###
post: The OH radical in 6-31G
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.
OH_631G_SEED_WSUM = 20260923

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

#| Reshape a flat row-major vector into r x c.
def oh_631g_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 oh_631g_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 oh_631g_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 oh_631g_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 oh_631g_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 oh_631g_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 oh_631g_e_elec(h: Arr, g: Arr, da: Arr, db: Arr, n) {
    pr = oh_631g_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 oh_631g_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 oh_631g_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 oh_631g_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 oh_631g_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 oh_631g_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 oh_631g_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
}

# ======== OH_631G: 6-31g, s and p only, so Cartesian = spherical ========

OH_631G_NATOM = 2
OH_631G_NSH = 7
OH_631G_NPRIMTOT = 18
OH_631G_NAO_CART = 11
OH_631G_NAO_SPH = 11
OH_631G_E_NUC = 4.365698347282665

#| (Z, x, y, z) in Bohr, one atom per row.
def oh_631g_atoms_flat() -> Arr {
    return [8.0, 0.0, 0.0, 0.0,
        1.0, 0.0, 0.0, 1.8324674229907405]
}

def oh_631g_atoms() -> Arr {
    return oh_631g_mat(oh_631g_atoms_flat(), 2, 4)
}

#| (atom, l, nprim, p0, cart0, sph0, ncart, nsph); general contractions split.
def oh_631g_shells_flat() -> Arr {
    return [0, 0, 6, 0,
        0, 0, 1, 1,
        0, 0, 3, 6,
        1, 1, 1, 1,
        0, 0, 1, 9,
        2, 2, 1, 1,
        0, 1, 3, 10,
        3, 3, 3, 3,
        0, 1, 1, 13,
        6, 6, 3, 3,
        1, 0, 3, 14,
        9, 9, 1, 1,
        1, 0, 1, 17,
        10, 10, 1, 1]
}

def oh_631g_shells() -> Arr {
    return oh_631g_mat(oh_631g_shells_flat(), 7, 8)
}

#| (exponent, raw bas_ctr_coeff).
def oh_631g_prims_flat() -> Arr {
    return [5484.6717, 0.0018310998055270163, 825.23495, 0.013950098518421949,
        188.04696, 0.06844509273075047, 52.9645, 0.23271427528444968,
        16.89757, 0.47019295006289363, 5.7996353, 0.3585208619230904,
        15.539616, -0.11077750382508463, 3.5999336, -0.14802630511126472,
        1.0137618, 1.1307670390447473, 0.2700058, 1.0000000000000002,
        15.539616, 0.0708742995433115, 3.5999336, 0.3397527978107552,
        1.0137618, 0.7271585953144516, 0.2700058, 1.0000000000000002,
        18.731137, 0.03349459952309008, 2.8253937, 0.2347269466578609,
        0.6401217, 0.8137573184133876, 0.1612778, 1.0000000000000002]
}

def oh_631g_prims() -> Arr {
    return oh_631g_mat(oh_631g_prims_flat(), 18, 2)
}

#| F per Cartesian AO: PySCF-Cartesian = F x unit-Cartesian.
def oh_631g_fc() -> Arr {
    return [1.0, 1.0, 1.0, 1.0,
        1.0, 1.0, 1.0, 1.0,
        1.0, 1.0, 1.0]
}

#| Overlap, unit-Cartesian, [11,11].
def oh_631g_s_unit_flat() -> Arr {
    return [1.0000000000000002, 0.23368990605916293, 0.16727975959589536, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0332882755389629, 0.0680949880811538, 0.23368990605916296,
        0.9999999999999997, 0.7636407733384438, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.2405758448590471, 0.3760252463261058, 0.16727975959589536, 0.7636407733384438,
        1.0000000000000004, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.4206274679973866,
        0.6782128196567272, 0.0, 0.0, 0.0,
        0.9999999999999996, 0.0, 0.0, 0.5015206410748108,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.9999999999999996, 0.0, 0.0, 0.5015206410748108,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.9999999999999996, 0.0, 0.0, 0.5015206410748108,
        0.2804828436809418, 0.14790172730306428, 0.0, 0.0,
        0.0, 0.5015206410748108, 0.0, 0.0,
        1.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.5015206410748108, 0.0, 0.0,
        1.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.5015206410748108, 0.0, 0.0,
        1.0, 0.5815899043203999, 0.4829814446321068, 0.03328827553896291,
        0.24057584485904707, 0.4206274679973866, 0.0, 0.0,
        0.2804828436809418, 0.0, 0.0, 0.5815899043203998,
        0.9999999999999999, 0.6582920493393297, 0.0680949880811538, 0.3760252463261058,
        0.6782128196567273, 0.0, 0.0, 0.14790172730306417,
        0.0, 0.0, 0.48298144463210696, 0.6582920493393297,
        1.0000000000000002]
}

def oh_631g_s_unit() -> Arr {
    return oh_631g_mat(oh_631g_s_unit_flat(), 11, 11)
}

