###
post: Triplet O2 in STO-3G
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.
O2_STO3G_SEED_WSUM = 20260923

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

#| Reshape a flat row-major vector into r x c.
def o2_sto3g_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 o2_sto3g_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 o2_sto3g_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 o2_sto3g_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 o2_sto3g_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 o2_sto3g_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 o2_sto3g_e_elec(h: Arr, g: Arr, da: Arr, db: Arr, n) {
    pr = o2_sto3g_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 o2_sto3g_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 o2_sto3g_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 o2_sto3g_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 o2_sto3g_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 o2_sto3g_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 o2_sto3g_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
}

# ======== O2_STO3G: sto-3g, s and p only, so Cartesian = spherical ========

O2_STO3G_NATOM = 2
O2_STO3G_NSH = 6
O2_STO3G_NPRIMTOT = 18
O2_STO3G_NAO_CART = 10
O2_STO3G_NAO_SPH = 10
O2_STO3G_E_NUC = 28.047487783751553

#| (Z, x, y, z) in Bohr, one atom per row.
def o2_sto3g_atoms_flat() -> Arr {
    return [8.0, 0.0, 0.0, 0.0,
        8.0, 0.0, 0.0, 2.2818442954123124]
}

def o2_sto3g_atoms() -> Arr {
    return o2_sto3g_mat(o2_sto3g_atoms_flat(), 2, 4)
}

#| (atom, l, nprim, p0, cart0, sph0, ncart, nsph); general contractions split.
def o2_sto3g_shells_flat() -> Arr {
    return [0, 0, 3, 0,
        0, 0, 1, 1,
        0, 0, 3, 3,
        1, 1, 1, 1,
        0, 1, 3, 6,
        2, 2, 3, 3,
        1, 0, 3, 9,
        5, 5, 1, 1,
        1, 0, 3, 12,
        6, 6, 1, 1,
        1, 1, 3, 15,
        7, 7, 3, 3]
}

def o2_sto3g_shells() -> Arr {
    return o2_sto3g_mat(o2_sto3g_shells_flat(), 6, 8)
}

#| (exponent, raw bas_ctr_coeff).
def o2_sto3g_prims_flat() -> Arr {
    return [130.70932, 0.15432896872315646, 23.808861, 0.5353281355709528,
        6.4436083, 0.4446345363213081, 5.0331513, -0.09996722865667348,
        1.1695961, 0.3995128246314789, 0.380389, 0.7001154605920802,
        5.0331513, 0.15591626847815623, 1.1695961, 0.6076837140686134,
        0.380389, 0.3919573861742421, 130.70932, 0.15432896872315646,
        23.808861, 0.5353281355709528, 6.4436083, 0.4446345363213081,
        5.0331513, -0.09996722865667348, 1.1695961, 0.3995128246314789,
        0.380389, 0.7001154605920802, 5.0331513, 0.15591626847815623,
        1.1695961, 0.6076837140686134, 0.380389, 0.3919573861742421]
}

def o2_sto3g_prims() -> Arr {
    return o2_sto3g_mat(o2_sto3g_prims_flat(), 18, 2)
}

#| F per Cartesian AO: PySCF-Cartesian = F x unit-Cartesian.
def o2_sto3g_fc() -> Arr {
    return [1.0, 1.0, 1.0, 1.0,
        1.0, 1.0, 1.0, 1.0,
        1.0, 1.0]
}

#| Overlap, unit-Cartesian, [10,10].
def o2_sto3g_s_unit_flat() -> Arr {
    return [1.0, 0.2367039365108476, 0.0, 0.0,
        0.0, 1.0247615616525904e-08, 0.022877431137186738, 0.0,
        0.0, -0.03863378448130246, 0.23670393651084762, 1.0,
        0.0, 0.0, 0.0, 0.022877431137186745,
        0.281375699578693, 0.0, 0.0, -0.32186646871691293,
        0.0, 0.0, 1.0, 0.0,
        0.0, 0.0, 0.0, 0.1524445711461619,
        0.0, -0.0, 0.0, 0.0,
        0.0, 1.0, 0.0, 0.0,
        0.0, 0.0, 0.1524445711461619, -0.0,
        0.0, 0.0, 0.0, 0.0,
        1.0, 0.038633784481302454, 0.32186646871691305, 0.0,
        0.0, -0.3077433559186039, 1.0247615616525904e-08, 0.022877431137186738,
        0.0, 0.0, 0.03863378448130246, 1.0,
        0.2367039365108476, 0.0, 0.0, 0.0,
        0.022877431137186745, 0.281375699578693, 0.0, 0.0,
        0.32186646871691293, 0.23670393651084762, 1.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.1524445711461619, 0.0, 0.0, 0.0,
        0.0, 1.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.1524445711461619,
        0.0, 0.0, 0.0, 0.0,
        1.0, 0.0, -0.038633784481302454, -0.32186646871691305,
        -0.0, -0.0, -0.3077433559186039, 0.0,
        0.0, 0.0, 0.0, 1.0]
}

def o2_sto3g_s_unit() -> Arr {
    return o2_sto3g_mat(o2_sto3g_s_unit_flat(), 10, 10)
}

