065, 0.0, 0.0,
        0.0, 0.0, 1.0000000000000002, 0.0,
        0.0, 0.0, -0.0, 0.03784591602610543,
        -0.04785460032374623, 0.32932204024788264, 0.5110637904358925, 0.0,
        0.22234476894334804, 0.17241265438539666, 0.0, 0.49180463764013643,
        0.38135973883059454, 0.0, 0.190757733260054, 0.01438628367117828,
        0.0, -0.12300136633548625, 0.12116903885173679, 0.30763577680074294,
        0.0, 0.14171411608090512, 0.0, 0.9999999999999997,
        0.6847998247453728, 0.0, 0.0, 0.0,
        -0.06252157963143692, 0.39146457170818133, 0.690354848817107, 0.0,
        0.08370298247361324, 0.06490574730780842, 0.0, 0.3088256707351786,
        0.23947248179861272, 0.0, 0.019856741624293354, 0.001497526275398453,
        0.0, -0.012803708185340767, 0.30763577680074294, 0.6070681526935895,
        0.0, 0.1587920912149586, 0.0, 0.6847998247453728,
        1.0, 0.0, 0.0, 0.0,
        -0.0, 0.0, 0.0, 0.18318229508363296,
        0.0, 0.0, 0.36398345112063346, 0.0,
        0.0, 0.2471228753249856, 0.0, 0.0,
        0.1916263247236018, 0.0, 0.0, 0.0,
        0.03784591602610543, 0.0, 0.0, 0.0,
        0.0, 1.0000000000000002, 0.0, 0.0,
        0.07212249497292919, -0.34431059327457875, -0.26026247518897516, -0.0,
        -0.17369703851412885, -0.27673470121781524, -0.0, 0.05794675942438186,
        -0.23730982566142633, -0.0, -0.18483112538383967, -0.1710675679576777,
        -0.0, -0.0043815723170357035, -0.1417141160809051, -0.15879209121495874,
        -0.0, -0.20998671804645133, -0.0, 0.0,
        0.0, 0.0, 1.0000000000000002, 0.0,
        0.05592589768706662, -0.2669885313767209, -0.20181515579382883, -0.0,
        -0.2767347012178153, -0.0314059078422026, -0.0, -0.23730982566142633,
        0.17996645288647595, -0.0, -0.04479327158791809, 0.19925572151782533,
        -0.0, 0.18822872505372065, 0.0, 0.0,
        0.0, 0.0, 0.03784591602610543, 0.0,
        0.0, 0.0, 0.0, 1.0000000000000002]
}

def watersvp_s_sph() -> Arr {
    return watersvp_mat(watersvp_s_sph_flat(), 24, 24)
}

#| Kinetic energy, spherical.
def watersvp_t_sph_flat() -> Arr {
    return [29.356654381441977, -0.7681118715965942, -0.11754936196761044, -0.0,
        -0.0, -0.0, -0.0, -0.0,
        -0.0, -0.0, -0.0, 0.0,
        -0.0, 0.0, 0.0036718301591963255, -0.016632898965150182,
        0.0, -0.009528610627034485, 0.00738876411898181, 0.0036718301591963255,
        -0.016632898965150182, 0.0, 0.009528610627034485, 0.00738876411898181,
        -0.7681118715965938, 1.2146396350200004, 0.4594187165589615, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, -3.3306690738754696e-16,
        0.0, 0.0, 0.08064849338325045, 0.09565145880517822,
        0.0, 0.3273611037237572, -0.25384540011340223, 0.08064849338325045,
        0.09565145880517822, 0.0, -0.3273611037237572, -0.25384540011340223,
        -0.11754936196761027, 0.4594187165589617, 0.3829615835100001, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, -1.6653345369377348e-16,
        0.0, 0.0, 0.16226927917565803, 0.14010699152154277,
        0.0, 0.1879657234073066, -0.14575413426696027, 0.16226927917565803,
        0.14010699152154277, 0.0, -0.1879657234073066, -0.14575413426696027,
        -0.0, 0.0, 0.0, 4.332326592391174,
        0.0, 0.0, 0.5611807178111391, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.15884366695204688, 0.0, 0.0, 0.0,
        0.0, 0.15884366695204688, 0.0, 0.0,
        -0.0, 0.0, 0.0, 0.0,
        4.332326592391174, 0.0, 0.0, 0.5611807178111391,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, -0.1736696530577731, -0.03942968381559875,
        0.0, -0.4892303831476449, 0.5025356240535257, 0.1736696530577731,
        0.03942968381559875, 0.0, -0.4892303831476449, -0.5025356240535257,
        0.0, 0.0, 0.0, 0.0,
        0.0, 4.3323265923911745, 0.0, 0.0,
        0.561180717811139, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.13466854206725604, 0.030574933156877745,
        0.0, 0.5025356240535258, -0.23083719344348758, 0.13466854206725604,
        0.030574933156877745, 0.0, -0.5025356240535258, -0.23083719344348758,
        -0.0, 0.0, 0.0, 0.5611807178111393,
        0.0, 0.0, 0.6910386102750002, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.27319922256602525, 0.0, -0.0, 0.0,
        0.0, 0.27319922256602525, -0.0, -0.0,
        -0.0, 0.0, 0.0, 0.0,
        0.5611807178111393, 0.0, 0.0, 0.6910386102750002,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, -0.33844703816829463, -0.11616875376215421,
        -0.0, -0.08224693554445205, 0.27562337491525785, 0.33844703816829463,
        0.11616875376215421, 0.0, -0.08224693554445205, -0.27562337491525785,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.5611807178111393, 0.0, 0.0,
        0.6910386102750004, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.26244175879100257, 0.09008065846550134,
        0.0, 0.2756233749152579, 0.05947277464626793, 0.26244175879100257,
        0.09008065846550134, 0.0, -0.2756233749152579, 0.05947277464626793,
        -0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 4.200000000000002, 0.0, 0.0,
        0.0, 0.0, 0.0, -0.0,
        -0.4571814596861261, 0.0, 0.0, 0.0,
        0.0, 0.4571814596861261, 0.0, -0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 4.200000000000004, 0.0,
        0.0, 0.0, -0.29708944201622095, -0.013792214845553773,
        -0.0, -0.7033398307525297, 0.36310780394744163, 0.29708944201622095,
        0.013792214845553773, 0.0, -0.7033398307525297, -0.36310780394744163,
        0.0, -2.220446049250313e-16, -5.551115123125783e-17, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 4.2,
        0.0, 0.0, 0.02240545070186388, 0.0010401607936464247,
        0.0, 0.343733331805462, 0.34749173631334684, 0.02240545070186388,
        0.0010401607936464247, 0.0, -0.343733331805462, 0.34749173631334684,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        4.200000000000004, 0.0, 0.0, 0.0,
        0.35451191127576737, 0.0, 0.0, 0.0,
        0.0, 0.35451191127576737, -0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 4.200000000000001, -0.19156448688780178, -0.008893276523069968,
        0.0, -0.224925668691575, 0.5289258710141488, -0.19156448688780178,
        -0.008893276523069968, 0.0, 0.224925668691575, 0.5289258710141488,
        0.0036718301591964183, 0.08064849338325042, 0.16226927917565803, 0.0,
        -0.17366965305777324, 0.13466854206725606, 0.0, -0.3384470381682946,
        0.26244175879100246, 0.0, -0.2970894420162213, 0.022405450701863783,
        0.0, -0.19156448688780184, 0.969225931578449, 0.20114159492026099,
        0.0, 0.0, 0.0, -0.030366562053356867,
        0.04193098006107518, 0.0, 0.0054302735134623414, 0.0,
        -0.01663289896515019, 0.09565145880517825, 0.14010699152154282, 0.0,
        -0.03942968381559884, 0.03057493315687783, 0.0, -0.11616875376215416,
        0.09008065846550131, -0.0, -0.013792214845553789, 0.001040160793646494,
        0.0, -0.00889327652307001, 0.2011415949202609, 0.18292443,
        0.0, 0.0, 0.0, 0.04193098006107515,
        0.07409730663441164, 0.0, -0.05490651658161447, 0.0,
        0.0, 0.0, 0.0, 0.15884366695204688,
        0.0, 0.0, 0.27319922256602536, -0.0,
        0.0, -0.4571814596861261, -0.0, 0.0,
        0.35451191127576737, -0.0, 0.0, 0.0,
        2.0000000000000004, 0.0, 0.0, 0.0,
        0.0, -0.023441221576811846, 0.0, 0.0,
        -0.0095286106270346, 0.32736110372375726, 0.18796572340730666, 0.0,
        -0.4892303831476447, 0.5025356240535258, 0.0, -0.08224693554445187,
        0.2756233749152579, 0.0, -0.7033398307525301, 0.3437333318054624,
        0.0, -0.22492566869157526, 0.0, 0.0,
        0.0, 2.0000000000000004, 0.0, -0.0054302735134623865,
        0.05490651658161446, 0.0, -0.06820332366683736, 0.0,
        0.0073887641189818755, -0.25384540011340223, -0.14575413426696038, 0.0,
        0.5025356240535255, -0.23083719344348758, -0.0, 0.27562337491525785,
        0.05947277464626794, 0.0, 0.3631078039474414, 0.34749173631334745,
        0.0, 0.5289258710141485, 0.0, 0.0,
        0.0, 0.0, 2.0000000000000004, 0.0,
        0.0, 0.0, 0.0, -0.02344122157681184,
        0.0036718301591964183, 0.08064849338325042, 0.16226927917565803, 0.0,
        0.17366965305777324, 0.13466854206725606, 0.0, 0.3384470381682946,
        0.26244175879100246, 0.0, 0.2970894420162213, 0.022405450701863783,
        0.0, -0.19156448688780184, -0.030366562053356867, 0.04193098006107518,
        0.0, -0.0054302735134623414, 0.0, 0.969225931578449,
        0.20114159492026099, 0.0, 0.0, 0.0,
        -0.01663289896515019, 0.09565145880517825, 0.14010699152154282, 0.0,
        0.03942968381559884, 0.03057493315687783, 0.0, 0.11616875376215416,
        0.09008065846550131, 0.0, 0.013792214845553789, 0.001040160793646494,
        0.0, -0.00889327652307001, 0.04193098006107515, 0.07409730663441164,
        0.0, 0.05490651658161447, 0.0, 0.2011415949202609,
        0.18292443, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.15884366695204688,
        0.0, 0.0, 0.27319922256602536, 0.0,
        0.0, 0.4571814596861261, 0.0, 0.0,
        0.35451191127576737, -0.0, 0.0, 0.0,
        -0.023441221576811846, 0.0, 0.0, 0.0,
        0.0, 2.0000000000000004, 0.0, 0.0,
        0.0095286106270346, -0.32736110372375726, -0.18796572340730666, 0.0,
        -0.4892303831476447, -0.5025356240535258, -0.0, -0.08224693554445187,
        -0.2756233749152579, 0.0, -0.7033398307525301, -0.3437333318054624,
        -0.0, 0.22492566869157526, 0.0054302735134623865, -0.05490651658161446,
        0.0, -0.06820332366683736, 0.0, 0.0,
        0.0, 0.0, 2.0000000000000004, 0.0,
        0.0073887641189818755, -0.25384540011340223, -0.14575413426696038, 0.0,
        -0.5025356240535255, -0.23083719344348758, -0.0, -0.27562337491525785,
        0.05947277464626794, -0.0, -0.3631078039474414, 0.34749173631334745,
        0.0, 0.5289258710141485, 0.0, 0.0,
        0.0, 0.0, -0.02344122157681184, 0.0,
        0.0, 0.0, 0.0, 2.0000000000000004]
}

def watersvp_t_sph() -> Arr {
    return watersvp_mat(watersvp_t_sph_flat(), 24, 24)
}