#| Kinetic energy, unit-Cartesian.
def oh_631g_t_unit_flat() -> Arr {
    return [29.540139797820466, -2.185402729908697, 0.1312824993202389, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, -0.022738811380480776, 0.020871982510231517, -2.185402729908697,
        1.711210960211668, 0.48004782078660324, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.013844617829634566, 0.10759544784854064, 0.13128249932023878, 0.48004782078660313,
        0.4050087000000002, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.13792460852876706,
        0.15899963946204007, 0.0, 0.0, 0.0,
        4.251877061027584, 0.0, 0.0, 0.5472432238224882,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        4.251877061027584, 0.0, 0.0, 0.5472432238224882,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        4.251877061027585, 0.0, 0.0, 0.5472432238224882,
        0.2107859321238526, 0.0844175193484968, 0.0, 0.0,
        0.0, 0.5472432238224884, 0.0, 0.0,
        0.6750145000000001, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.5472432238224884, 0.0, 0.0,
        0.6750145000000001, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.5472432238224882, 0.0, 0.0,
        0.6750145000000001, 0.4206569927712456, 0.2107613236106196, -0.02273881138048094,
        0.01384461782963469, 0.1379246085287671, 0.0, 0.0,
        0.21078593212385252, 0.0, 0.0, 0.42065699277124563,
        1.395678281298843, 0.2597350827253875, 0.02087198251023148, 0.10759544784854053,
        0.1589996394620401, 0.0, 0.0, 0.08441751934849673,
        0.0, 0.0, 0.21076132361061972, 0.2597350827253875,
        0.24191670000000004]
}

def oh_631g_t_unit() -> Arr {
    return oh_631g_mat(oh_631g_t_unit_flat(), 11, 11)
}

#| Nuclear attraction, unit-Cartesian.
def oh_631g_v_unit_flat() -> Arr {
    return [-62.026913042757045, -5.051370956534985, -5.40968843298749, 0.0,
        0.0, -0.02165251573388019, 0.0, 0.0,
        -0.002983677574190744, -1.0338862682106085, -2.173510814893726, -5.051370956534987,
        -11.076737245886585, -7.44526727460228, 0.0, 0.0,
        -0.14730941969964406, 0.0, 0.0, -0.09451630885459456,
        -2.182268119931329, -3.4947447886257716, -5.40968843298749, -7.44526727460228,
        -7.1482413706146115, 0.0, 0.0, -0.13936872889657198,
        0.0, 0.0, -0.19924197117854633, -2.8174795338232412,
        -4.1866387508858995, 0.0, 0.0, 0.0,
        -12.153776635922966, 0.0, 0.0, -4.022112443241034,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        -12.153776635922966, 0.0, 0.0, -4.022112443241034,
        0.0, 0.0, 0.0, -0.02165251573388019,
        -0.14730941969964406, -0.13936872889657198, 0.0, 0.0,
        -12.2370038464474, 0.0, 0.0, -4.098568600867555,
        -2.3183305700268444, -1.219931900406093, 0.0, 0.0,
        0.0, -4.022112443241034, 0.0, 0.0,
        -4.83243185844709, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, -4.022112443241034, 0.0, 0.0,
        -4.83243185844709, 0.0, 0.0, 0.0,
        -0.002983677574190744, -0.09451630885459456, -0.19924197117854633, 0.0,
        0.0, -4.098568600867555, 0.0, 0.0,
        -5.01105074448699, -3.3148313134703065, -2.2787430367727897, -1.0338862682106087,
        -2.1822681199313285, -2.817479533823242, 0.0, 0.0,
        -2.3183305700268444, 0.0, 0.0, -3.3148313134703056,
        -6.009198222205471, -3.564316388200907, -2.173510814893726, -3.4947447886257716,
        -4.1866387508859, 0.0, 0.0, -1.2199319004060918,
        0.0, 0.0, -2.27874303677279, -3.564316388200907,
        -4.390678342510322]
}

def oh_631g_v_unit() -> Arr {
    return oh_631g_mat(oh_631g_v_unit_flat(), 11, 11)
}