#| Kinetic energy, unit-Cartesian.
def o2_sto3g_t_unit_flat() -> Arr {
    return [29.003199945539567, -0.16801093931649205, 0.0, 0.0,
        0.0, -1.008840521182081e-06, -0.012752970541868486, 0.0,
        0.0, 0.016448766549774247, -0.16801093931649186, 0.8081279549303472,
        0.0, 0.0, 0.0, -0.012752970541868573,
        0.026424633031478358, 0.0, 0.0, -0.15405872417129599,
        0.0, 0.0, 2.5287311981947633, 0.0,
        0.0, 0.0, 0.0, 0.06225043977523005,
        0.0, 0.0, 0.0, 0.0,
        0.0, 2.5287311981947633, 0.0, 0.0,
        0.0, 0.0, 0.06225043977523005, 0.0,
        0.0, 0.0, 0.0, 0.0,
        2.5287311981947633, -0.016448766549774292, 0.15405872417129607, 0.0,
        0.0, -0.3511390437465514, -1.008840521182081e-06, -0.012752970541868486,
        0.0, 0.0, -0.016448766549774247, 29.003199945539567,
        -0.16801093931649205, 0.0, 0.0, 0.0,
        -0.012752970541868573, 0.026424633031478358, 0.0, 0.0,
        0.15405872417129599, -0.16801093931649186, 0.8081279549303472, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.06225043977523005, 0.0, 0.0, 0.0,
        0.0, 2.5287311981947633, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.06225043977523005,
        0.0, 0.0, 0.0, 0.0,
        2.5287311981947633, 0.0, 0.016448766549774292, -0.15405872417129607,
        0.0, 0.0, -0.3511390437465514, 0.0,
        0.0, 0.0, 0.0, 2.5287311981947633]
}

def o2_sto3g_t_unit() -> Arr {
    return o2_sto3g_mat(o2_sto3g_t_unit_flat(), 10, 10)
}

#| Nuclear attraction, unit-Cartesian.
def o2_sto3g_v_unit_flat() -> Arr {
    return [-64.12439087839158, -8.012948290650858, 0.0, 0.0,
        -0.07803917797405678, -1.4371824866976437e-07, -0.7890920928499656, 0.0,
        0.0, 1.33634156141574, -8.01294829065086, -12.549371684899533,
        0.0, 0.0, -0.9683735404976579, -0.7890920928499657,
        -3.482154002196574, 0.0, 0.0, 4.084999678404042,
        0.0, 0.0, -12.285966022059881, 0.0,
        0.0, 0.0, 0.0, -1.5896046981905454,
        0.0, 0.0, 0.0, 0.0,
        0.0, -12.285966022059881, 0.0, 0.0,
        0.0, 0.0, -1.5896046981905454, 0.0,
        -0.07803917797405678, -0.968373540497658, 0.0, 0.0,
        -12.85193776984558, -1.3363415614157397, -4.084999678404043, 0.0,
        0.0, 4.059711271087343, -1.4371824866976437e-07, -0.7890920928499656,
        0.0, 0.0, -1.3363415614157397, -64.12439087839158,
        -8.012948290650858, 0.0, 0.0, 0.07803917797405678,
        -0.7890920928499658, -3.482154002196573, 0.0, 0.0,
        -4.084999678404042, -8.01294829065086, -12.549371684899533, 0.0,
        0.0, 0.9683735404976579, 0.0, 0.0,
        -1.5896046981905452, 0.0, 0.0, 0.0,
        0.0, -12.285966022059881, 0.0, 0.0,
        0.0, 0.0, 0.0, -1.5896046981905452,
        0.0, 0.0, 0.0, 0.0,
        -12.285966022059881, 0.0, 1.33634156141574, 4.084999678404043,
        0.0, 0.0, 4.059711271087343, 0.07803917797405678,
        0.968373540497658, 0.0, 0.0, -12.851937769845582]
}

def o2_sto3g_v_unit() -> Arr {
    return o2_sto3g_mat(o2_sto3g_v_unit_flat(), 10, 10)
}