#| Nuclear attraction, spherical.
def watersvp_v_sph_flat() -> Arr {
    return [-62.38880199569874, 11.885422094704943, 5.250893247884067, 0.0,
        0.0, 0.026618755186472314, 0.0, 0.0,
        0.0035687065317149256, 0.0, 0.0, 0.00020796415679447122,
        0.0, -0.0017780738944975782, 1.5600943210125888, 2.054917809075752,
        0.0, 2.3611379221699584, -1.8299113505899274, 1.5600943210125886,
        2.054917809075752, 0.0, -2.3611379221699584, -1.8299113505899274,
        11.885422094704943, -12.5914355789141, -8.214313277761326, 0.0,
        0.0, -0.18582135169234293, 0.0, 0.0,
        -0.1371540592423394, 0.0, 0.0, -0.010430187716009343,
        0.0, 0.08917711964592545, -3.202339145199478, -3.799101367119256,
        0.0, -3.812546214365835, 2.9259743893637267, -3.202339145199478,
        -3.799101367119256, 0.0, 3.8125462143658355, 2.9259743893637267,
        5.250893247884067, -8.214313277761326, -7.480910287875368, 0.0,
        0.0, -0.16904141186578137, 0.0, 0.0,
        -0.25015762894523746, 0.0, 0.0, -0.012643716015226403,
        0.0, 0.10810257749514651, -3.5918583579725145, -4.3836435147764305,
        0.0, -2.6786798166896952, 2.0284499173737816, -3.5918583579725145,
        -4.3836435147764305, 0.0, 2.6786798166896952, 2.0284499173737816,
        0.0, 0.0, 0.0, -12.790700677339071,
        0.0, 0.0, -4.321483413804592, 0.0,
        0.0, 0.0, 0.0, 0.0,
        -0.12362457365993453, 0.0, 0.0, 0.0,
        -1.5508211425508347, 0.0, 0.0, 0.0,
        0.0, -1.5508211425508347, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        -12.896533434180043, 0.0, 0.0, -4.41838838103884,
        0.0, 0.0, -0.21076486529008706, 0.0,
        0.0, 0.0, 1.9320017126547635, 0.6919311505449771,
        0.0, 1.8528673237998992, -2.6291946296866437, -1.9320017126547633,
        -0.6919311505449771, 0.0, 1.8528673237998992, 2.6291946296866437,
        0.026618755186472318, -0.18582135169234293, -0.16904141186578137, 0.0,
        0.0, -12.85433692344008, 0.0, 0.0,
        -4.379751463578586, 0.0, 0.0, -0.14784534155448928,
        0.0, 0.04357014581507627, -1.5399199053766628, -0.615812339966486,
        0.0, -2.690725583646429, 0.5122380871172001, -1.5399199053766628,
        -0.615812339966486, 0.0, 2.690725583646429, 0.5122380871172,
        0.0, 0.0, 0.0, -4.321483413804593,
        0.0, 0.0, -5.304549819426528, 0.0,
        0.0, 0.0, 0.0, 0.0,
        -0.10365261370476854, 0.0, 0.0, 0.0,
        -2.0615794048977465, 0.0, 0.0, 0.0,
        0.0, -2.0615794048977465, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        -4.418388381038841, 0.0, 0.0, -5.530303790878689,
        0.0, 0.0, -0.2180885550068259, 0.0,
        0.0, 0.0, 2.864159613759814, 1.4545083359287205,
        0.0, 0.23399023078729264, -1.7535947656408535, -2.864159613759814,
        -1.4545083359287205, 0.0, 0.23399023078729264, 1.7535947656408535,
        0.0035687065317149256, -0.13715405924233942, -0.2501576289452375, 0.0,
        0.0, -4.379751463578587, 0.0, 0.0,
        -5.4402935694187615, 0.0, 0.0, -0.12637996310165195,
        0.0, 0.057217970651028675, -2.275446955795145, -1.2815568341839265,
        0.0, -1.8263920579692507, -0.6904528721518781, -2.275446955795145,
        -1.2815568341839263, 0.0, 1.8263920579692507, -0.6904528721518781,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, -8.526132372257049, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        1.7747780367281767, 0.0, 0.0, 0.0,
        0.0, -1.7747780367281767, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        -0.210764865290087, 0.0, 0.0, -0.2180885550068259,
        0.0, 0.0, -8.682156639296267, 0.0,
        0.0, 0.0, 1.5008019996900575, 0.17505551846239778,
        0.0, 1.5761724933777712, -0.5201831275513699, -1.5008019996900575,
        -0.17505551846239775, 0.0, 1.5761724933777712, 0.52018312755137,
        0.00020796415679447122, -0.010430187716009343, -0.012643716015226403, 0.0,
        0.0, -0.1478453415544892, 0.0, 0.0,
        -0.12637996310165195, 0.0, 0.0, -8.538855837965958,
        0.0, -0.04695502461652389, -0.14087950722084663, -0.03339860069887335,
        0.0, -1.2972865205914976, -1.4170081283416174, -0.1408795072208462,
        -0.03339860069887379, 0.0, 1.2972865205914976, -1.4170081283416174,
        0.0, 0.0, 0.0, -0.1236245736599345,
        0.0, 0.0, -0.10365261370476854, 0.0,
        0.0, 0.0, 0.0, 0.0,
        -8.490281935345969, 0.0, 0.0, 0.0,
        -1.397408401609294, 0.0, 0.0, 0.0,
        0.0, -1.397408401609294, 0.0, 0.0,
        -0.0017780738944975782, 0.08917711964592545, 0.10810257749514651, 0.0,
        0.0, 0.043570145815076254, 0.0, 0.0,
        0.057217970651028675, 0.0, 0.0, -0.04695502461652401,
        0.0, -8.568523888605785, 0.9681080149414634, 0.15394260866145837,
        0.0, 0.12895443057882372, -1.4696010969654068, 0.9681080149414638,
        0.15394260866145837, 0.0, -0.12895443057882372, -1.4696010969654068,
        1.5600943210125893, -3.202339145199478, -3.5918583579725145, 0.0,
        1.9320017126547644, -1.5399199053766635, 0.0, 2.864159613759814,
        -2.275446955795145, 0.0, 1.5008019996900592, -0.14087950722084708,
        0.0, 0.968108014941464, -6.100278179236541, -3.7699879363066824,
        0.0, -1.216268539266853, 0.8848738113246929, -0.9114969785334522,
        -1.9289854178717003, 0.0, 1.158942242292568, 0.1949145162424069,
        2.054917809075752, -3.799101367119257, -4.3836435147764305, 0.0,
        0.6919311505449782, -0.6158123399664869, 0.0, 1.4545083359287203,
        -1.2815568341839263, 0.0, 0.17505551846239792, -0.03339860069887335,
        0.0, 0.15394260866145926, -3.7699879363066824, -4.399252231054096,
        0.0, -0.9955284743007471, 0.7207923913980393, -1.9289854178717003,
        -3.037424252547639, 0.0, 1.4244099088617406, 0.43519666523291123,
        0.0, 0.0, 0.0, -1.5508211425508347,
        0.0, 0.0, -2.0615794048977465, 0.0,
        0.0, 1.774778036728177, 0.0, 0.0,
        -1.3974084016092942, 0.0, 0.0, 0.0,
        -5.286570830760588, 0.0, 0.0, 0.0,
        0.0, -0.2543193888006198, 0.0, 0.0,
        2.361137922169959, -3.812546214365836, -2.6786798166896952, 0.0,
        1.8528673237998992, -2.6907255836464294, 0.0, 0.23399023078729242,
        -1.826392057969251, 0.0, 1.5761724933777712, -1.2972865205914985,
        0.0, 0.1289544305788235, -1.216268539266853, -0.9955284743007469,
        0.0, -6.066776588730966, 0.5739557104596804, -1.1589422422925675,
        -1.4244099088617415, 0.0, 1.7734705223790537, 0.25755457872351417,
        -1.8299113505899276, 2.925974389363727, 2.0284499173737816, 0.0,
        -2.629194629686643, 0.5122380871171995, 0.0, -1.753594765640854,
        -0.6904528721518781, 0.0, -0.5201831275513699, -1.4170081283416178,
        0.0, -1.4696010969654074, 0.8848738113246929, 0.7207923913980391,
        0.0, 0.5739557104596804, -5.731632920641476, 0.19491451624240688,
        0.4351966652329113, 0.0, -0.25755457872351417, -0.346143018327155,
        1.5600943210125893, -3.202339145199478, -3.5918583579725145, 0.0,
        -1.9320017126547644, -1.5399199053766635, 0.0, -2.864159613759814,
        -2.275446955795145, 0.0, -1.5008019996900592, -0.14087950722084708,
        0.0, 0.968108014941464, -0.9114969785334522, -1.9289854178717003,
        0.0, -1.158942242292568, 0.1949145162424069, -6.100278179236541,
        -3.769987936306682, 0.0, 1.216268539266853, 0.8848738113246929,
        2.054917809075752, -3.799101367119257, -4.3836435147764305, 0.0,
        -0.6919311505449782, -0.6158123399664869, 0.0, -1.4545083359287203,
        -1.2815568341839263, 0.0, -0.17505551846239792, -0.03339860069887424,
        0.0, 0.1539426086614588, -1.9289854178717003, -3.037424252547639,
        0.0, -1.4244099088617406, 0.43519666523291123, -3.769987936306682,
        -4.399252231054096, 0.0, 0.9955284743007471, 0.7207923913980393,
        0.0, 0.0, 0.0, -1.5508211425508347,
        0.0, 0.0, -2.0615794048977465, 0.0,
        0.0, -1.774778036728177, 0.0, 0.0,
        -1.3974084016092942, 0.0, 0.0, 0.0,
        -0.2543193888006198, 0.0, 0.0, 0.0,
        0.0, -5.286570830760588, 0.0, 0.0,
        -2.361137922169959, 3.812546214365836, 2.6786798166896952, 0.0,
        1.8528673237998992, 2.6907255836464294, 0.0, 0.23399023078729242,
        1.826392057969251, 0.0, 1.5761724933777714, 1.2972865205914985,
        0.0, -0.1289544305788235, 1.1589422422925675, 1.4244099088617415,
        0.0, 1.773470522379054, -0.25755457872351417, 1.216268539266853,
        0.9955284743007469, 0.0, -6.066776588730966, -0.5739557104596804,
        -1.8299113505899276, 2.925974389363727, 2.0284499173737816, 0.0,
        2.629194629686643, 0.5122380871171995, 0.0, 1.753594765640854,
        -0.6904528721518781, 0.0, 0.52018312755137, -1.4170081283416178,
        0.0, -1.4696010969654074, 0.19491451624240688, 0.4351966652329113,
        0.0, 0.25755457872351417, -0.346143018327155, 0.8848738113246929,
        0.7207923913980391, 0.0, -0.5739557104596804, -5.731632920641476]
}

def watersvp_v_sph() -> Arr {
    return watersvp_mat(watersvp_v_sph_flat(), 24, 24)
}