# Packed-8 length n(n+1)/2 (n(n+1)/2 + 1)/2 for n = 11.
OH_631G_ERI8_CART_LEN = 2211
# sum of Gp^2 (math.fsum).
OH_631G_ERI8_CART_SUMSQ = 77.51184628084933
# sum of w_k Gp_k with the LCG weights from OH_631G_SEED_WSUM (math.fsum).
OH_631G_ERI8_CART_WSUM = 58.657140121313866
#| Every packed-8 two-electron integral, unit-Cartesian, chemist's notation.
def oh_631g_eri8_cart() -> Arr {
    return [4.7804457081113805, 0.5983784514509743, 0.11285400979250193, 1.3114362842533671,
        0.29498127617380526, 1.0296771719698425, 0.5379732156476946, 0.08663569805702304,
        0.2133854027485799, 0.07039782993883162, 0.8750647906945591, 0.1974128208517195,
        0.7159143761050138, 0.14272034892008603, 0.505125599143268, 0.8216638374470009,
        0.1864909853335337, 0.7224936261383073, 0.13462613384102884, 0.5251403995921171,
        0.5863293117931712, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.060930805139579346,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.07436470375582598, 0.23306869473401048,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.04654142860157757, 0.1597925248248912,
        0.11492893127026124, 1.4330401311580432, 0.3108514544447305, 1.0392128678439634,
        0.22749314559994974, 0.7203286611253504, 0.7243812725168677, 0.0,
        0.0, 0.0, 1.1368753426236395, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.060930805139579346, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.07436470375582598, 0.23306869473401048, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.04654142860157757, 0.1597925248248912, 0.11492893127026124, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.06116096577519476, 1.4330401311580432, 0.3108514544447305, 1.0392128678439634,
        0.22749314559994974, 0.7203286611253504, 0.7243812725168677, 0.0,
        0.0, 0.0, 1.0145534110732504, 0.0,
        0.0, 0.0, 0.0, 1.1368753426236395,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.060930805139579346,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.07436470375582598,
        0.23306869473401048, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.04654142860157757, 0.1597925248248912, 0.11492893127026124, 0.0,
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        0.045297488609353696, 0.0892450393844015, 0.0, 0.0,
        0.16940365546604225, 0.0, 0.0, 0.2967291534107234,
        0.011580933032746833, 0.10888621469728749, 0.19786720234150107, 0.0,
        0.0, 0.14495338625700752, 0.0, 0.0,
        0.29016282956550077, 0.5442197691704004, 0.12692190245356497, 0.5359130096798269,
        0.09090307280102969, 0.40386142909808287, 0.4921940213353379, 0.0,
        0.0, 0.0, 0.5144462956765011, 0.0,
        0.0, 0.0, 0.0, 0.5144462956765011,
        0.020871056385643433, 0.13266343331057762, 0.11969023740286004, 0.0,
        0.0, 0.5769877848280995, 0.0, 0.0,
        0.0, 0.24275118155122116, 0.0, 0.0,
        0.40664442923029137, 0.0, 0.0, 0.0,
        0.0, 0.24275118155122116, 0.0, 0.0,
        0.40664442923029137, 0.0028551828232272593, 0.07977964797008698, 0.16291862953728337,
        0.0, 0.0, 0.293769818108386, 0.0,
        0.0, 0.5259786618835702, 0.019459708917168, 0.1920342745985102,
        0.3638760884819305, 0.0, 0.0, 0.26190603522888345,
        0.0, 0.0, 0.5478325060106741, 1.0765661114047185,
        0.21668235808790018, 0.0350628063138993, 0.08672320331770976, 0.02843839576886455,
        0.05801818817423776, 0.05475206951964342, 0.0, 0.0,
        0.0, 0.09235103915358414, 0.0, 0.0,
        0.0, 0.0, 0.09235103915358414, 0.0013025972316221698,
        0.0020987715489894226, 0.0013218226349418878, 0.0, 0.0,
        0.09244662818845298, 0.0, 0.0, 0.0,
        0.031557002462922486, 0.0, 0.0, 0.03757426259078768,
        0.0, 0.0, 0.0, 0.0,
        0.031557002462922486, 0.0, 0.0, 0.03757426259078768,
        0.0001308134635735735, 0.0006155455217266947, 0.0006081402559470991, 0.0,
        0.0, 0.03158283077550978, 0.0, 0.0,
        0.03758931084160477, 0.0055846111901679185, 0.016610371971043855, 0.02005644362996074,
        0.0, 0.0, 0.017188694640005883, 0.0,
        0.0, 0.022419577186958348, 0.0376920475803834, 0.011519450257454433,
        0.40588489444769515, 0.09197337787521428, 0.3391597030066227, 0.06640657345677162,
        0.24064937380886775, 0.2531687840191188, 0.0, 0.0,
        0.0, 0.34006131322199457, 0.0, 0.0,
        0.0, 0.0, 0.34006131322199457, 0.005250190117370719,
        0.023978563215217012, 0.01828337109903258, 0.0, 0.0,
        0.34222226299908054, 0.0, 0.0, 0.0,
        0.14261514834713004, 0.0, 0.0, 0.19729898030807858,
        0.0, 0.0, 0.0, 0.0,
        0.14261514834713004, 0.0, 0.0, 0.19729898030807858,
        0.0006842817153106857, 0.011181904944637154, 0.015898053233294226, 0.0,
        0.0, 0.14385666779832976, 0.0, 0.0,
        0.19903246857173462, 0.013471260815987547, 0.07793126230892973, 0.10708891658876114,
        0.0, 0.0, 0.08762248893497028, 0.0,
        0.0, 0.13096822616089007, 0.22340069010742106, 0.02716171873413248,
        0.11807222171701424, 0.46762028815786405, 0.10704953739732094, 0.426095861259185,
        0.07708362011954989, 0.31334357111204264, 0.3611369265863012, 0.0,
        0.0, 0.0, 0.4254733319196021, 0.0,
        0.0, 0.0, 0.0, 0.4254733319196021,
        0.006035337914204683, 0.03417199282869431, 0.02938349662284582, 0.0,
        0.0, 0.4290560060160917, 0.0, 0.0,
        0.0, 0.19445628273101734, 0.0, 0.0,
        0.3092725433177893, 0.0, 0.0, 0.0,
        0.0, 0.19445628273101734, 0.0, 0.0,
        0.3092725433177893, 0.0008097273704127225, 0.019146694307469903, 0.03693462292360938,
        0.0, 0.0, 0.19724745608224462, 0.0,
        0.0, 0.3161894015252923, 0.015671631188686797, 0.10740302947483282,
        0.16899869911896126, 0.0, 0.0, 0.1264547011035414,
        0.0, 0.0, 0.22347962310267466, 0.3892408596593847,
        0.031550289356675615, 0.15747874855977484, 0.24102024449809809, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.020372142493223937, 0.07342088863937508, 0.053668872255318474,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.005977729985298051, 0.0, 0.0,
        0.0024895310887690174, 0.03150140210885692, 0.042243348912052635, 0.0,