# Packed-8 length n(n+1)/2 (n(n+1)/2 + 1)/2 for n = 10.
O2_STO3G_ERI8_CART_LEN = 1540
# sum of Gp^2 (math.fsum).
O2_STO3G_ERI8_CART_SUMSQ = 78.53865152669667
# sum of w_k Gp_k with the LCG weights from O2_STO3G_SEED_WSUM (math.fsum).
O2_STO3G_ERI8_CART_WSUM = 23.26880704310067
#| Every packed-8 two-electron integral, unit-Cartesian, chemist's notation.
def o2_sto3g_eri8_cart() -> Arr {
    return [4.785065404705503, 0.7413803519734079, 0.13687338535438834, 1.1189468663424704,
        0.2566333947309737, 0.8172063215260582, 0.0, 0.0,
        0.0, 0.024477412258099275, 0.0, 0.0,
        0.0, 0.03780860741636099, 0.18051839210463208, 1.1158138121524277,
        0.25668398581010293, 0.8170226053209142, 0.0, 0.0,
        0.8801590933750454, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.024477412258099275,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.03780860741636099, 0.18051839210463208,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.04744444511838415, 1.1158138121524277, 0.25668398581010293, 0.8170226053209142,
        0.0, 0.0, 0.7852702031382774, 0.0,
        0.0, 0.0, 0.8801590933750454, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.024477412258099275, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.03780860741636099, 0.18051839210463208, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.04744444511838415, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.04744444511838415, 1.1158138121524277, 0.25668398581010293, 0.8170226053209142,
        0.0, 0.0, 0.7852702031382774, 0.0,
        0.0, 0.0, 0.7852702031382774, 0.0,
        0.0, 0.0, 0.0, 0.8801590933750452,
        8.982296684046789e-09, 2.1251946703990763e-09, 7.963521445078962e-09, 0.0,
        0.0, 7.178267183884637e-09, 0.0, 0.0,
        0.0, 7.178267183884637e-09, 3.9833011559406887e-10, 3.1571796061776792e-09,
        0.0, 0.0, 9.525210618162417e-09, 3.0075812702693e-16,
        0.010512431975718668, 0.0024883340033583744, 0.010456469255556917, 0.0,
        0.0, 0.009854068344269919, 0.0, 0.0,
        0.0, 0.009854068344269919, 0.0002455580592701909, 0.002996407898217846,
        0.0, 0.0, 0.011640741945257889, 2.2643473448968262e-10,
        0.0013095292206310846, 0.0, 0.0, 0.0,
        5.275822262119284e-06, 6.386919571154058e-05, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 3.8584011388333116e-05, 0.0, 0.0,
        0.0, 0.0, 5.824067238665696e-06, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 5.275822262119284e-06, 6.386919571154058e-05, 0.0,
        0.0, 0.0, 0.0, 0.0,
        3.8584011388333116e-05, 0.0, 0.0, 0.0,
        0.0, 5.824067238665696e-06, 0.01770265117402676, 0.004190287173592214,
        0.017609524143899477, 0.0, 0.0, 0.016598393466785117,
        0.0, 0.0, 0.0, 0.016598393466785117,
        0.00041257703775126323, 0.005036012527864472, 0.0, 0.0,
        0.019597475606818994, 3.806445465061332e-10, 0.0022116444940016976, 0.0,
        0.0, 0.003735763528714212, 0.438241996621118, 0.10373360574449768,
        0.4370503148792493, 0.0, 0.0, 0.41331294148136133,
        0.0, 0.0, 0.0, 0.41331294148136133,
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        0.0, 0.0, 0.0, 0.0,
        0.0, -0.01691508417412056, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.00503601252786447,
        0.06064160639326516, 0.0, 0.0, 0.07855534717719244,
        0.03780860741636099, 0.18051839210463208, -0.0, 0.0,
        0.0, -0.00154753622766398, -0.015524147572074935, -0.0,
        -0.0, 0.0, -0.0, -0.0,
        0.0, 0.0, -0.00881761918596925, 0.0,
        -0.0, -0.0, 0.0, -0.00010205193342560081,
        -0.0, -0.0, 0.0, 0.0,
        0.0, -0.006866252667141351, 0.0, 0.0,
        0.0, 0.0, -3.858401138833311e-05, -0.007752093575828631,
        -0.0, -0.0, -0.009999122854794266, 0.0,
        0.0, 0.0, -0.0, 0.0,
        -0.0, -0.0, -0.0, 0.0,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.009357175087798864, 0.0, 0.0,
        0.0, 0.0, 0.04744444511838415, -0.0,
        0.0, 0.0, -0.0, 0.0,
        -0.0, -0.00154753622766398, -0.015524147572074935, -0.0,
        -0.0, 0.0, 0.0, 0.0,
        -0.00881761918596925, -0.0, -0.0, 0.0,
        -0.0, -0.00010205193342560081, -0.0, 0.0,
        0.0, 0.0, 0.0, -0.006866252667141351,
        0.0, 0.0, 0.0, -0.0,
        0.0, -0.0, -0.0, -0.0,
        0.0, 0.0, 0.0, -3.858401138833311e-05,
        -0.007752093575828631, -0.0, -0.0, -0.009999122854794266,
        0.0, 0.0, 0.0, 0.0,
        0.0, 0.0, 0.0, 0.009357175087798864,
        0.0, 0.0, 0.0, 0.0,
        0.04744444511838415, 0.4836838177310513, 0.11424680223171496, 0.46250614215690977,
        0.0, 0.0, 0.4405833876207908, 0.0,
        0.0, 0.0, 0.4405833876207908, 0.01206292389180109,
        0.12506503536312094, 0.0, 0.0, 0.5059304780593662,
        9.525210618162421e-09, 0.02491677718027305, 0.0, 0.0,
        0.04210433613722276, 1.1158138121524277, 0.011640741945257892, 0.19163644338355962,
        0.0, 0.0, 0.24948394469679372, 0.25668398581010293,
        0.8170226053209142, 0.0, 0.0, 0.09175015370376059,
        0.0, 0.0, 0.0, 0.0,
        0.7852702031382774, 0.0, 0.0, 0.0,
        0.09175015370376059, 0.0, 0.0, 0.0,
        0.0, 0.7852702031382774, -0.01959747560681899, -0.21050726049625082,
        -0.0, -0.0, -0.24280593553364155, 0.0,
        0.0, 0.0, 0.0, 0.8801590933750452]
}