# Packed-8 length n(n+1)/2 (n(n+1)/2 + 1)/2 for n = 24.
WATERSVP_ERI8_SPH_LEN = 45150
# sum of Gp^2 (math.fsum).
WATERSVP_ERI8_SPH_SUMSQ = 238.42272161881078
# sum of w_k Gp_k with the LCG weights from WATERSVP_SEED_WSUM (math.fsum).
WATERSVP_ERI8_SPH_WSUM = 190.70526740917492
#| 256 packed indices: 128 uniform, then 128 from quartets holding the top l.
def watersvp_eri8_sph_idx() -> Arr {
    return [274, 9249, 4755, 16757,
        43350, 5927, 24998, 21576,
        36720, 11575, 44297, 26481,
        29802, 38943, 24367, 26053,
        21810, 44314, 41265, 42279,
        17455, 28101, 28663, 42854,
        21296, 19128, 20620, 4290,
        10452, 37252, 14415, 10288,
        41807, 39728, 42243, 1715,
        25291, 33002, 1627, 39196,
        42857, 19936, 22896, 16140,
        10381, 21533, 35224, 18847,
        40438, 4138, 25574, 8920,
        33895, 27208, 6722, 16980,
        1083, 21623, 20529, 2640,
        41332, 645, 7172, 40120,
        28034, 37017, 35861, 22550,
        18638, 13681, 2230, 21601,
        13209, 1632, 27709, 39479,
        6385, 41323, 31450, 20269,
        9664, 18461, 14863, 41979,
        28355, 7008, 2097, 29127,
        26131, 18990, 8687, 544,
        33358, 36737, 13330, 14794,
        8432, 38547, 11717, 34386,
        21906, 25816, 7405, 25312,
        19885, 7936, 21186, 30826,
        12078, 14405, 14236, 19116,
        41161, 4651, 22931, 11954,
        6292, 13902, 14883, 15440,
        31582, 16027, 14930, 40899,
        39861, 23921, 33691, 18542,
        22444, 30441, 6663, 26912,
        35086, 15665, 33784, 9281,
        10918, 25873, 8669, 1366,
        20446, 13351, 4425, 4107,
        1792, 24904, 41304, 40519,
        23722, 22204, 33285, 41294,
        7237, 2574, 41732, 17492,
        1687, 1295, 44244, 23521,
        6539, 19979, 41283, 2318,
        24596, 14631, 13288, 6811,
        35164, 41498, 5052, 25098,
        1798, 7484, 38031, 25365,
        43714, 20327, 33501, 23970,
        16857, 22036, 40891, 12169,
        8777, 2203, 8334, 13214,
        39427, 5739, 4483, 20217,
        8703, 10692, 5473, 7323,
        26184, 13540, 34533, 12663,
        24981, 1360, 23974, 16838,
        34771, 23958, 29913, 13770,
        29492, 3973, 3507, 40865,
        1411, 16336, 2495, 5347,
        43496, 11309, 35746, 17099,
        41005, 1082, 27341, 12173,
        40833, 34413, 42003, 2494,
        7938, 34559, 21694, 26855,
        5207, 41133, 30831, 18276,
        22676, 11877, 39666, 41369,
        28061, 9810, 33012, 30430,
        13285, 11319, 13298, 39504,
        40573, 17928, 29028, 39954,
        4796, 1061, 23403, 10897]
}

#| The packed values at those indices.
def watersvp_eri8_sph_val() -> Arr {
    return [-0.0026243698514644117, 0.0, 0.0, 0.14684884460676012,
        0.0, 0.0, 0.0, -0.0003762555205060261,
        -0.09545873245569146, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.029429221669917106, 0.0352723599710313,
        0.0023032551560915764, -0.001407667019617615, -0.008782519944588998, 0.0007266643653172346,
        0.0, 0.0, 0.008965414489864177, 0.0,
        0.008782519944588996, 0.0, 0.00971572401545183, 0.0,
        -0.0, 0.0023385122152534887, -0.005208706278583679, 0.16956362286916185,
        -0.0, -0.01401544639338074, -0.0018877512329532622, 0.0,
        7.549798813963511e-05, -0.0, 0.0, 0.0004512312075896425,
        -0.000486399495592775, -0.0, -0.0, -0.00824783892937509,
        0.004704691556693275, 0.08491370176694454, 0.0, 0.016100656351831152,
        -0.15563787831610892, 0.0, 0.0, 0.014707677928675583,
        -0.0, 0.003393400680532188, -0.0, -0.004355905901529711,
        0.0, 0.00014091021684092326, 0.009143018665446529, 0.0,
        0.10616265206194339, -0.0, 0.2701182183003951, -0.0,
        0.0, -0.0016249477402443982, -0.0, 0.046661743956953695,
        0.05650639283013177, 0.0, 0.0, -3.0795694306092646e-05,
        0.005997081717332845, -0.0, 0.018834943573744885, -0.028535426717527627,
        0.017861071030722892, 0.0, -0.016452858513306086, 0.0,
        0.0, 0.025149730467595763, -0.012971900988744824, 0.0011218916111621572,
        0.131332408318088, -0.0, 0.0, 0.023375936465094213,
        0.0, 0.0, 0.015331813396152555, 0.0,
        -0.04195746244564923, -0.12106643694004393, 0.0, -0.0,
        0.028927299969095616, -0.137207239299133, 0.0, -0.05405887865843939,
        0.0, 0.012506825212117961, 0.14499365773059483, -0.1000136083662519,
        0.027021933704542523, -0.0, 0.021767181863491677, 0.009884305459078702,
        -0.0, 0.0, -0.0026119071563500333, -0.0,
        0.0031530827214628033, 0.0, -0.007032261534925373, -0.00948812999775732,
        0.0, -0.0028303949174443843, -0.18203768789318503, -0.0024592907892027503,
        0.0, -0.000875294856472311, -0.0, -0.003083290371449893,
        -0.013281302509486202, 0.0, 0.000775196491239522, 0.3359258632668097,
        -0.0, 0.0, -0.012719624163584322, 0.0,
        -0.04679354713785486, 0.0, 0.003354273931316073, 0.003979095666857936,
        0.0, 0.005748596386335212, 0.0, 0.0,
        -0.005679923944198876, -0.0, 0.0, 0.0,
        0.0, 0.009830376787736943, 0.030659809295920715, 0.0,
        0.0, -0.0, -0.0, -0.004577640232405014,
        0.0, 0.0, 0.0, 9.652445248886556e-06,
        0.0, 0.0, 0.0, 0.0003679780070679187,
        0.015807526568134677, 0.005289696246307526, 0.0, 0.0,
        0.012370276339879704, -0.0051233651407359415, 0.003978640223642765, 0.0,
        -0.017773003538038998, 0.0782619569601349, 0.0, -0.002832204430326765,
        -0.0, 0.0, 0.07137400481916985, 0.0,
        -0.09542055884231251, 0.0, -0.2232674545554832, -0.0002457729387419297,
        0.00025036194942186035, 0.0006543309655584785, 0.0002241563257214628, 0.0,
        0.01666155974065652, 0.0, -0.0, 0.0,
        -0.0039034198932809297, 0.0006655890584836011, 0.0, 0.0,
        -0.00036400584785585625, -0.09726654133202367, 0.0, 0.0002491004644143041,
        0.0, -0.0011622250328967012, -0.007310206415666784, 0.00019471923535056834,
        -0.007254762617798116, 0.0, 0.0, -0.0,
        0.0017861288355962546, 0.004301166111346728, 0.007116249693486287, 0.0031627608852933713,
        0.004624138165990001, 0.0, -0.004382969434850881, 0.0,
        0.0, -0.029622939621478796, 0.02009909730882605, 0.0,
        0.0009461487375035035, 0.0, 0.0, 0.0,
        -0.03265938335824582, -0.0, 0.013491050776614836, 0.0,
        0.00014454588142614433, -0.0, -0.03932170106463645, 0.0,
        -0.0010400877318875032, 0.0, -0.0008648398252855231, -0.0,
        -0.04581286918585757, 0.004581430424020837, -0.0023093610594455225, -0.0001895440347854209,
        -0.013130094399378811, 2.238838844649104e-05, 0.0, 0.05881989398919442,
        0.0, 0.0, 0.0, 0.01613554950988541,
        0.0056888319357724934, -0.0009064668297365207, 0.0, -0.02882080441052455,
        0.0, 0.0, 0.0, -0.0,
        0.0, -0.0, -0.0, 0.0]
}