        0.0, 0.0031429089691022843, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0031429089691022843, 0.0,
        0.0, 0.0041051298879705034, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.012846115863327665,
        0.0, 0.0, 0.011530171305999117, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0261057047056773, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.020372142493223937, 0.07342088863937508, 0.053668872255318474, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.005977729985298051, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0024895310887690174, 0.03150140210885692,
        0.042243348912052635, 0.0, 0.0, 0.0031429089691022843,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0031429089691022843, 0.0,
        0.0, 0.0041051298879705034, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.012846115863327665,
        0.0, 0.0, 0.011530171305999117, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0261057047056773, 0.12982760903496676, 0.029833042083356357,
        0.1163540618256496, 0.02145364655180386, 0.08420050134482654, 0.09238676790796732,
        0.0, 0.0, 0.0, 0.11231860411861146,
        0.0, 0.0, 0.0, 0.0,
        0.11231860411861146, 0.02142541803948147, 0.07898362877640286, 0.058175101446977864,
        0.0, 0.0, 0.12467026400717417, 0.0,
        0.0, 0.0, 0.04915597213337694, 0.0,
        0.0, 0.0724658328421487, 0.0, 0.0,
        0.0, 0.0, 0.04915597213337694, 0.0,
        0.0, 0.0724658328421487, 0.0026301990800065627, 0.03436224404741583,
        0.04683224098152244, 0.0, 0.0, 0.05570591572414955,
        0.0, 0.0, 0.08112971780645933, 0.005441105001852345,
        0.04564309092664404, 0.06680210172176912, 0.0, 0.0,
        0.06020240996985708, 0.0, 0.0, 0.08855924816046519,
        0.15550825435211432, 0.009349650918562987, 0.05027921040128477, 0.07319344636993584,
        0.0, 0.0, 0.04578298958121302, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.010611512363853819, 0.06008222398712174, 0.05166294615794911,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0062991651852797505, 0.0, 0.0,
        0.0014236869790277067, 0.03366429291265628, 0.06493956318265356, 0.0,
        0.0, 0.004907524805943001, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.004907524805943001, 0.0,
        0.0, 0.012161427815863084, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.013647144748778168,
        0.0, 0.0, 0.020424346411120634, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.027157959370331317, 0.0, 0.0,
        0.05029703883315183, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.010611512363853819,
        0.06008222398712174, 0.05166294615794911, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0062991651852797505, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0014236869790277067, 0.03366429291265628, 0.06493956318265356,
        0.0, 0.0, 0.004907524805943001, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.004907524805943001, 0.0, 0.0,
        0.012161427815863084, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.013647144748778168, 0.0,
        0.0, 0.020424346411120634, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.027157959370331317, 0.0, 0.0, 0.05029703883315183,
        0.22932012545873265, 0.05353374719348693, 0.22634542787969542, 0.038330258560275006,
        0.17080762790247492, 0.21093353933551806, 0.0, 0.0,
        0.0, 0.22156555978325715, 0.0, 0.0,
        0.0, 0.0, 0.22156555978325715, 0.012488069941063787,
        0.0723741904926031, 0.06305049793122643, 0.0, 0.0,
        0.2351765696245962, 0.0, 0.0, 0.0,
        0.10659615407249995, 0.0, 0.0, 0.18616034422777178,
        0.0, 0.0, 0.0, 0.0,
        0.10659615407249995, 0.0, 0.0, 0.18616034422777178,
        0.0016815114951271239, 0.04132020140187127, 0.08258150862294816, 0.0,
        0.0, 0.11733175449974623, 0.0, 0.0,
        0.21346693953915416, 0.008391855234882784, 0.07979341958231669, 0.14621683200168017,
        0.0, 0.0, 0.10527927849725188, 0.0,
        0.0, 0.21347686843184244, 0.38680568344269955, 0.016003367920085082,
        0.09615664632467824, 0.17163978989986403, 0.0, 0.0,
        0.06964394667421722, 0.0, 0.0, 0.17252833744550528,
        0.35218664502525115, 0.08184572372227307, 0.3416000689241397, 0.05867840805455812,
        0.2563451254321695, 0.31107876057036965, 0.0, 0.0,
        0.0, 0.332043649215351, 0.0, 0.0,
        0.0, 0.0, 0.332043649215351, 0.012071365343881302,
        0.07397281252714456, 0.06600338885636509, 0.0, 0.0,
        0.36009170800356616, 0.0, 0.0, 0.0,
        0.15656631332941012, 0.0, 0.0, 0.2635874333904214,
        0.0, 0.0, 0.0, 0.0,
        0.15656631332941012, 0.0, 0.0, 0.2635874333904214,
        0.0016407883855955848, 0.04373831107824031, 0.0904413656299301, 0.0,
        0.0, 0.17920814544552868, 0.0, 0.0,
        0.3200489478857985, 0.012445305806008514, 0.1127639147345078, 0.20803858029761393,
        0.0, 0.0, 0.14865534328535498, 0.0,
        0.0, 0.307108820738026, 0.5784703754509466, 0.02427688991183269,
        0.1390969405083255, 0.24043019802516866, 0.0, 0.0,
        0.0902328261486231, 0.0, 0.0, 0.22956399143284487,
        0.3294232122281213, 0.46753149098581215, 0.10834470856115738, 0.44932601411358813,
        0.07774077618184837, 0.3370266082931338, 0.412448989862188, 0.0,
        0.0, 0.0, 0.4454778147216103, 0.0,
        0.0, 0.0, 0.0, 0.4454778147216103,
        0.009705271847748798, 0.05989695564035742, 0.05426817798181513, 0.0,
        0.0, 0.45718180968617017, 0.0, 0.0,
        0.0, 0.21249862707545258, 0.0, 0.0,
        0.3696902961717483, 0.0, 0.0, 0.0,
        0.0, 0.21249862707545258, 0.0, 0.0,
        0.3696902961717483, 0.0013189332868432744, 0.036124885984008495, 0.081428649809307,
        0.0, 0.0, 0.22263196890373682, 0.0,
        0.0, 0.40172022371598076, 0.016058771557621032, 0.12842323426102886,
        0.2295144278520057, 0.0, 0.0, 0.15991208608646007,
        0.0, 0.0, 0.32841646919735884, 0.5873958936909296,
        0.03195231002469129, 0.17579142418397278, 0.30396699020711276, 0.0,
        0.0, 0.09609169320710689, 0.0, 0.0,
        0.2648871717059659, 0.36130384954057454, 0.45315038634860366]
}