def o2_sto3g_s_sph() -> Arr {
    return o2_sto3g_s_unit()
}

def o2_sto3g_t_sph() -> Arr {
    return o2_sto3g_t_unit()
}

def o2_sto3g_v_sph() -> Arr {
    return o2_sto3g_v_unit()
}

#| Only s and p: the spherical and Cartesian sets are the same.
def o2_sto3g_eri8_sph() -> Arr {
    return o2_sto3g_eri8_cart()
}

def o2_sto3g_m() -> Arr {
    return o2_sto3g_eye(10)
}

# ---- O2_STO3G UHF: nalpha 9, nbeta 7; default state is not the lowest ----

O2_STO3G_E_UHF = -147.63394678545012
O2_STO3G_E_UHF_DEFAULT = -147.63394678545012
O2_STO3G_E_UHF_STABLE = -147.63522998065827
# 1: no restart from the stability orbitals lowers the minao state; 0: one does; -1: not analyzed (stability restart).
O2_STO3G_UHF_IS_STABLE = 0
O2_STO3G_UHF_NALPHA = 9
O2_STO3G_UHF_NBETA = 7
# <S^2> of the default UHF state.
O2_STO3G_UHF_S2 = 2.003410857663093
O2_STO3G_UHF_S2_STABLE = 2.0033260307261678
# Third state: the 1e guess converges here, to neither the default nor the stable state.
O2_STO3G_E_UHF_GUESS_1E = -147.37855914166403
# Third state: the huckel guess converges here, to neither the default nor the stable state.
O2_STO3G_E_UHF_GUESS_HUCKEL = -147.37855914166408