#| (ij|ij) for every pair ij, in pair order: the Schwarz bounds.
def watersvp_eri8_sph_diag() -> Arr {
    return [4.776656448422735, 0.31650683157109694, 1.01539063612981, 0.0638458168258978,
        0.512527826443317, 0.5701472512952711, 0.06218150563170958, 0.2274708859765999,
        0.10825094513235449, 1.1470819441911333, 0.06218150563170958, 0.2274708859765999,
        0.10825094513235449, 0.06171990488135421, 1.1470819441911333, 0.06218150563170958,
        0.2274708859765999, 0.10825094513235449, 0.06171990488135421, 0.06171990488135421,
        1.1470819441911337, 0.0005704631675362924, 0.04663363287850644, 0.10057984081406116,
        0.1981260067992479, 0.011424788094711045, 0.011424788094711043, 0.48448578731405173,
        0.0005704631675362924, 0.04663363287850644, 0.10057984081406116, 0.011424788094711045,
        0.1981260067992479, 0.011424788094711043, 0.029662395141676637, 0.48448578731405173,
        0.0005704631675362924, 0.04663363287850644, 0.10057984081406116, 0.011424788094711043,
        0.011424788094711043, 0.1981260067992479, 0.029662395141676637, 0.029662395141676637,
        0.48448578731405173, 0.001084122245626977, 0.07613424299911194, 0.05760943019519636,
        0.12325525647369492, 0.12325525647369492, 0.017819385553705214, 0.0547715534448474,
        0.0547715534448474, 0.008134389125472385, 0.8424456406029571, 0.0010841222456269765,
        0.07613424299911194, 0.05760943019519637, 0.017819385553705214, 0.12325525647369492,
        0.12325525647369491, 0.008134389125472385, 0.0547715534448474, 0.054771553444847396,
        0.043409862703558476, 0.8424456406029571, 0.0010841222456269763, 0.07613424299911184,
        0.057609430195196286, 0.05296467586036843, 0.05296467586036843, 0.15840054678035814,
        0.02368011056526406, 0.02368011056526406, 0.07031727488463901, 0.04929594578200708,
        0.03163769654666124, 0.8424456406029563, 0.0010841222456269765, 0.07613424299911194,
        0.05760943019519637, 0.12325525647369492, 0.017819385553705214, 0.12325525647369491,
        0.0547715534448474, 0.008134389125472385, 0.054771553444847396, 0.043409862703558476,
        0.043409862703558476, 0.03163769654666126, 0.8424456406029571, 0.0010841222456269765,
        0.07613424299911184, 0.05760943019519628, 0.12325525647369494, 0.12325525647369494,
        0.017819385553705214, 0.0547715534448474, 0.0547715534448474, 0.008134389125472388,
        0.025751613468212625, 0.043409862703558455, 0.04929594578200706, 0.043409862703558455,
        0.8424456406029568, 0.005844088550885168, 0.09814581275674861, 0.18313140147493415,
        0.013579073668941791, 0.06582716419235965, 0.04499536146206866, 0.0198767724307995,
        0.19920522520864056, 0.12770529258388919, 0.019634215858564712, 0.07268864363483973,
        0.021671900790290268, 0.014376226715226707, 0.03839589706065974, 0.8971413572489102,
        0.009891965811013342, 0.11802261201370255, 0.2335627989264997, 0.023531337692385933,
        0.029799530454124087, 0.027300343330157496, 0.05239104646521531, 0.10042048065227102,
        0.08127069568962648, 0.01636541915228439, 0.018036454469774282, 0.01666155974065652,
        0.015497221247613133, 0.01651580918314443, 0.2999243474108789, 0.3940445135380343,
        5.494122926326517e-05, 0.011997736287739287, 0.03660439268797713, 0.030288535734716376,
        0.009529737045686854, 0.006429388092303605, 0.08956495832903524, 0.049963242366932274,
        0.0322287802198664, 0.06260268762315277, 0.015501268460469777, 0.006154533844831518,
        0.04016478717044976, 0.005492813437120169, 0.1604564612845814, 0.06893333251070242,
        0.8242232905265858, 0.013584720757371358, 0.13200882176122672, 0.0921248111907686,
        0.02173563413771192, 0.05645129877152279, 0.11306534144496629, 0.010793711990415115,
        0.032463035955508465, 0.0841577632521346, 0.016913299904809616, 0.0772597821235815,
        0.06849805879818718, 0.031113730983826093, 0.012655931159774656, 0.1604564612845814,
        0.06893333251070242, 0.05046265044040321, 0.8242232905265858, 0.008190271021690575,
        0.08415927868727945, 0.06998830066633213, 0.013768679767364527, 0.10819873602800219,
        0.011470161930357867, 0.008676508228629802, 0.09977502163741511, 0.03664273905101718,
        0.029396544724690665, 0.023603538826703567, 0.04521565911515153, 0.004578418360056488,
        0.07313552282993077, 0.1604564612845814, 0.06893333251070242, 0.05046265044040321,
        0.05046265044040321, 0.8242232905265856, 0.005844088550885168, 0.09814581275674861,
        0.18313140147493415, 0.013579073668941791, 0.06582716419235965, 0.04499536146206866,
        0.0198767724307995, 0.19920522520864056, 0.12770529258388919, 0.019634215858564712,
        0.07268864363483973, 0.021671900790290268, 0.014376226715226707, 0.03839589706065974,
        0.011124705808519814, 0.0596122437571924, 0.0010580514395239103, 0.018980308562478513,
        0.0010580514395239103, 0.8971413572489102, 0.009891965811013342, 0.11802261201370255,
        0.2335627989264997, 0.023531337692385933, 0.029799530454124087, 0.027300343330157496,
        0.05239104646521531, 0.10042048065227102, 0.08127069568962648, 0.01636541915228439,
        0.018036454469774282, 0.01666155974065652, 0.015497221247613133, 0.01651580918314443,
        0.0596122437571924, 0.14521791100554912, 0.012191775281988946, 0.03150929626714507,
        0.012191775281988946, 0.2999243474108789, 0.3940445135380343, 5.494122926326517e-05,
        0.011997736287739287, 0.03660439268797713, 0.030288535734716376, 0.009529737045686854,
        0.006429388092303605, 0.08956495832903524, 0.049963242366932274, 0.0322287802198664,
        0.06260268762315277, 0.015501268460469777, 0.006154533844831518, 0.04016478717044976,
        0.005492813437120169, 0.0010580514395239103, 0.012191775281988948, 0.0011805460305248966,
        0.0016499851982987581, 7.227832839948347e-05, 0.1604564612845814, 0.06893333251070242,
        0.8242232905265858, 0.013584720757371358, 0.13200882176122672, 0.0921248111907686,
        0.02173563413771192, 0.05645129877152279, 0.11306534144496629, 0.010793711990415115,
        0.032463035955508465, 0.0841577632521346, 0.016913299904809616, 0.0772597821235815,
        0.06849805879818718, 0.031113730983826093, 0.012655931159774656, 0.018980308562478496,
        0.03150929626714512, 0.0016499851982987581, 0.047392821031147635, 0.0016499851982987581,
        0.1604564612845814, 0.06893333251070242, 0.05046265044040321, 0.8242232905265858,
        0.008190271021690575, 0.08415927868727945, 0.06998830066633213, 0.013768679767364527,
        0.10819873602800219, 0.011470161930357867, 0.008676508228629802, 0.09977502163741511,
        0.03664273905101718, 0.029396544724690665, 0.023603538826703567, 0.04521565911515153,
        0.004578418360056488, 0.07313552282993077, 0.0010580514395239103, 0.012191775281988948,
        7.227832839948347e-05, 0.0016499851982987581, 0.0011805460305248966, 0.1604564612845814,
        0.06893333251070242, 0.05046265044040321, 0.05046265044040321, 0.8242232905265856]
}

#| Overlap, unit-Cartesian, [25,25].
def watersvp_s_unit_flat() -> Arr {
    return [0.9999999999999999, -0.3440165538027238, -0.15787004200514215, -0.0,
        -0.0, -0.0, -0.0, -0.0,
        -0.0, -0.05704297474097041, -0.0, -0.0,
        -0.05704297474097041, -0.0, -0.05704297474097041, -0.04785460032374623,
        -0.06252157963143691, -0.0, -0.07212249497292916, 0.05592589768706661,
        -0.04785460032374623, -0.06252157963143691, -0.0, 0.07212249497292916,
        0.05592589768706661, -0.34401655380272383, 1.0000000000000002, 0.7889407941247987,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.6698665940612796, 0.0,
        0.0, 0.6698665940612796, 0.0, 0.6698665940612796,
        0.32932204024788264, 0.3914645717081812, 0.0, 0.3443105932745787,
        -0.26698853137672085, 0.32932204024788264, 0.3914645717081812, 0.0,
        -0.3443105932745787, -0.26698853137672085, -0.15787004200514215, 0.7889407941247987,
        1.0000000000000002, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.6316731558572563,
        0.0, 0.0, 0.6316731558572563, 0.0,
        0.6316731558572563, 0.5110637904358923, 0.6903548488171068, 0.0,
        0.26026247518897516, -0.20181515579382875, 0.5110637904358923, 0.6903548488171068,
        0.0, -0.26026247518897516, -0.20181515579382875, -0.0,
        0.0, 0.0, 1.0, 0.0,
        0.0, 0.5021408928230414, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.18318229508363296, 0.0, -0.0, 0.0,
        0.0, 0.18318229508363296, -0.0, -0.0,
        -0.0, 0.0, 0.0, 0.0,
        1.0, 0.0, 0.0, 0.5021408928230414,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, -0.22234476894334795,
        -0.0837029824736131, -0.0, -0.1736970385141288, 0.2767347012178153,
        0.22234476894334795, 0.0837029824736131, 0.0, -0.1736970385141288,
        -0.2767347012178153, -0.0, 0.0, 0.0,
        0.0, 0.0, 1.0, 0.0,
        0.0, 0.5021408928230414, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.17241265438539663, 0.06490574730780832, 0.0, 0.27673470121781524,
        -0.031405907842202666, 0.17241265438539663, 0.06490574730780832, 0.0,
        -0.27673470121781524, -0.031405907842202666, -0.0, 0.0,
        0.0, 0.5021408928230416, 0.0, 0.0,
        1.0000000000000004, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.36398345112063346,
        0.0, -0.0, 0.0, 0.0,
        0.36398345112063346, -0.0, -0.0, -0.0,
        0.0, 0.0, 0.0, 0.5021408928230416,
        0.0, 0.0, 1.0000000000000004, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, -0.49180463764013643, -0.30882567073517864,
        -0.0, 0.05794675942438177, 0.23730982566142628, 0.49180463764013643,
        0.30882567073517864, 0.0, 0.05794675942438177, -0.23730982566142628,
        -0.0, 0.0, 0.0, 0.0,
        0.0, 0.5021408928230416, 0.0, 0.0,
        1.0000000000000004, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.3813597388305946,
        0.23947248179861277, 0.0, 0.2373098256614264, 0.17996645288647595,
        0.3813597388305946, 0.23947248179861277, 0.0, -0.2373098256614264,
        0.17996645288647595, -0.05704297474097041, 0.6698665940612796, 0.6316731558572563,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 1.0000000000000004, 0.0,
        0.0, 0.3333333333333335, 0.0, 0.33333333333333354,
        0.2068877010323504, 0.3210995142504918, 0.0, 0.21401468788769207,
        -0.16595326524448514, 0.2068877010323504, 0.3210995142504918, 0.0,
        -0.21401468788769207, -0.16595326524448514, -0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        1.0000000000000007, 0.0, 0.0, 0.0,
        0.0, -0.0, -0.0, -0.24712287532498559,
        -0.0, 0.0, 0.0, 0.0,
        0.24712287532498559, -0.0, -0.0, -0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 1.0000000000000009, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.19162632472360178, 0.0, -0.0, 0.0,
        0.0, 0.19162632472360178, -0.0, -0.0,
        -0.05704297474097041, 0.6698665940612796, 0.6316731558572563, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.3333333333333335, 0.0, 0.0,
        1.0000000000000004, 0.0, 0.33333333333333354, 0.3489174449613198,
        0.3358839629853556, 0.0, 0.20895528397426333, -0.3833010754024565,
        0.3489174449613198, 0.3358839629853556, 0.0, -0.20895528397426333,
        -0.3833010754024565, -0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 1.0000000000000009, 0.0,
        -0.19075773326005377, -0.01985674162429333, -0.0, -0.18483112538383964,
        0.04479327158791809, 0.19075773326005377, 0.01985674162429333, 0.0,
        -0.18483112538383964, -0.04479327158791809, -0.05704297474097041, 0.6698665940612796,
        0.6316731558572563, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.33333333333333354,
        0.0, 0.0, 0.33333333333333354, 0.0,
        1.0000000000000004, 0.2922888566680134, 0.3299892648933222, 0.0,
        0.3825525538886554, -0.07537144880564553, 0.2922888566680134, 0.3299892648933222,
        0.0, -0.3825525538886554, -0.07537144880564553, -0.04785460032374623,
        0.32932204024788264, 0.5110637904358925, 0.0, -0.22234476894334804,
        0.17241265438539666, 0.0, -0.49180463764013643, 0.38135973883059454,
        0.2068877010323504, -0.0, 0.0, 0.34891744496132,
        -0.190757733260054, 0.2922888566680135, 0.9999999999999997, 0.6847998247453728,
        0.0, 0.0, 0.0, 0.12116903885173679,
        0.30763577680074294, 0.0, -0.14171411608090512, 0.0,
        -0.06252157963143692, 0.39146457170818133, 0.690354848817107, 0.0,
        -0.08370298247361324, 0.06490574730780842, 0.0, -0.3088256707351786,
        0.23947248179861272, 0.3210995142504918, -0.0, 0.0,
        0.3358839629853556, -0.019856741624293354, 0.3299892648933222, 0.6847998247453728,
        1.0, 0.0, 0.0, 0.0,
        0.30763577680074294, 0.6070681526935895, 0.0, -0.1587920912149586,
        0.0, -0.0, 0.0, 0.0,
        0.18318229508363296, -0.0, 0.0, 0.36398345112063346,
        -0.0, 0.0, 0.0, -0.24712287532498564,
        0.1916263247236018, 0.0, -0.0, 0.0,
        0.0, 0.0, 1.0000000000000002, 0.0,
        0.0, 0.0, 0.0, 0.03784591602610543,
        -0.0, 0.0, -0.07212249497292919, 0.34431059327457875,
        0.26026247518897516, 0.0, -0.17369703851412885, 0.27673470121781524,
        0.0, 0.05794675942438186, 0.23730982566142633, 0.2140146878876921,
        -0.0, 0.0, 0.20895528397426336, -0.18483112538383967,
        0.38255255388865544, 0.0, 0.0, 0.0,
        1.0000000000000002, 0.0, 0.1417141160809051, 0.15879209121495874,
        0.0, -0.20998671804645133, 0.0, 0.05592589768706662,
        -0.2669885313767209, -0.20181515579382883, -0.0, 0.2767347012178153,
        -0.0314059078422026, -0.0, 0.23730982566142633, 0.17996645288647595,
        -0.16595326524448514, 0.0, -0.0, -0.3833010754024565,
        0.04479327158791809, -0.07537144880564546, 0.0, 0.0,
        0.0, 0.0, 1.0000000000000002, 0.0,
        0.0, 0.0, -0.0, 0.03784591602610543,
        -0.04785460032374623, 0.32932204024788264, 0.5110637904358925, 0.0,
        0.22234476894334804, 0.17241265438539666, 0.0, 0.49180463764013643,
        0.38135973883059454, 0.2068877010323504, 0.0, 0.0,
        0.34891744496132, 0.190757733260054, 0.2922888566680135, 0.12116903885173679,
        0.30763577680074294, 0.0, 0.14171411608090512, 0.0,
        0.9999999999999997, 0.6847998247453728, 0.0, 0.0,
        0.0, -0.06252157963143692, 0.39146457170818133, 0.690354848817107,
        0.0, 0.08370298247361324, 0.06490574730780842, 0.0,
        0.3088256707351786, 0.23947248179861272, 0.3210995142504918, 0.0,
        0.0, 0.3358839629853556, 0.019856741624293354, 0.3299892648933222,
        0.30763577680074294, 0.6070681526935895, 0.0, 0.1587920912149586,
        0.0, 0.6847998247453728, 1.0, 0.0,
        0.0, 0.0, -0.0, 0.0,
        0.0, 0.18318229508363296, 0.0, 0.0,
        0.36398345112063346, 0.0, 0.0, 0.0,
        0.24712287532498564, 0.1916263247236018, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.03784591602610543,
        0.0, 0.0, 0.0, 0.0,
        1.0000000000000002, 0.0, 0.0, 0.07212249497292919,
        -0.34431059327457875, -0.26026247518897516, -0.0, -0.17369703851412885,
        -0.27673470121781524, -0.0, 0.05794675942438186, -0.23730982566142633,
        -0.2140146878876921, -0.0, -0.0, -0.20895528397426336,
        -0.18483112538383967, -0.38255255388865544, -0.1417141160809051, -0.15879209121495874,
        -0.0, -0.20998671804645133, -0.0, 0.0,
        0.0, 0.0, 1.0000000000000002, 0.0,
        0.05592589768706662, -0.2669885313767209, -0.20181515579382883, -0.0,
        -0.2767347012178153, -0.0314059078422026, -0.0, -0.23730982566142633,
        0.17996645288647595, -0.16595326524448514, -0.0, -0.0,
        -0.3833010754024565, -0.04479327158791809, -0.07537144880564546, 0.0,
        0.0, 0.0, 0.0, 0.03784591602610543,
        0.0, 0.0, 0.0, 0.0,
        1.0000000000000002]
}