def oh_631g_s_sph() -> Arr {
    return oh_631g_s_unit()
}

def oh_631g_t_sph() -> Arr {
    return oh_631g_t_unit()
}

def oh_631g_v_sph() -> Arr {
    return oh_631g_v_unit()
}

#| Only s and p: the spherical and Cartesian sets are the same.
def oh_631g_eri8_sph() -> Arr {
    return oh_631g_eri8_cart()
}

def oh_631g_m() -> Arr {
    return oh_631g_eye(11)
}

# ---- OH_631G UHF: nalpha 5, nbeta 4; default state is stable ----

OH_631G_E_UHF = -75.36316991969719
OH_631G_E_UHF_DEFAULT = -75.36316991969719
OH_631G_E_UHF_STABLE = -75.36316991969719
# 1: no restart from the stability orbitals lowers the minao state; 0: one does; -1: not analyzed (stability restart).
OH_631G_UHF_IS_STABLE = 1
OH_631G_UHF_NALPHA = 5
OH_631G_UHF_NBETA = 4
# <S^2> of the default UHF state.
OH_631G_UHF_S2 = 0.753768089366905
OH_631G_UHF_S2_STABLE = 0.753768089366905

# Max |D' - D| after one PySCF step (get_fock, eig, get_occ, make_rdm1) from the default density below.
OH_631G_UHF_SELF_STEP = 1.513567049471476e-12
#| Converged alpha density, default state.
def oh_631g_uhf_da_flat() -> Arr {
    return [1.0455178203689963, -0.10406013903349555, -0.1367538911601133, -7.565287009291404e-18,
        -7.339015307410422e-18, 0.01610290917500273, -1.876516654896009e-18, -1.8033195490947195e-18,
        0.00693575824034716, -0.013507480140160254, 0.016459082525719895, -0.10406013903349555,
        0.2945045566161461, 0.30213503403393993, 3.677989425153699e-17, 7.077852062300161e-18,
        -0.03464519637533436, 1.7115664231063597e-17, -3.6747176196934554e-18, -0.02122858443439804,
        0.030424171365563413, -0.032322568102106146, -0.1367538911601133, 0.30213503403393993,
        0.323821990072301, 5.590107690946347e-17, 9.704771488277521e-17, -0.09895065640566973,
        1.1954080948157114e-17, 5.3334550295212294e-17, -0.058473642038067826, -0.005021290798347516,
        -0.0470742890023062, -7.565287009291404e-18, 3.677989425153699e-17, 5.590107690946347e-17,
        0.4763021459590522, 0.00412657996836427, -1.1310497165078078e-16, 0.314736217578006,
        -0.0009178459384558554, 4.079738117509376e-17, 6.327336382186832e-18, -1.6089129526724285e-16,
        -7.339015307410422e-18, 7.077852062300161e-18, 9.704771488277521e-17, 0.00412657996836427,
        0.44964841530497596, -1.977372754039409e-17, -0.0009178459384552921, 0.32066461799992463,
        9.403779340336912e-17, -2.3474099867091526e-17, -1.4690433193664432e-16, 0.01610290917500273,
        -0.03464519637533436, -0.09895065640566973, -1.1310497165078078e-16, -1.977372754039409e-17,
        0.3130352382309255, 8.589429692925214e-18, 2.087175496136493e-17, 0.1816924501740773,
        0.17367422797479126, 0.07100843325246657, -1.876516654896009e-18, 1.7115664231063597e-17,
        1.1954080948157114e-17, 0.314736217578006, -0.0009178459384552921, 8.589429692925214e-18,
        0.20800443482258182, -0.0032059426014401445, 7.44695550277241e-17, 5.087464748572005e-17,
        -8.64449364833427e-17, -1.8033195490947195e-18, -3.6747176196934554e-18, 5.3334550295212294e-17,
        -0.0009178459384558554, 0.32066461799992463, 2.087175496136493e-17, -0.0032059426014401445,
        0.22871173511636103, 8.652482919733175e-17, 1.3070927090848311e-18, -9.535347041576259e-17,
        0.00693575824034716, -0.02122858443439804, -0.058473642038067826, 4.079738117509376e-17,
        9.403779340336912e-17, 0.1816924501740773, 7.44695550277241e-17, 8.652482919733175e-17,
        0.10547035607822701, 0.10062686870981319, 0.04129740566016853, -0.013507480140160254,
        0.030424171365563413, -0.005021290798347516, 6.327336382186832e-18, -2.3474099867091526e-17,
        0.17367422797479126, 5.087464748572005e-17, 1.3070927090848311e-18, 0.10062686870981319,
        0.10485955274509455, 0.03519697277116359, 0.016459082525719895, -0.032322568102106146,
        -0.0470742890023062, -1.6089129526724285e-16, -1.4690433193664432e-16, 0.07100843325246657,
        -8.64449364833427e-17, -9.535347041576259e-17, 0.04129740566016853, 0.03519697277116359,
        0.01818385895402441]
}

def oh_631g_uhf_da() -> Arr {
    return oh_631g_mat(oh_631g_uhf_da_flat(), 11, 11)
}