# Max |D' - D| after one PySCF step (get_fock, eig, get_occ, make_rdm1) from the default density below.
O2_STO3G_UHF_SELF_STEP = 2.930988785010413e-14
#| Converged alpha density, default state.
def o2_sto3g_uhf_da_flat() -> Arr {
    return [1.0574383291046487, -0.2446094311717191, 7.384482685017463e-18, -7.93079446100955e-17,
        0.04044229518490332, -0.0012920649599237112, 0.02490985857937973, -3.53633717138957e-18,
        1.3569761450107609e-17, 0.017570071576318187, -0.2446094311717191, 1.0668648980998967,
        -1.0251061205277089e-16, 4.461503435221409e-16, -0.20898933768961556, 0.02490985857937993,
        -0.189324726676692, 2.6391164749295073e-17, -8.457296008402744e-17, 0.0005035486287530226,
        7.384482685017463e-18, -1.0251061205277089e-16, 1.0237922639564054, 3.144592613369e-17,
        -1.565439540949725e-16, -1.2425257701134895e-17, 9.115668741197045e-17, -0.15607157262159227,
        4.145837289316397e-17, -3.3813840657587114e-16, -7.93079446100955e-17, 4.461503435221409e-16,
        3.144592613369e-17, 1.0237922639564052, 4.544142973177122e-16, -3.110977852352201e-16,
        -9.592231896892879e-17, -2.3506290951238854e-16, -0.15607157262159194, 7.692689203203522e-16,
        0.04044229518490332, -0.20898933768961556, -1.565439540949725e-16, 4.544142973177122e-16,
        0.42516971075778903, -0.01757007157631872, -0.000503548628749181, -1.1788731431418456e-17,
        -7.481470447727839e-17, -0.39039176019605915, -0.0012920649599237112, 0.02490985857937993,
        -1.2425257701134895e-17, -3.110977852352201e-16, -0.01757007157631872, 1.0574383291046485,
        -0.2446094311717188, 5.61419651887231e-18, 5.354739145399556e-17, -0.040442295184902895,
        0.02490985857937973, -0.189324726676692, 9.115668741197045e-17, -9.592231896892879e-17,
        -0.000503548628749181, -0.2446094311717188, 1.0668648980998954, -1.1147270349376428e-17,
        -2.7070783258870216e-17, 0.20898933768961406, -3.53633717138957e-18, 2.6391164749295073e-17,
        -0.15607157262159227, -2.3506290951238854e-16, -1.1788731431418456e-17, 5.61419651887231e-18,
        -1.1147270349376428e-17, 1.0237922639564054, -1.0151935786294583e-16, 6.81313954053761e-17,
        1.3569761450107609e-17, -8.457296008402744e-17, 4.145837289316397e-17, -0.15607157262159194,
        -7.481470447727839e-17, 5.354739145399556e-17, -2.7070783258870216e-17, -1.0151935786294583e-16,
        1.0237922639564057, -2.061253523559347e-16, 0.017570071576318187, 0.0005035486287530226,
        -3.3813840657587114e-16, 7.692689203203522e-16, -0.39039176019605915, -0.040442295184902895,
        0.20898933768961406, 6.81313954053761e-17, -2.061253523559347e-16, 0.42516971075779747]
}

def o2_sto3g_uhf_da() -> Arr {
    return o2_sto3g_mat(o2_sto3g_uhf_da_flat(), 10, 10)
}

#| Converged beta density, default state.
def o2_sto3g_uhf_db_flat() -> Arr {
    return [1.0555177530432047, -0.23440107397806106, -2.0069997172498654e-17, -5.937626857795036e-17,
        0.049141426255865234, 0.0006285111015209445, 0.014701501385721733, -2.9762079299491693e-18,
        -1.4425154020216136e-17, 0.02626920264728045, -0.23440107397806106, 1.013982675870279,
        4.653083172714946e-17, 7.901393547944442e-18, -0.24636694942204096, 0.01470150138572163,
        -0.13644250444707465, 4.677806631433176e-19, 1.2290291292170976e-16, -0.03687406310367413,
        -2.0069997172498654e-17, 4.653083172714946e-17, 0.43386034566741793, 2.16307596111405e-15,
        -2.9182387307432146e-17, -3.9861834708392363e-17, 1.2770127789696233e-16, 0.4338603456674065,
        1.7242973091775843e-16, -3.1720915917342967e-17, -5.937626857795036e-17, 7.901393547944442e-18,
        2.16307596111405e-15, 0.4338603456674008, 4.570640990308066e-16, 4.4245061584278465e-17,
        -3.917769833941099e-16, -1.4245118388504462e-16, 0.43386034566740633, -1.7936429483782157e-16,
        0.049141426255865234, -0.24636694942204096, -2.9182387307432146e-17, 4.570640990308066e-16,
        0.44274751564676507, -0.026269202647280793, 0.03687406310367613, -1.514750511024457e-18,
        -1.343058080165291e-16, -0.37281395530708533, 0.0006285111015209445, 0.01470150138572163,
        -3.9861834708392363e-17, 4.4245061584278465e-17, -0.026269202647280793, 1.055517753043204,
        -0.23440107397806093, 1.1750234190552978e-17, 6.912471818212215e-17, -0.04914142625586515,
        0.014701501385721733, -0.13644250444707465, 1.2770127789696233e-16, -3.917769833941099e-16,
        0.03687406310367613, -0.23440107397806093, 1.0139826758702781, -3.6645574570217174e-17,
        2.705448633066784e-16, 0.2463669494220407, -2.9762079299491693e-18, 4.677806631433176e-19,
        0.4338603456674065, -1.4245118388504462e-16, -1.514750511024457e-18, 1.1750234190552978e-17,
        -3.6645574570217174e-17, 0.43386034566739506, -2.1330974140813675e-15, -8.863595753851445e-17,
        -1.4425154020216136e-17, 1.2290291292170976e-16, 1.7242973091775843e-16, 0.43386034566740633,
        -1.343058080165291e-16, 6.912471818212215e-17, 2.705448633066784e-16, -2.1330974140813675e-15,
        0.43386034566741194, 5.45374147118791e-16, 0.02626920264728045, -0.03687406310367413,
        -3.1720915917342967e-17, -1.7936429483782157e-16, -0.37281395530708533, -0.04914142625586515,
        0.2463669494220407, -8.863595753851445e-17, 5.45374147118791e-16, 0.4427475156467688]
}