def watersvp_s_unit() -> Arr {
    return watersvp_mat(watersvp_s_unit_flat(), 25, 25)
}

#| Kinetic energy, unit-Cartesian.
def watersvp_t_unit_flat() -> Arr {
    return [29.356654381441977, -0.7681118715965942, -0.11754936196761044, -0.0,
        -0.0, -0.0, -0.0, -0.0,
        -0.0, 0.7774287331032164, -0.0, -0.0,
        0.7774287331032164, -0.0, 0.7774287331032164, 0.0036718301591963255,
        -0.016632898965150182, 0.0, -0.009528610627034485, 0.00738876411898181,
        0.0036718301591963255, -0.016632898965150182, 0.0, 0.009528610627034485,
        0.00738876411898181, -0.7681118715965938, 1.2146396350200004, 0.4594187165589615,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.5345285810947409, 0.0,
        0.0, 0.5345285810947409, 0.0, 0.5345285810947406,
        0.08064849338325045, 0.09565145880517822, 0.0, 0.3273611037237572,
        -0.25384540011340223, 0.08064849338325045, 0.09565145880517822, 0.0,
        -0.3273611037237572, -0.25384540011340223, -0.11754936196761027, 0.4594187165589617,
        0.3829615835100001, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.3423525046482533,
        0.0, 0.0, 0.3423525046482533, 0.0,
        0.3423525046482531, 0.16226927917565803, 0.14010699152154277, 0.0,
        0.1879657234073066, -0.14575413426696027, 0.16226927917565803, 0.14010699152154277,
        0.0, -0.1879657234073066, -0.14575413426696027, -0.0,
        0.0, 0.0, 4.332326592391174, 0.0,
        0.0, 0.5611807178111391, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.15884366695204688, 0.0, 0.0, 0.0,
        0.0, 0.15884366695204688, 0.0, 0.0,
        -0.0, 0.0, 0.0, 0.0,
        4.332326592391174, 0.0, 0.0, 0.5611807178111391,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, -0.1736696530577731,
        -0.03942968381559875, 0.0, -0.4892303831476449, 0.5025356240535257,
        0.1736696530577731, 0.03942968381559875, 0.0, -0.4892303831476449,
        -0.5025356240535257, 0.0, 0.0, 0.0,
        0.0, 0.0, 4.3323265923911745, 0.0,
        0.0, 0.561180717811139, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.13466854206725604, 0.030574933156877745, 0.0, 0.5025356240535258,
        -0.23083719344348758, 0.13466854206725604, 0.030574933156877745, 0.0,
        -0.5025356240535258, -0.23083719344348758, -0.0, 0.0,
        0.0, 0.5611807178111393, 0.0, 0.0,
        0.6910386102750002, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.27319922256602525,
        0.0, -0.0, 0.0, 0.0,
        0.27319922256602525, -0.0, -0.0, -0.0,
        0.0, 0.0, 0.0, 0.5611807178111393,
        0.0, 0.0, 0.6910386102750002, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, -0.33844703816829463, -0.11616875376215421,
        -0.0, -0.08224693554445205, 0.27562337491525785, 0.33844703816829463,
        0.11616875376215421, 0.0, -0.08224693554445205, -0.27562337491525785,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.5611807178111393, 0.0, 0.0,
        0.6910386102750004, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.26244175879100257,
        0.09008065846550134, 0.0, 0.2756233749152579, 0.05947277464626793,
        0.26244175879100257, 0.09008065846550134, 0.0, -0.2756233749152579,
        0.05947277464626793, 0.777428733103216, 0.5345285810947409, 0.3423525046482534,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 2.6000000000000005, 0.0,
        0.0, -0.20000000000000015, 0.0, -0.19999999999999984,
        -0.02535247250069763, 0.07362400450697583, 0.0, 0.05350725760712887,
        -0.04149109671781329, -0.02535247250069763, 0.07362400450697583, 0.0,
        -0.05350725760712887, -0.04149109671781329, -0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        4.200000000000003, 0.0, 0.0, 0.0,
        0.0, 0.0, -0.0, -0.4571814596861261,
        0.0, 0.0, 0.0, 0.0,
        0.4571814596861261, 0.0, -0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 4.200000000000004, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.35451191127576737, 0.0, 0.0, 0.0,
        0.0, 0.35451191127576737, -0.0, 0.0,
        0.777428733103216, 0.5345285810947409, 0.3423525046482534, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, -0.20000000000000015, 0.0, 0.0,
        2.6000000000000005, 0.0, -0.19999999999999984, 0.19584714364299216,
        0.08389307569612028, 0.0, 0.31322904834060367, -0.6522420847405653,
        0.19584714364299216, 0.08389307569612028, 0.0, -0.31322904834060367,
        -0.6522420847405653, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 4.200000000000004, 0.0,
        -0.29708944201622095, -0.013792214845553773, -0.0, -0.7033398307525297,
        0.36310780394744163, 0.29708944201622095, 0.013792214845553773, 0.0,
        -0.7033398307525297, -0.36310780394744163, 0.777428733103216, 0.5345285810947407,
        0.34235250464825334, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, -0.2000000000000001,
        0.0, 0.0, -0.2000000000000001, 0.0,
        2.600000000000001, 0.10765278627301114, 0.07979870089519447, 0.0,
        0.5271014847793284, 0.0006251455841575736, 0.10765278627301114, 0.07979870089519447,
        0.0, -0.5271014847793284, 0.0006251455841575736, 0.0036718301591964183,
        0.08064849338325042, 0.16226927917565803, 0.0, -0.17366965305777324,
        0.13466854206725606, 0.0, -0.3384470381682946, 0.26244175879100246,
        -0.025352472500697745, 0.0, 0.0, 0.1958471436429921,
        -0.2970894420162213, 0.10765278627301098, 0.969225931578449, 0.20114159492026099,
        0.0, 0.0, 0.0, -0.030366562053356867,
        0.04193098006107518, 0.0, 0.0054302735134623414, 0.0,
        -0.01663289896515019, 0.09565145880517825, 0.14010699152154282, 0.0,
        -0.03942968381559884, 0.03057493315687783, 0.0, -0.11616875376215416,
        0.09008065846550131, 0.07362400450697583, -0.0, 0.0,
        0.08389307569612034, -0.013792214845553789, 0.07979870089519459, 0.2011415949202609,
        0.18292443, 0.0, 0.0, 0.0,
        0.04193098006107515, 0.07409730663441164, 0.0, -0.05490651658161447,
        0.0, 0.0, 0.0, 0.0,
        0.15884366695204688, 0.0, 0.0, 0.27319922256602536,
        -0.0, 0.0, -0.0, -0.4571814596861261,
        0.35451191127576737, 0.0, -0.0, 0.0,
        0.0, 0.0, 2.0000000000000004, 0.0,
        0.0, 0.0, 0.0, -0.023441221576811846,
        0.0, 0.0, -0.0095286106270346, 0.32736110372375726,
        0.18796572340730666, 0.0, -0.4892303831476447, 0.5025356240535258,
        0.0, -0.08224693554445187, 0.2756233749152579, 0.053507257607128815,
        0.0, 0.0, 0.3132290483406039, -0.7033398307525301,
        0.5271014847793288, 0.0, 0.0, 0.0,
        2.0000000000000004, 0.0, -0.0054302735134623865, 0.05490651658161446,
        0.0, -0.06820332366683736, 0.0, 0.0073887641189818755,
        -0.25384540011340223, -0.14575413426696038, 0.0, 0.5025356240535255,
        -0.23083719344348758, -0.0, 0.27562337491525785, 0.05947277464626794,
        -0.041491096717813314, 0.0, 0.0, -0.6522420847405651,
        0.36310780394744147, 0.0006251455841583089, 0.0, 0.0,
        0.0, 0.0, 2.0000000000000004, 0.0,
        0.0, 0.0, 0.0, -0.02344122157681184,
        0.0036718301591964183, 0.08064849338325042, 0.16226927917565803, 0.0,
        0.17366965305777324, 0.13466854206725606, 0.0, 0.3384470381682946,
        0.26244175879100246, -0.025352472500697745, 0.0, 0.0,
        0.1958471436429921, 0.2970894420162213, 0.10765278627301098, -0.030366562053356867,
        0.04193098006107518, 0.0, -0.0054302735134623414, 0.0,
        0.969225931578449, 0.20114159492026099, 0.0, 0.0,
        0.0, -0.01663289896515019, 0.09565145880517825, 0.14010699152154282,
        0.0, 0.03942968381559884, 0.03057493315687783, 0.0,
        0.11616875376215416, 0.09008065846550131, 0.07362400450697583, 0.0,
        0.0, 0.08389307569612034, 0.013792214845553789, 0.07979870089519459,
        0.04193098006107515, 0.07409730663441164, 0.0, 0.05490651658161447,
        0.0, 0.2011415949202609, 0.18292443, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.15884366695204688, 0.0, 0.0,
        0.27319922256602536, 0.0, 0.0, -0.0,
        0.4571814596861261, 0.35451191127576737, 0.0, 0.0,
        0.0, 0.0, 0.0, -0.023441221576811846,
        0.0, 0.0, 0.0, 0.0,
        2.0000000000000004, 0.0, 0.0, 0.0095286106270346,
        -0.32736110372375726, -0.18796572340730666, 0.0, -0.4892303831476447,
        -0.5025356240535258, -0.0, -0.08224693554445187, -0.2756233749152579,
        -0.053507257607128815, 0.0, -0.0, -0.3132290483406039,
        -0.7033398307525301, -0.5271014847793288, 0.0054302735134623865, -0.05490651658161446,
        0.0, -0.06820332366683736, 0.0, 0.0,
        0.0, 0.0, 2.0000000000000004, 0.0,
        0.0073887641189818755, -0.25384540011340223, -0.14575413426696038, 0.0,
        -0.5025356240535255, -0.23083719344348758, -0.0, -0.27562337491525785,
        0.05947277464626794, -0.041491096717813314, -0.0, 0.0,
        -0.6522420847405651, -0.36310780394744147, 0.0006251455841583089, 0.0,
        0.0, 0.0, 0.0, -0.02344122157681184,
        0.0, 0.0, 0.0, 0.0,
        2.0000000000000004]
}

def watersvp_t_unit() -> Arr {
    return watersvp_mat(watersvp_t_unit_flat(), 25, 25)
}