#| Converged beta density, default state.
def oh_631g_uhf_db_flat() -> Arr {
    return [1.0440875970859655, -0.09687396361246292, -0.13633723058564884, -5.583582107057858e-18,
        -1.0590193910792523e-17, 0.018385539417373895, 2.356103444246632e-18, -5.945125693041261e-18,
        0.012680287220793054, -0.01806934046678766, 0.01438140925160449, -0.09687396361246292,
        0.2631920604549702, 0.29242833036787474, 1.1649792309666224e-17, 2.705801727110143e-17,
        -0.037192818417018166, -5.5413873944869916e-18, 1.5488553742289694e-17, -0.03256579847527737,
        0.04125007424481454, -0.026784171570458655, -0.13633723058564884, 0.29242833036787474,
        0.3456578915344953, 3.168424355494231e-17, 3.836962185374445e-17, -0.11489944606001683,
        -8.24839832679589e-18, 2.0886673234268135e-17, -0.08065324692244111, -0.0031903080668092506,
        -0.051912498079153005, -5.583582107057858e-18, 1.1649792309666224e-17, 3.168424355494231e-17,
        0.009463989028394185, -0.06255995072183036, -6.466396650794095e-17, 0.007282792069438679,
        -0.048141551264955944, -4.7974988355199024e-17, -3.5349500353135243e-17, -2.35873011849343e-17,
        -1.0590193910792523e-17, 2.705801727110143e-17, 3.836962185374445e-17, -0.06255995072183036,
        0.4135409944554758, -7.346694430460993e-17, -0.0481415512649561, 0.31823082906924444,
        9.995923750843164e-18, -7.505502803622841e-17, -5.08667820185558e-19, 0.018385539417373895,
        -0.037192818417018166, -0.11489944606001683, -6.466396650794095e-17, -7.346694430460993e-17,
        0.27592507639762276, 1.3010263561082797e-17, -4.580354692366727e-17, 0.16841356959253911,
        0.17511864293952695, 0.08497031761820817, 2.356103444246632e-18, -5.5413873944869916e-18,
        -8.24839832679589e-18, 0.007282792069438679, -0.0481415512649561, 1.3010263561082797e-17,
        0.005604302812223187, -0.03704620818039834, 1.6252313001181433e-18, 1.1115713023921957e-17,
        1.538825092392395e-18, -5.945125693041261e-18, 1.5488553742289694e-17, 2.0886673234268135e-17,
        -0.048141551264955944, 0.31823082906924444, -4.580354692366727e-17, -0.03704620818039834,
        0.24488711379979536, 1.4390406215011793e-17, -5.1922946093876736e-17, 3.1442275524268178e-18,
        0.012680287220793054, -0.03256579847527737, -0.08065324692244111, -4.7974988355199024e-17,
        9.995923750843164e-18, 0.16841356959253911, 1.6252313001181433e-18, 1.4390406215011793e-17,
        0.10317437249077026, 0.10442016260113522, 0.05244160488941618, -0.01806934046678766,
        0.04125007424481454, -0.0031903080668092506, -3.5349500353135243e-17, -7.505502803622841e-17,
        0.17511864293952695, 1.1115713023921957e-17, -5.1922946093876736e-17, 0.10442016260113522,
        0.1274684653198803, 0.05005755429163899, 0.01438140925160449, -0.026784171570458655,
        -0.051912498079153005, -2.35873011849343e-17, -5.08667820185558e-19, 0.08497031761820817,
        1.538825092392395e-18, 3.1442275524268178e-18, 0.05244160488941618, 0.05005755429163899,
        0.027086325034412384]
}

def oh_631g_uhf_db() -> Arr {
    return oh_631g_mat(oh_631g_uhf_db_flat(), 11, 11)
}

# ---- OH_631G ROHF: nalpha 5, nbeta 4; default state is stable ----

OH_631G_E_ROHF = -75.36184838040772
OH_631G_E_ROHF_DEFAULT = -75.36184838040772
OH_631G_E_ROHF_STABLE = -75.36184838040772
# 1: no restart from the stability orbitals lowers the minao state; 0: one does; -1: not analyzed (stability restart).
OH_631G_ROHF_IS_STABLE = 1
OH_631G_ROHF_NALPHA = 5
OH_631G_ROHF_NBETA = 4