def o2_sto3g_uhf_db() -> Arr {
    return o2_sto3g_mat(o2_sto3g_uhf_db_flat(), 10, 10)
}

# Max |D' - D| after one PySCF step (get_fock, eig, get_occ, make_rdm1) from the stable density below.
O2_STO3G_UHF_STABLE_SELF_STEP = 8.199996237578944e-12
#| Converged alpha density, stable state.
def o2_sto3g_uhf_stable_da_flat() -> Arr {
    return [1.057458589736728, -0.24471875448423644, -7.719273462677485e-18, -6.033570127421154e-17,
        0.04034251662279284, -0.001312325592002284, 0.02501918189189693, -3.2667990587051222e-18,
        8.549926533450605e-18, 0.01747029301420789, -0.24471875448423644, 1.0674396867806968,
        -6.62763034879634e-18, 3.2241802690764965e-16, -0.2085502277967773, 0.025019181891896565,
        -0.18989951535749136, 1.5365053695098705e-17, -5.286517019202155e-17, 0.000942658521589975,
        -7.719273462677485e-18, -6.62763034879634e-18, 1.0237922639564054, -8.610544451198115e-18,
        -5.352333641390646e-17, -6.097439986732738e-17, 8.6898136077352e-17, -0.15607157262159274,
        -7.747376197834841e-17, 1.1861060329591887e-18, -6.033570127421154e-17, 3.2241802690764965e-16,
        -8.610544451198115e-18, 1.023792263956406, 8.443977125570072e-16, -9.132390892720048e-17,
        -4.2113328013791567e-16, -2.579966442702646e-16, -0.15607157262159246, 2.9232039048194556e-16,
        0.04034251662279284, -0.2085502277967773, -5.352333641390646e-17, 8.443977125570072e-16,
        0.42500849100140864, -0.017470293014208327, -0.0009426585215872002, 2.6847202462571526e-17,
        -1.3716268527006527e-18, -0.39055297995244254, -0.001312325592002284, 0.025019181891896565,
        -6.097439986732738e-17, -9.132390892720048e-17, -0.017470293014208327, 1.0574585897367272,
        -0.24471875448423577, -9.905992382519508e-18, 5.602414686933396e-17, -0.040342516622793104,
        0.02501918189189693, -0.18989951535749136, 8.6898136077352e-17, -4.2113328013791567e-16,
        -0.0009426585215872002, -0.24471875448423577, 1.0674396867806946, -1.1904570479871285e-17,
        -2.643556827659904e-17, 0.2085502277967779, -3.2667990587051222e-18, 1.5365053695098705e-17,
        -0.15607157262159274, -2.579966442702646e-16, 2.6847202462571526e-17, -9.905992382519508e-18,
        -1.1904570479871285e-17, 1.023792263956405, 3.907234493542348e-16, 8.981001342963141e-18,
        8.549926533450605e-18, -5.286517019202155e-17, -7.747376197834841e-17, -0.15607157262159246,
        -1.3716268527006527e-18, 5.602414686933396e-17, -2.643556827659904e-17, 3.907234493542348e-16,
        1.0237922639564057, -1.3160081732775455e-16, 0.01747029301420789, 0.000942658521589975,
        1.1861060329591887e-18, 2.9232039048194556e-16, -0.39055297995244254, -0.040342516622793104,
        0.2085502277967779, 8.981001342963141e-18, -1.3160081732775455e-16, 0.4250084910014119]
}

def o2_sto3g_uhf_stable_da() -> Arr {
    return o2_sto3g_mat(o2_sto3g_uhf_stable_da_flat(), 10, 10)
}