#| Nuclear attraction, unit-Cartesian.
def watersvp_v_unit_flat() -> Arr {
    return [-62.38880199569874, 11.885422094704943, 5.250893247884067, 0.0,
        0.0, 0.026618755186472314, 0.0, 0.0,
        0.0035687065317149256, 1.140036095376063, 0.0, 0.0,
        1.1420892382593175, 0.0, 1.141270630974485, 1.5600943210125888,
        2.054917809075752, 0.0, 2.3611379221699584, -1.8299113505899274,
        1.5600943210125886, 2.054917809075752, 0.0, -2.3611379221699584,
        -1.8299113505899274, 11.885422094704943, -12.5914355789141, -8.214313277761326,
        0.0, 0.0, -0.18582135169234293, 0.0,
        0.0, -0.1371540592423394, -6.398910388801486, 0.0,
        0.0, -6.501883256867747, 0.0, -6.460827010550626,
        -3.202339145199478, -3.799101367119256, 0.0, -3.812546214365835,
        2.9259743893637267, -3.202339145199478, -3.799101367119256, 0.0,
        3.8125462143658355, 2.9259743893637267, 5.250893247884067, -8.214313277761326,
        -7.480910287875368, 0.0, 0.0, -0.16904141186578137,
        0.0, 0.0, -0.25015762894523746, -5.210889686233952,
        0.0, 0.0, -5.335715790667782, 0.0,
        -5.285946454466093, -3.5918583579725145, -4.3836435147764305, 0.0,
        -2.6786798166896952, 2.0284499173737816, -3.5918583579725145, -4.3836435147764305,
        0.0, 2.6786798166896952, 2.0284499173737816, 0.0,
        0.0, 0.0, -12.790700677339071, 0.0,
        0.0, -4.321483413804592, 0.0, 0.0,
        0.0, 0.0, -0.12362457365993453, 0.0,
        0.0, 0.0, 0.0, 0.0,
        -1.5508211425508347, 0.0, 0.0, 0.0,
        0.0, -1.5508211425508347, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        -12.896533434180043, 0.0, 0.0, -4.41838838103884,
        0.0, 0.0, 0.0, 0.0,
        0.0, -0.21076486529008706, 0.0, 1.9320017126547635,
        0.6919311505449771, 0.0, 1.8528673237998992, -2.6291946296866437,
        -1.9320017126547633, -0.6919311505449771, 0.0, 1.8528673237998992,
        2.6291946296866437, 0.026618755186472318, -0.18582135169234293, -0.16904141186578137,
        0.0, 0.0, -12.85433692344008, 0.0,
        0.0, -4.379751463578586, -0.07137468088101592, 0.0,
        0.0, -0.12168515171094697, 0.0, -0.24437525785047073,
        -1.5399199053766628, -0.615812339966486, 0.0, -2.690725583646429,
        0.5122380871172001, -1.5399199053766628, -0.615812339966486, 0.0,
        2.690725583646429, 0.5122380871172, 0.0, 0.0,
        0.0, -4.321483413804593, 0.0, 0.0,
        -5.304549819426528, 0.0, 0.0, 0.0,
        0.0, -0.10365261370476854, 0.0, 0.0,
        0.0, 0.0, 0.0, -2.0615794048977465,
        0.0, 0.0, 0.0, 0.0,
        -2.0615794048977465, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, -4.418388381038841,
        0.0, 0.0, -5.530303790878689, 0.0,
        0.0, 0.0, 0.0, 0.0,
        -0.2180885550068259, 0.0, 2.864159613759814, 1.4545083359287205,
        0.0, 0.23399023078729264, -1.7535947656408535, -2.864159613759814,
        -1.4545083359287205, 0.0, 0.23399023078729264, 1.7535947656408535,
        0.0035687065317149256, -0.13715405924233942, -0.2501576289452375, 0.0,
        0.0, -4.379751463578587, 0.0, 0.0,
        -5.4402935694187615, -0.05984386442465641, 0.0, 0.0,
        -0.12591348594036744, 0.0, -0.21925863828416386, -2.275446955795145,
        -1.2815568341839265, 0.0, -1.8263920579692507, -0.6904528721518781,
        -2.275446955795145, -1.2815568341839263, 0.0, 1.8263920579692507,
        -0.6904528721518781, 1.140036095376063, -6.398910388801486, -5.210889686233952,
        0.0, 0.0, -0.0713746808810159, 0.0,
        0.0, -0.05984386442465641, -8.436216156301795, 0.0,
        0.0, -2.842044124085682, 0.0, -2.830093978448656,
        -1.7021108617048795, -2.527860190551505, 0.0, -1.915723523754479,
        1.4732721490727372, -1.7021108617048795, -2.527860190551505, 0.0,
        1.915723523754479, 1.4732721490727372, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        -8.526132372257047, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 1.7747780367281767,
        0.0, 0.0, 0.0, 0.0,
        -1.7747780367281767, 0.0, 0.0, 0.0,
        0.0, 0.0, -0.1236245736599345, 0.0,
        0.0, -0.10365261370476854, 0.0, 0.0,
        0.0, 0.0, -8.490281935345969, 0.0,
        0.0, 0.0, 0.0, 0.0,
        -1.397408401609294, 0.0, 0.0, 0.0,
        0.0, -1.397408401609294, 0.0, 0.0,
        1.1420892382593175, -6.501883256867747, -5.335715790667782, 0.0,
        0.0, -0.12168515171094695, 0.0, 0.0,
        -0.12591348594036744, -2.842044124085682, 0.0, 0.0,
        -8.672570610010615, 0.0, -2.8940522130987554, -2.819985707767056,
        -2.7056178036523977, 0.0, -2.0646272741702365, 3.170221326941431,
        -2.8199857077670565, -2.7056178036523977, 0.0, 2.0646272741702365,
        3.170221326941431, 0.0, 0.0, 0.0,
        0.0, -0.210764865290087, 0.0, 0.0,
        -0.2180885550068259, 0.0, 0.0, 0.0,
        0.0, 0.0, -8.682156639296267, 0.0,
        1.5008019996900575, 0.17505551846239778, 0.0, 1.5761724933777712,
        -0.52018312755137, -1.5008019996900575, -0.17505551846239775, 0.0,
        1.5761724933777712, 0.52018312755137, 1.141270630974485, -6.460827010550626,
        -5.285946454466093, 0.0, 0.0, -0.24437525785047065,
        0.0, 0.0, -0.21925863828416386, -2.830093978448656,
        0.0, 0.0, -2.8940522130987554, 0.0,
        -8.564783275892426, -2.4019277919568145, -2.650137597800825, 0.0,
        -3.2874619195538557, 0.9047386096654668, -2.4019277919568145, -2.6501375978008253,
        0.0, 3.2874619195538557, 0.9047386096654668, 1.5600943210125893,
        -3.202339145199478, -3.5918583579725145, 0.0, 1.9320017126547644,
        -1.5399199053766635, 0.0, 2.864159613759814, -2.275446955795145,
        -1.7021108617048792, 0.0, 0.0, -2.8199857077670565,
        1.5008019996900592, -2.4019277919568145, -6.100278179236541, -3.7699879363066824,
        0.0, -1.216268539266853, 0.8848738113246929, -0.9114969785334522,
        -1.9289854178717003, 0.0, 1.158942242292568, 0.1949145162424069,
        2.054917809075752, -3.799101367119257, -4.3836435147764305, 0.0,
        0.6919311505449782, -0.6158123399664869, 0.0, 1.4545083359287203,
        -1.2815568341839263, -2.5278601905515043, 0.0, 0.0,
        -2.7056178036523977, 0.17505551846239792, -2.650137597800824, -3.7699879363066824,
        -4.399252231054096, 0.0, -0.9955284743007471, 0.7207923913980393,
        -1.9289854178717003, -3.037424252547639, 0.0, 1.4244099088617406,
        0.43519666523291123, 0.0, 0.0, 0.0,
        -1.5508211425508347, 0.0, 0.0, -2.0615794048977465,
        0.0, 0.0, 0.0, 1.774778036728177,
        -1.3974084016092942, 0.0, 0.0, 0.0,
        0.0, 0.0, -5.286570830760588, 0.0,
        0.0, 0.0, 0.0, -0.2543193888006198,
        0.0, 0.0, 2.361137922169959, -3.812546214365836,
        -2.6786798166896952, 0.0, 1.8528673237998992, -2.6907255836464294,
        0.0, 0.23399023078729242, -1.826392057969251, -1.9157235237544792,
        0.0, 0.0, -2.0646272741702365, 1.5761724933777712,
        -3.287461919553856, -1.216268539266853, -0.9955284743007469, 0.0,
        -6.066776588730966, 0.5739557104596804, -1.1589422422925675, -1.4244099088617415,
        0.0, 1.7734705223790537, 0.25755457872351417, -1.8299113505899276,
        2.925974389363727, 2.0284499173737816, 0.0, -2.629194629686643,
        0.5122380871171995, 0.0, -1.753594765640854, -0.6904528721518781,
        1.4732721490727376, 0.0, 0.0, 3.170221326941432,
        -0.52018312755137, 0.9047386096654668, 0.8848738113246929, 0.7207923913980391,
        0.0, 0.5739557104596804, -5.731632920641476, 0.19491451624240688,
        0.4351966652329113, 0.0, -0.25755457872351417, -0.346143018327155,
        1.5600943210125893, -3.202339145199478, -3.5918583579725145, 0.0,
        -1.9320017126547644, -1.5399199053766635, 0.0, -2.864159613759814,
        -2.275446955795145, -1.7021108617048792, 0.0, 0.0,
        -2.8199857077670565, -1.5008019996900592, -2.4019277919568145, -0.9114969785334522,
        -1.9289854178717003, 0.0, -1.158942242292568, 0.1949145162424069,
        -6.100278179236541, -3.769987936306682, 0.0, 1.216268539266853,
        0.8848738113246929, 2.054917809075752, -3.799101367119257, -4.3836435147764305,
        0.0, -0.6919311505449782, -0.6158123399664869, 0.0,
        -1.4545083359287203, -1.2815568341839263, -2.5278601905515043, 0.0,
        0.0, -2.7056178036523972, -0.17505551846239792, -2.650137597800825,
        -1.9289854178717003, -3.037424252547639, 0.0, -1.4244099088617406,
        0.43519666523291123, -3.769987936306682, -4.399252231054096, 0.0,
        0.9955284743007471, 0.7207923913980393, 0.0, 0.0,
        0.0, -1.5508211425508347, 0.0, 0.0,
        -2.0615794048977465, 0.0, 0.0, 0.0,
        -1.774778036728177, -1.3974084016092942, 0.0, 0.0,
        0.0, 0.0, 0.0, -0.2543193888006198,
        0.0, 0.0, 0.0, 0.0,
        -5.286570830760588, 0.0, 0.0, -2.361137922169959,
        3.812546214365836, 2.6786798166896952, 0.0, 1.8528673237998992,
        2.6907255836464294, 0.0, 0.23399023078729242, 1.826392057969251,
        1.9157235237544792, 0.0, 0.0, 2.0646272741702365,
        1.5761724933777714, 3.287461919553856, 1.1589422422925675, 1.4244099088617415,
        0.0, 1.773470522379054, -0.25755457872351417, 1.216268539266853,
        0.9955284743007469, 0.0, -6.066776588730966, -0.5739557104596804,
        -1.8299113505899276, 2.925974389363727, 2.0284499173737816, 0.0,
        2.629194629686643, 0.5122380871171995, 0.0, 1.753594765640854,
        -0.6904528721518781, 1.4732721490727376, 0.0, 0.0,
        3.170221326941432, 0.52018312755137, 0.9047386096654668, 0.19491451624240688,
        0.4351966652329113, 0.0, 0.25755457872351417, -0.346143018327155,
        0.8848738113246929, 0.7207923913980391, 0.0, -0.5739557104596804,
        -5.731632920641476]
}

def watersvp_v_unit() -> Arr {
    return watersvp_mat(watersvp_v_unit_flat(), 25, 25)
}