# Max |D' - D| after one PySCF step (get_fock, eig, get_occ, make_rdm1) from the default density below.
OH_631G_ROHF_SELF_STEP = 3.166911177743259e-13
#| Converged alpha density, default state.
def oh_631g_rohf_da_flat() -> Arr {
    return [1.0448452141222246, -0.10062760525211643, -0.1366244712311029, -2.3736419592838497e-18,
        3.2818874061681467e-18, 0.017224994433734823, 5.3018879173476456e-18, 9.487520408184736e-18,
        0.00967828943777144, -0.01573700193459719, 0.015517843380324426, -0.10062760525211643,
        0.2792647421510625, 0.2977800292425738, 2.842027553136299e-17, 1.0990913619837238e-17,
        -0.035991530804431654, 6.025959091256412e-18, -9.077305161550778e-18, -0.02675574729986838,
        0.03578265398196669, -0.029818051445978672, -0.1366244712311029, 0.2977800292425738,
        0.33451287388303463, -1.18906969764176e-16, -1.684834595396074e-16, -0.10688517093167585,
        -9.483428992689427e-17, -1.3761493766562046e-16, -0.0690341096572777, -0.0041135574744052055,
        -0.04947776457361132, -2.3736419592838497e-18, 2.842027553136299e-17, -1.18906969764176e-16,
        0.43925640490890255, 0.010016237047605387, -7.099198764182795e-18, 0.3226191281691266,
        -0.0021050136816927714, -1.3023470864720308e-16, 4.2304287713222406e-17, 1.9863856792871097e-16,
        3.2818874061681467e-18, 1.0990913619837238e-17, -1.684834595396074e-16, 0.010016237047605387,
        0.4705573176600847, -1.8812999994447249e-16, -0.0021050136816924163, 0.316040924271041,
        -3.464226693683226e-16, 3.284820022730995e-17, 3.125678813267551e-16, 0.017224994433734823,
        -0.035991530804431654, -0.10688517093167585, -7.099198764182795e-18, -1.8812999994447249e-16,
        0.29443926340663845, -1.999660698158777e-17, -8.276584887112579e-17, 0.17508560246918775,
        0.17484424553402733, 0.0782075020119716, 5.3018879173476456e-18, 6.025959091256412e-18,
        -9.483428992689427e-17, 0.3226191281691266, -0.0021050136816924163, -1.999660698158777e-17,
        0.2371432911263437, -0.007904821425377954, -9.94585266457861e-17, 1.587845025332969e-17,
        1.360197646681159e-16, 9.487520408184736e-18, -9.077305161550778e-18, -1.3761493766562046e-16,
        -0.0021050136816927714, 0.316040924271041, -8.276584887112579e-17, -0.007904821425377954,
        0.21244058844733846, -2.0411069975142041e-16, 4.4868337909954224e-17, 2.184116934813094e-16,
        0.00967828943777144, -0.02675574729986838, -0.0690341096572777, -1.3023470864720308e-16,
        -3.464226693683226e-16, 0.17508560246918775, -9.94585266457861e-17, -2.0411069975142041e-16,
        0.10422343718580836, 0.10286976970992019, 0.04689088785781307, -0.01573700193459719,
        0.03578265398196669, -0.0041135574744052055, 4.2304287713222406e-17, 3.284820022730995e-17,
        0.17484424553402733, 1.587845025332969e-17, 4.4868337909954224e-17, 0.10286976970992019,
        0.11574075533964344, 0.04220880473249042, 0.015517843380324426, -0.029818051445978672,
        -0.04947776457361132, 1.9863856792871097e-16, 3.125678813267551e-16, 0.0782075020119716,
        1.360197646681159e-16, 2.184116934813094e-16, 0.04689088785781307, 0.04220880473249042,
        0.022279597810788962]
}

def oh_631g_rohf_da() -> Arr {
    return oh_631g_mat(oh_631g_rohf_da_flat(), 11, 11)
}

#| Converged beta density, default state.
def oh_631g_rohf_db_flat() -> Arr {
    return [1.0448452141222246, -0.10062760525211643, -0.1366244712311029, -5.8375354567569204e-18,
        -8.556379355167722e-18, 0.017224994433734823, 2.994335464304177e-18, 1.6011862801777358e-18,
        0.00967828943777144, -0.01573700193459719, 0.015517843380324426, -0.10062760525211643,
        0.2792647421510625, 0.2977800292425738, 2.931223702865017e-17, 1.4039297801807403e-17,
        -0.035991530804431654, 6.620159791303011e-18, -7.046553811356065e-18, -0.02675574729986838,
        0.03578265398196669, -0.029818051445978672, -0.1366244712311029, 0.2977800292425738,
        0.33451287388303463, -5.682163449779656e-17, 4.370053554758197e-17, -0.10688517093167585,
        -5.3474713543707904e-17, 3.7363188661376174e-18, -0.0690341096572777, -0.0041135574744052055,
        -0.04947776457361132, -5.8375354567569204e-18, 2.931223702865017e-17, -5.682163449779656e-17,
        0.4019154172182471, -0.11760101612031636, 4.006931020008764e-17, 0.29774356897323995,
        -0.08712018687138035, -2.913816058510498e-17, 2.8847755085942026e-17, 9.722556053970731e-17,
        -8.556379355167722e-18, 1.4039297801807403e-17, 4.370053554758197e-17, -0.11760101612031636,
        0.034410222648963415, -2.6926027518401448e-17, -0.08712018687138043, 0.025491489158532898,
        -9.1322876848662e-19, -1.3141095644683991e-17, -3.402309654717834e-17, 0.017224994433734823,
        -0.035991530804431654, -0.10688517093167585, 4.006931020008764e-17, -2.6926027518401448e-17,
        0.29443926340663845, 1.1425781912963191e-17, 2.4623891108898513e-17, 0.17508560246918775,
        0.17484424553402733, 0.0782075020119716, 2.994335464304177e-18, 6.620159791303011e-18,
        -5.3474713543707904e-17, 0.29774356897323995, -0.08712018687138043, 1.1425781912963191e-17,
        0.2205718642954752, -0.06453963758900744, -3.21107321350413e-17, 6.914071037804538e-18,
        6.84611534862979e-17, 1.6011862801777358e-18, -7.046553811356065e-18, 3.7363188661376174e-18,
        -0.08712018687138035, 0.025491489158532898, 2.4623891108898513e-17, -0.06453963758900744,
        0.018884388693113426, 2.6058373803365613e-17, 1.4231508983031947e-17, -1.2477871044611297e-17,
        0.00967828943777144, -0.02675574729986838, -0.0690341096572777, -2.913816058510498e-17,
        -9.1322876848662e-19, 0.17508560246918775, -3.21107321350413e-17, 2.6058373803365613e-17,
        0.10422343718580836, 0.10286976970992019, 0.04689088785781307, -0.01573700193459719,
        0.03578265398196669, -0.0041135574744052055, 2.8847755085942026e-17, -1.3141095644683991e-17,
        0.17484424553402733, 6.914071037804538e-18, 1.4231508983031947e-17, 0.10286976970992019,
        0.11574075533964344, 0.04220880473249042, 0.015517843380324426, -0.029818051445978672,
        -0.04947776457361132, 9.722556053970731e-17, -3.402309654717834e-17, 0.0782075020119716,
        6.84611534862979e-17, -1.2477871044611297e-17, 0.04689088785781307, 0.04220880473249042,
        0.022279597810788962]
}