#| Converged beta density, stable state.
def o2_sto3g_uhf_stable_db_flat() -> Arr {
    return [1.055564498211108, -0.23464737265259034, 2.2487785931784675e-18, 3.288862438220146e-17,
        0.04894648607019514, 0.0005817659336175883, 0.014947800060250751, -4.2942190723322894e-18,
        -4.460942615946884e-18, 0.02607426246161028, -0.23464737265259034, 1.01524981781057,
        -2.1917035752958913e-17, 9.721724407379059e-18, -0.2455389105959535, 0.01494780006025049,
        -0.13770964638736405, 2.051362770083772e-18, -1.1810397421902974e-18, -0.0360460242775864,
        2.2487785931784675e-18, -2.1917035752958913e-17, 0.23663886884772453, -0.013742424612772423,
        4.372543835830517e-18, 8.872075414296766e-17, -7.674153512225659e-17, 0.3902511707311523,
        -1.4608022754398986e-17, -1.3305215707947565e-16, 3.288862438220146e-17, 9.721724407379059e-18,
        -0.013742424612772423, 0.6443777864294815, -2.6983155019836357e-16, -2.1716794648579038e-17,
        2.1999831942082346e-16, -8.177133704530074e-17, 0.3902511707311517, 5.563984322261563e-17,
        0.04894648607019514, -0.2455389105959535, 4.372543835830517e-18, -2.6983155019836357e-16,
        0.4422649771556384, -0.026074262461611278, 0.03604602427759043, -1.0934908795526617e-16,
        2.1726573056454774e-17, -0.3732964937982121, 0.0005817659336175883, 0.01494780006025049,
        8.872075414296766e-17, -2.1716794648579038e-17, -0.026074262461611278, 1.0555644982111076,
        -0.23464737265258942, 1.0158445694919274e-16, -4.415989448492132e-17, -0.048946486070195694,
        0.014947800060250751, -0.13770964638736405, -7.674153512225659e-17, 2.1999831942082346e-16,
        0.03604602427759043, -0.23464737265258942, 1.0152498178105667, -1.4296206173145003e-17,
        -1.1745081786288846e-16, 0.245538910595955, -4.2942190723322894e-18, 2.051362770083772e-18,
        0.3902511707311523, -8.177133704530074e-17, -1.0934908795526617e-16, 1.0158445694919274e-16,
        -1.4296206173145003e-17, 0.6443777864294797, 0.0137424246127723, -9.407143077273414e-17,
        -4.460942615946884e-18, -1.1810397421902974e-18, -1.4608022754398986e-17, 0.3902511707311517,
        2.1726573056454774e-17, -4.415989448492132e-17, -1.1745081786288846e-16, 0.0137424246127723,
        0.2366388688477231, -2.1433322860402078e-16, 0.02607426246161028, -0.0360460242775864,
        -1.3305215707947565e-16, 5.563984322261563e-17, -0.3732964937982121, -0.048946486070195694,
        0.245538910595955, -9.407143077273414e-17, -2.1433322860402078e-16, 0.44226497715564234]
}

def o2_sto3g_uhf_stable_db() -> Arr {
    return o2_sto3g_mat(o2_sto3g_uhf_stable_db_flat(), 10, 10)
}

# ---- O2_STO3G ROHF: nalpha 9, nbeta 7; default state is not the lowest ----

O2_STO3G_E_ROHF = -147.6321669906825
O2_STO3G_E_ROHF_DEFAULT = -147.6321669906825
O2_STO3G_E_ROHF_STABLE = -147.6334958793004
# 1: no restart from the stability orbitals lowers the minao state; 0: one does; -1: not analyzed (stability restart).
O2_STO3G_ROHF_IS_STABLE = 0
O2_STO3G_ROHF_NALPHA = 9
O2_STO3G_ROHF_NBETA = 7