# Packed-8 length n(n+1)/2 (n(n+1)/2 + 1)/2 for n = 25.
WATERSVP_ERI8_CART_LEN = 52975
# sum of Gp^2 (math.fsum).
WATERSVP_ERI8_CART_SUMSQ = 333.60896886684833
# sum of w_k Gp_k with the LCG weights from WATERSVP_SEED_WSUM (math.fsum).
WATERSVP_ERI8_CART_WSUM = 292.3776949338243
#| 256 packed indices: 128 uniform, then 128 from quartets holding the top l.
def watersvp_eri8_cart_idx() -> Arr {
    return [322, 10852, 5580, 19661,
        50863, 6954, 29330, 25315,
        43084, 13581, 51974, 31070,
        34967, 45692, 28590, 30569,
        25590, 51994, 48417, 49606,
        20480, 32971, 33631, 50281,
        24986, 22443, 24194, 5034,
        12263, 43709, 16914, 12071,
        49053, 46614, 49564, 2012,
        29674, 38721, 1909, 45990,
        50284, 23392, 26865, 18937,
        12180, 25265, 41329, 22113,
        47446, 4855, 30007, 10466,
        39770, 31923, 7887, 19923,
        1271, 25371, 24087, 3098,
        48496, 756, 8415, 47073,
        32893, 43433, 42077, 26458,
        21869, 16053, 2617, 25345,
        15498, 1915, 32512, 46321,
        7491, 48485, 36901, 23782,
        11338, 21661, 17439, 49254,
        33269, 8223, 2460, 34175,
        30660, 22281, 10193, 639,
        39140, 43103, 15641, 17358,
        9893, 45228, 13748, 40346,
        25702, 30290, 8688, 29699,
        23331, 9312, 24858, 36169,
        14172, 16901, 16703, 22429,
        48294, 5457, 26905, 14026,
        7382, 16312, 17462, 18116,
        37055, 18805, 17518, 47988,
        46770, 28067, 39530, 21756,
        26435, 35948, 8049, 31715,
        41427, 18483, 39704, 11225,
        13256, 30482, 10559, 1462,
        24471, 15983, 5407, 4997,
        29691, 8178, 48552, 47409,
        27859, 26164, 39142, 48540,
        8846, 3020, 49104, 20909,
        1876, 1370, 51922, 27660,
        7801, 23617, 48525, 2689,
        29293, 17359, 15817, 8345,
        41527, 48803, 6217, 29941,
        2019, 9021, 44657, 30173,
        51281, 24318, 39398, 28256,
        20278, 25985, 48020, 14429,
        10717, 2542, 9847, 15637,
        46257, 6984, 5483, 24176,
        10622, 12788, 6759, 8886,
        30849, 16354, 40616, 14983,
        29790, 1454, 28260, 20254,
        41021, 28169, 35514, 16651,
        34970, 4825, 4224, 47986,
        1520, 19354, 2919, 6597,
        51130, 13760, 42279, 20590,
        48166, 1096, 32196, 14435,
        47944, 40353, 49453, 2917,
        9405, 40714, 25607, 31575,
        6416, 48332, 36364, 21610,
        26715, 14137, 46457, 48636,
        32998, 11624, 38849, 35934,
        15813, 13774, 15829, 46422,
        47649, 21198, 34273, 46777,
        5886, 1069, 27570, 13229]
}

#| The packed values at those indices.
def watersvp_eri8_cart_val() -> Arr {
    return [0.0, -0.0, 0.0, 0.0,
        -0.0, 0.0, -0.005572761209580406, 0.0,
        0.0007598301845683457, 0.0, -0.0, 0.0,
        0.11338149798215064, -0.0, 0.005730683757886504, 0.0,
        0.0, 0.011804600353326668, -0.0, -0.021455265508062326,
        -0.0, 0.0, 0.00794082753505005, 0.0014062851104392241,
        -0.006566560672139283, 0.24587054643664366, 0.14572921270803285, 0.0,
        0.0126161263838458, -0.000851991873496693, -0.012933255484251248, -0.0,
        -0.028584820152735075, -0.0, -0.00780012176335612, 0.07533510054378137,
        -0.0005292628261383483, -0.09786542551429459, 0.0, -0.0,
        0.0037012960709234786, 0.05758052038929092, -0.0004309585539723846, 0.0,
        0.0, 0.19671381255523088, 0.0, 0.0,
        -0.0, 0.0, 0.00456263884717737, 0.0,
        0.0003646371686883074, -0.024639201677160452, -0.011895341052405452, -0.0,
        0.0, -0.018022967811662172, 0.0, -0.0,
        0.0, -0.019109429670396284, -0.012862462872169245, -0.006290798039318702,
        -0.0003317456405121227, -0.0, -0.04877046496376408, -0.0,
        0.006869566000965014, 0.00026614349436224547, 0.0, 0.06045224335164606,
        -0.011936620435882504, 0.0, -0.0, -0.011207778847676856,
        0.03683603954133091, 0.0, -0.0, 0.04420063138250193,
        -0.0, 0.0, 0.0, -0.01873337417302772,
        0.005575235390837103, -0.02328634374578937, -0.0, 0.0,
        0.13827100312581472, -0.0, -0.0, 0.5334222164852669,
        -0.0, -0.0, 0.2020873390050493, -0.0,
        -0.0, -0.006504514315207268, 0.0, 0.0,
        0.0, 0.0, 0.011585414249111364, 0.0017205713420786453,
        0.0, 0.2846627903558279, -0.015862582825471927, 0.0021946384865659187,
        0.0, 0.17595539186827108, 0.0, 0.0,
        -0.0021291639285925127, 0.0, -0.00032110055776320146, -0.01341839898485904,
        -0.1140425984508788, 0.0, 0.0, 0.0,
        -0.0, -0.011754699682400444, 0.005649307179627648, -0.0016425906468089534,
        0.0030354794758823945, 0.0, -0.009520572447605957, -0.0443314958027167,
        0.00013072021214332615, 0.0, 0.043818469596030474, 0.0,
        -0.0, -0.0, -0.033585963402015105, -0.005167525193029617,
        0.0, 0.0, 0.11662177739823698, 0.0,
        0.0021369843068695486, 0.0029822181772243264, 0.0, 0.0,
        -0.015731905185247207, -0.009773551461077851, 0.0, 0.0,
        0.005205195356337577, -0.0003762555205060261, -0.0, -0.0,
        0.0, 0.0, -0.025629744972770364, 0.02360353882670357,
        0.0, 0.0, -0.0, 0.00875899498229642,
        -0.0, -0.0036182474938025832, -0.0, 0.0,
        0.0, 0.0, -0.007483668666410499, 0.0,
        0.0, 0.008432781409403681, -0.0, 0.0,
        -0.0, -0.0489182497409632, -0.0, 0.014179865622025018,
        0.0, 0.022417828229191087, -0.04142341548456258, 0.0,
        0.0, 0.0, -0.01888720715242609, -0.018030088677276,
        0.07456889558009301, 0.0, 0.0, -0.00904417494340792,
        0.0017555946300589543, 0.0, 0.0, 0.0038998638531534736,
        0.003236696545587193, 0.0, 0.0, 0.0,
        0.0, -0.0, 0.0, -0.02215656991802674,
        0.03690332833127512, 0.0, 0.006719253185173898, 0.015513150438852832,
        -0.0, 0.010809985782151544, -0.0, -0.0,
        0.0, 0.0, -0.0, 8.345360355163613e-05,
        0.5053102543956404, -0.028013910403768987, 0.0, 0.0,
        0.024844453891658187, 0.0, -0.0, -0.09917585522735561,
        -0.0, -0.0, -0.0, -0.004437697046516367,
        -0.012021367162235397, 0.0, 0.03418987438833827, 0.07935021707041194,
        -0.0, -0.015194304370480177, 0.0, -0.0,
        0.0, 0.0, 0.0, 0.0,
        0.1720459103188041, -0.0, -0.0, 0.0,
        0.0, 0.12812740747150148, -0.0, 0.0,
        -0.0020425131071857157, 0.0, 0.0, -0.0,
        0.0, 0.0010131182046202907, 0.0, -0.0017911793322880336,
        0.0, -0.0, 0.0037457836040229995, 0.004186750673715462]
}