def oh_631g_rohf_db() -> Arr {
    return oh_631g_mat(oh_631g_rohf_db_flat(), 11, 11)
}

test "oh_631g packs" {
    assert_near(oh_631g_pack_bad(oh_631g_shells(), OH_631G_NSH, OH_631G_NPRIMTOT, OH_631G_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(OH_631G_NAO_CART - OH_631G_NAO_SPH, 0.0, 0.0)
    assert_near(len(oh_631g_fc()), OH_631G_NAO_CART, 0.0)
}

test "oh_631g unit one-electron integrals are symmetric with a unit overlap diagonal" {
    assert_near(oh_631g_asym(oh_631g_s_unit(), 11), 0.0, 1.0e-14)
    assert_near(oh_631g_asym(oh_631g_t_unit(), 11), 0.0, 1.0e-14)
    assert_near(oh_631g_asym(oh_631g_v_unit(), 11), 0.0, 1.0e-14)
    assert_near(oh_631g_diag_dev(oh_631g_s_unit(), 11), 0.0, 1.0e-14)
}

test "oh_631g unit packed ERIs match their checksums and the Schwarz bound" {
    assert_near(len(oh_631g_eri8_cart()), OH_631G_ERI8_CART_LEN, 0.0)
    assert_near(oh_631g_sumsq(oh_631g_eri8_cart()) / OH_631G_ERI8_CART_SUMSQ, 1.0, 1.0e-12)
    assert_near(oh_631g_wsum(oh_631g_eri8_cart(), OH_631G_SEED_WSUM), OH_631G_ERI8_CART_WSUM, 1.0e-12 * OH_631G_ERI8_CART_SUMSQ)
    assert_lt(oh_631g_schwarz(oh_631g_eri8_cart(), 11), 1.0e-12)
}

test "oh_631g uhf energies, labels and densities" {
    assert_lt(OH_631G_E_UHF_STABLE, OH_631G_E_UHF_DEFAULT + 1.0e-12)
    assert_lt(0.75 - 1.0e-10, OH_631G_UHF_S2)
    assert_lt(0.75 - 1.0e-10, OH_631G_UHF_S2_STABLE)
    assert_lt(OH_631G_UHF_SELF_STEP, 1.0e-10)
    assert_near(oh_631g_asym(oh_631g_uhf_da(), 11) + oh_631g_asym(oh_631g_uhf_db(), 11), 0.0, 1.0e-12)
    assert_near(oh_631g_trace2(oh_631g_uhf_da(), oh_631g_s_unit(), 11) + oh_631g_trace2(oh_631g_uhf_db(), oh_631g_s_unit(), 11), 9.0, 1.0e-10)
    assert_near(oh_631g_e_elec(oh_631g_t_unit() + oh_631g_v_unit(), oh_631g_eri8_cart(), oh_631g_uhf_da(), oh_631g_uhf_db(), 11) + OH_631G_E_NUC, OH_631G_E_UHF_DEFAULT, 1.0e-10)
}

test "oh_631g rohf energies, labels and densities" {
    assert_lt(OH_631G_E_ROHF_STABLE, OH_631G_E_ROHF_DEFAULT + 1.0e-12)
    assert_lt(OH_631G_ROHF_SELF_STEP, 1.0e-10)
    assert_near(oh_631g_asym(oh_631g_rohf_da(), 11) + oh_631g_asym(oh_631g_rohf_db(), 11), 0.0, 1.0e-12)
    assert_near(oh_631g_trace2(oh_631g_rohf_da(), oh_631g_s_unit(), 11) + oh_631g_trace2(oh_631g_rohf_db(), oh_631g_s_unit(), 11), 9.0, 1.0e-10)
    assert_near(oh_631g_e_elec(oh_631g_t_unit() + oh_631g_v_unit(), oh_631g_eri8_cart(), oh_631g_rohf_da(), oh_631g_rohf_db(), 11) + OH_631G_E_NUC, OH_631G_E_ROHF_DEFAULT, 1.0e-10)
}

test "oh_631g E_uhf <= E_rohf" {
    assert_lt(OH_631G_E_UHF_DEFAULT, OH_631G_E_ROHF_DEFAULT + 1.0e-12)
    assert_lt(OH_631G_E_UHF_STABLE, OH_631G_E_ROHF_STABLE + 1.0e-12)
}