#| (ij|ij) for every pair ij, in pair order: the Schwarz bounds.
def watersvp_eri8_cart_diag() -> Arr {
    return [4.776656448422735, 0.31650683157109694, 1.01539063612981, 0.0638458168258978,
        0.512527826443317, 0.5701472512952711, 0.06218150563170958, 0.2274708859765999,
        0.10825094513235449, 1.1470819441911333, 0.06218150563170958, 0.2274708859765999,
        0.10825094513235449, 0.06171990488135421, 1.1470819441911333, 0.06218150563170958,
        0.2274708859765999, 0.10825094513235449, 0.06171990488135421, 0.06171990488135421,
        1.1470819441911337, 0.0005704631675362924, 0.04663363287850644, 0.10057984081406116,
        0.1981260067992479, 0.011424788094711045, 0.011424788094711043, 0.48448578731405173,
        0.0005704631675362924, 0.04663363287850644, 0.10057984081406116, 0.011424788094711045,
        0.1981260067992479, 0.011424788094711043, 0.029662395141676637, 0.48448578731405173,
        0.0005704631675362924, 0.04663363287850644, 0.10057984081406116, 0.011424788094711043,
        0.011424788094711043, 0.1981260067992479, 0.029662395141676637, 0.029662395141676637,
        0.48448578731405173, 0.006313042185611475, 0.41450865632849815, 0.3136513421738468,
        0.2984882272062639, 0.04108508549123163, 0.04108508549123163, 0.13177710383265265,
        0.0182571844816158, 0.0182571844816158, 0.9359689606271958, 0.0010841222456269767,
        0.07613424299911192, 0.05760943019519636, 0.12325525647369492, 0.12325525647369492,
        0.017819385553705214, 0.0547715534448474, 0.0547715534448474, 0.008134389125472387,
        0.09589410348639188, 0.8424456406029571, 0.0010841222456269765, 0.07613424299911192,
        0.057609430195196376, 0.12325525647369492, 0.017819385553705214, 0.12325525647369491,
        0.0547715534448474, 0.008134389125472387, 0.054771553444847396, 0.09589410348639188,
        0.043409862703558476, 0.8424456406029571, 0.006313042185611475, 0.41450865632849815,
        0.3136513421738468, 0.04108508549123163, 0.2984882272062639, 0.04108508549123163,
        0.0182571844816158, 0.13177710383265265, 0.0182571844816158, 0.09360507117810632,
        0.09589410348639188, 0.01446995423451949, 0.9359689606271958, 0.0010841222456269765,
        0.07613424299911192, 0.057609430195196376, 0.017819385553705214, 0.12325525647369492,
        0.12325525647369491, 0.008134389125472387, 0.0547715534448474, 0.054771553444847396,
        0.01446995423451949, 0.043409862703558476, 0.043409862703558476, 0.09589410348639188,
        0.8424456406029571, 0.006313042185611474, 0.41450865632849815, 0.3136513421738468,
        0.04108508549123163, 0.04108508549123163, 0.2984882272062639, 0.018257184481615795,
        0.018257184481615795, 0.13177710383265262, 0.09360507117810632, 0.01446995423451949,
        0.09589410348639188, 0.09360507117810632, 0.09589410348639188, 0.9359689606271957,
        0.005844088550885168, 0.09814581275674861, 0.18313140147493415, 0.013579073668941791,
        0.06582716419235965, 0.04499536146206866, 0.0198767724307995, 0.19920522520864056,
        0.12770529258388919, 0.035792707863688926, 0.019634215858564712, 0.014376226715226707,
        0.12792675913818155, 0.07268864363483972, 0.08519481143226651, 0.8971413572489102,
        0.009891965811013342, 0.11802261201370255, 0.2335627989264997, 0.023531337692385933,
        0.029799530454124087, 0.027300343330157496, 0.05239104646521531, 0.10042048065227102,
        0.08127069568962648, 0.07724522463194396, 0.01636541915228439, 0.015497221247613135,
        0.08760750817541822, 0.018036454469774282, 0.08342789602034109, 0.2999243474108789,
        0.3940445135380343, 5.494122926326517e-05, 0.011997736287739287, 0.03660439268797713,
        0.030288535734716376, 0.009529737045686854, 0.006429388092303605, 0.08956495832903524,
        0.049963242366932274, 0.0322287802198664, 0.015220834951557436, 0.06260268762315277,
        0.04016478717044976, 0.017076348083054128, 0.015501268460469779, 0.009906600973928613,
        0.1604564612845814, 0.06893333251070242, 0.8242232905265858, 0.013584720757371358,
        0.13200882176122672, 0.0921248111907686, 0.02173563413771192, 0.05645129877152279,
        0.11306534144496629, 0.010793711990415115, 0.032463035955508465, 0.0841577632521346,
        0.04431603435572652, 0.01691329990480962, 0.031113730983826096, 0.05885437688205318,
        0.07725978212358152, 0.1791325173016908, 0.1604564612845814, 0.06893333251070242,
        0.05046265044040321, 0.8242232905265858, 0.008190271021690575, 0.08415927868727945,
        0.06998830066633213, 0.013768679767364527, 0.10819873602800219, 0.011470161930357867,
        0.008676508228629802, 0.09977502163741511, 0.03664273905101718, 0.027487609016199278,
        0.029396544724690665, 0.004578418360056487, 0.19072692647289832, 0.02360353882670357,
        0.011632044147110625, 0.1604564612845814, 0.06893333251070242, 0.05046265044040321,
        0.05046265044040321, 0.8242232905265856, 0.005844088550885168, 0.09814581275674861,
        0.18313140147493415, 0.013579073668941791, 0.06582716419235965, 0.04499536146206866,
        0.0198767724307995, 0.19920522520864056, 0.12770529258388919, 0.035792707863688926,
        0.019634215858564712, 0.014376226715226707, 0.12792675913818155, 0.07268864363483972,
        0.08519481143226651, 0.011124705808519814, 0.0596122437571924, 0.0010580514395239103,
        0.018980308562478513, 0.0010580514395239103, 0.8971413572489102, 0.009891965811013342,
        0.11802261201370255, 0.2335627989264997, 0.023531337692385933, 0.029799530454124087,
        0.027300343330157496, 0.05239104646521531, 0.10042048065227102, 0.08127069568962648,
        0.07724522463194396, 0.01636541915228439, 0.015497221247613135, 0.08760750817541822,
        0.018036454469774282, 0.08342789602034109, 0.0596122437571924, 0.14521791100554912,
        0.012191775281988946, 0.03150929626714507, 0.012191775281988946, 0.2999243474108789,
        0.3940445135380343, 5.494122926326517e-05, 0.011997736287739287, 0.03660439268797713,
        0.030288535734716376, 0.009529737045686854, 0.006429388092303605, 0.08956495832903524,
        0.049963242366932274, 0.0322287802198664, 0.015220834951557436, 0.06260268762315277,
        0.04016478717044976, 0.017076348083054128, 0.015501268460469779, 0.009906600973928613,
        0.0010580514395239103, 0.012191775281988948, 0.0011805460305248966, 0.0016499851982987581,
        7.227832839948347e-05, 0.1604564612845814, 0.06893333251070242, 0.8242232905265858,
        0.013584720757371358, 0.13200882176122672, 0.0921248111907686, 0.02173563413771192,
        0.05645129877152279, 0.11306534144496629, 0.010793711990415115, 0.032463035955508465,
        0.0841577632521346, 0.04431603435572652, 0.01691329990480962, 0.031113730983826096,
        0.05885437688205318, 0.07725978212358152, 0.1791325173016908, 0.018980308562478496,
        0.03150929626714512, 0.0016499851982987581, 0.047392821031147635, 0.0016499851982987581,
        0.1604564612845814, 0.06893333251070242, 0.05046265044040321, 0.8242232905265858,
        0.008190271021690575, 0.08415927868727945, 0.06998830066633213, 0.013768679767364527,
        0.10819873602800219, 0.011470161930357867, 0.008676508228629802, 0.09977502163741511,
        0.03664273905101718, 0.027487609016199278, 0.029396544724690665, 0.004578418360056487,
        0.19072692647289832, 0.02360353882670357, 0.011632044147110625, 0.0010580514395239103,
        0.012191775281988948, 7.227832839948347e-05, 0.0016499851982987581, 0.0011805460305248966,
        0.1604564612845814, 0.06893333251070242, 0.05046265044040321, 0.05046265044040321,
        0.8242232905265856]
}

#| M = diag(F) cart2sph_coeff(), [25,24]: X_sph = M^T X_unit M.
def watersvp_m_flat() -> Arr {
    return [1.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 1.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 1.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 1.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        1.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 1.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 1.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 1.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        1.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, -0.49999999999999994,
        0.0, 0.8660254037844387, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 1.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        1.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, -0.49999999999999994,
        0.0, -0.8660254037844387, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 1.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.9999999999999999,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 1.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 1.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        1.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 1.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 1.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 1.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        1.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 1.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 1.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 1.0]
}

def watersvp_m() -> Arr {
    return watersvp_mat(watersvp_m_flat(), 25, 24)
}

# ---- WATERSVP RHF: nalpha 5, nbeta 5; default state is stable ----

WATERSVP_E_RHF = -75.96097516698583
WATERSVP_E_RHF_DEFAULT = -75.96097516698583
WATERSVP_E_RHF_STABLE = -75.96097516698583
# 1: no restart from the stability orbitals lowers the minao state; 0: one does; -1: not analyzed (stability restart).
WATERSVP_RHF_IS_STABLE = 1
WATERSVP_RHF_NALPHA = 5
WATERSVP_RHF_NBETA = 5

# ---- WATERSVP RHF (cart): nalpha 5, nbeta 5; default state is stable ----

WATERSVP_E_RHF_CART = -75.96221113003139
WATERSVP_E_RHF_DEFAULT_CART = -75.96221113003139
WATERSVP_E_RHF_STABLE_CART = -75.96221113003139
# 1: no restart from the stability orbitals lowers the minao state; 0: one does; -1: not analyzed (stability restart).
WATERSVP_RHF_IS_STABLE_CART = 1
WATERSVP_RHF_NALPHA_CART = 5
WATERSVP_RHF_NBETA_CART = 5

test "watersvp packs" {
    assert_near(watersvp_pack_bad(watersvp_shells(), WATERSVP_NSH, WATERSVP_NPRIMTOT, WATERSVP_NATOM), 0.0, 0.0)
    # nao_cart - nao_sph = sum over shells of ncart - nsph: 1 per d shell, 3 per f shell
    assert_near(WATERSVP_NAO_CART - WATERSVP_NAO_SPH, 1.0, 0.0)
    assert_near(len(watersvp_fc()), WATERSVP_NAO_CART, 0.0)
}

test "watersvp sph one-electron integrals are symmetric with a unit overlap diagonal" {
    assert_near(watersvp_asym(watersvp_s_sph(), 24), 0.0, 1.0e-14)
    assert_near(watersvp_asym(watersvp_t_sph(), 24), 0.0, 1.0e-14)
    assert_near(watersvp_asym(watersvp_v_sph(), 24), 0.0, 1.0e-14)
    assert_near(watersvp_diag_dev(watersvp_s_sph(), 24), 0.0, 1.0e-14)
}

test "watersvp sph sampled ERIs obey the Schwarz bound" {
    assert_near(len(watersvp_eri8_sph_idx()), 256.0, 0.0)
    assert_near(len(watersvp_eri8_sph_diag()), 300.0, 0.0)
    assert_lt(watersvp_sample_schwarz(watersvp_eri8_sph_idx(), watersvp_eri8_sph_val(), watersvp_eri8_sph_diag()), 1.0e-12)
    assert_lt(0.0, WATERSVP_ERI8_SPH_SUMSQ)
}

test "watersvp unit one-electron integrals are symmetric with a unit overlap diagonal" {
    assert_near(watersvp_asym(watersvp_s_unit(), 25), 0.0, 1.0e-14)
    assert_near(watersvp_asym(watersvp_t_unit(), 25), 0.0, 1.0e-14)
    assert_near(watersvp_asym(watersvp_v_unit(), 25), 0.0, 1.0e-14)
    assert_near(watersvp_diag_dev(watersvp_s_unit(), 25), 0.0, 1.0e-14)
}

test "watersvp unit sampled ERIs obey the Schwarz bound" {
    assert_near(len(watersvp_eri8_cart_idx()), 256.0, 0.0)
    assert_near(len(watersvp_eri8_cart_diag()), 325.0, 0.0)
    assert_lt(watersvp_sample_schwarz(watersvp_eri8_cart_idx(), watersvp_eri8_cart_val(), watersvp_eri8_cart_diag()), 1.0e-12)
    assert_lt(0.0, WATERSVP_ERI8_CART_SUMSQ)
}

test "watersvp M^T X_unit M is the spherical X" {
    assert_lt(watersvp_mtxm_dev(watersvp_m(), watersvp_s_unit(), watersvp_s_sph(), 25, 24), 1.0e-13)
    assert_lt(watersvp_mtxm_dev(watersvp_m(), watersvp_t_unit(), watersvp_t_sph(), 25, 24), 1.0e-13)
    assert_lt(watersvp_mtxm_dev(watersvp_m(), watersvp_v_unit(), watersvp_v_sph(), 25, 24), 1.0e-13)
}

test "watersvp rhf energies, labels and densities" {
    assert_lt(WATERSVP_E_RHF_STABLE, WATERSVP_E_RHF_DEFAULT + 1.0e-12)
}

test "watersvp rhf cart energies, labels and densities" {
    assert_lt(WATERSVP_E_RHF_STABLE_CART, WATERSVP_E_RHF_DEFAULT_CART + 1.0e-12)
}