# Max |D' - D| after one PySCF step (get_fock, eig, get_occ, make_rdm1) from the default density below.
O2_STO3G_ROHF_SELF_STEP = 8.43769498715119e-15
#| Converged alpha density, default state.
def o2_sto3g_rohf_da_flat() -> Arr {
    return [1.056534296761317, -0.2397778838981144, -3.685762961130444e-17, 8.00208388566134e-17,
        0.0447189546153502, -0.0003880326165918496, 0.0200783113057755, 5.982781723432352e-18,
        -1.70052803188619e-17, 0.021846731006765797, -0.2397778838981144, 1.0417213348769006,
        2.1528769763707754e-16, -2.5519913777519077e-16, -0.22749339655306264, 0.02007831130577545,
        -0.164181163453698, -4.4304222436183326e-17, 1.0625324865198919e-16, -0.018000510234698338,
        -3.685762961130444e-17, 2.1528769763707754e-16, 1.0237922639564057, -7.156594029274939e-17,
        3.0953666514030626e-16, 8.29225893019571e-17, -2.6932299946084203e-16, -0.15607157262159269,
        9.20881110028124e-17, 2.7167930998202416e-16, 8.00208388566134e-17, -2.5519913777519077e-16,
        -7.156594029274939e-17, 1.0237922639564063, -3.7448748797105e-16, -2.783146073470999e-16,
        4.3046661365405897e-16, 5.703238101048498e-17, -0.15607157262159277, -3.2320368178095164e-16,
        0.0447189546153502, -0.22749339655306264, 3.0953666514030626e-16, -3.7448748797105e-16,
        0.4328624603811517, -0.021846731006765034, 0.01800051023469604, -1.0328482846238827e-16,
        2.5704435778971073e-16, -0.38269901057270467, -0.0003880326165918496, 0.02007831130577545,
        8.29225893019571e-17, -2.783146073470999e-16, -0.021846731006765034, 1.056534296761317,
        -0.23977788389811444, -3.4355220727908714e-17, -1.481737538999388e-16, -0.04471895461535049,
        0.0200783113057755, -0.164181163453698, -2.6932299946084203e-16, 4.3046661365405897e-16,
        0.01800051023469604, -0.23977788389811444, 1.0417213348769014, 6.187689436251909e-17,
        -1.0815669442221177e-16, 0.2274933965530645, 5.982781723432352e-18, -4.4304222436183326e-17,
        -0.15607157262159269, 5.703238101048498e-17, -1.0328482846238827e-16, -3.4355220727908714e-17,
        6.187689436251909e-17, 1.0237922639564057, -1.7990323680318216e-16, -9.07451951152316e-17,
        -1.70052803188619e-17, 1.0625324865198919e-16, 9.20881110028124e-17, -0.15607157262159277,
        2.5704435778971073e-16, -1.481737538999388e-16, -1.0815669442221177e-16, -1.7990323680318216e-16,
        1.0237922639564059, 1.790277699750579e-16, 0.021846731006765797, -0.018000510234698338,
        2.7167930998202416e-16, -3.2320368178095164e-16, -0.38269901057270467, -0.04471895461535049,
        0.2274933965530645, -9.07451951152316e-17, 1.790277699750579e-16, 0.43286246038114506]
}

def o2_sto3g_rohf_da() -> Arr {
    return o2_sto3g_mat(o2_sto3g_rohf_da_flat(), 10, 10)
}

#| Converged beta density, default state.
def o2_sto3g_rohf_db_flat() -> Arr {
    return [1.056534296761317, -0.2397778838981144, 1.3427672125125057e-17, -2.4407173738426427e-17,
        0.0447189546153502, -0.0003880326165918496, 0.0200783113057755, -4.4302520012997373e-17,
        8.742273227617911e-17, 0.021846731006765797, -0.2397778838981144, 1.0417213348769006,
        -6.907194129481614e-17, 2.97097900007445e-16, -0.22749339655306264, 0.02007831130577545,
        -0.164181163453698, 2.400554164957116e-16, -4.460437891306528e-16, -0.018000510234698338,
        1.3427672125125057e-17, -6.907194129481614e-17, 0.43386034566740855, -2.535285350927399e-16,
        3.79187642918364e-16, 4.2903269396066945e-17, -1.132585237755481e-16, 0.4338603456674065,
        -1.9275786425472084e-17, -1.5635705523911888e-16, -2.4407173738426427e-17, 2.97097900007445e-16,
        -2.535285350927399e-16, 0.4338603456674134, -3.949683750226121e-16, -2.5138995770269144e-16,
        -3.4074947630121266e-16, -3.1666511630603106e-17, 0.43386034566740667, 8.866653543969614e-17,
        0.0447189546153502, -0.22749339655306264, 3.79187642918364e-16, -3.949683750226121e-16,
        0.4328624603811517, -0.021846731006765034, 0.01800051023469604, -1.7293580624044627e-16,
        2.7752524484127306e-16, -0.38269901057270467, -0.0003880326165918496, 0.02007831130577545,
        4.2903269396066945e-17, -2.5138995770269144e-16, -0.021846731006765034, 1.056534296761317,
        -0.23977788389811444, 5.664099177981604e-18, -1.750984035443476e-16, -0.04471895461535049,
        0.0200783113057755, -0.164181163453698, -1.132585237755481e-16, -3.4074947630121266e-16,
        0.01800051023469604, -0.23977788389811444, 1.0417213348769014, -9.418758132277576e-17,
        6.630593955330684e-16, 0.2274933965530645, -4.4302520012997373e-17, 2.400554164957116e-16,
        0.4338603456674065, -3.1666511630603106e-17, -1.7293580624044627e-16, 5.664099177981604e-18,
        -9.418758132277576e-17, 0.43386034566740445, 2.0085151356068553e-16, 3.372911701059132e-16,
        8.742273227617911e-17, -4.460437891306528e-16, -1.9275786425472084e-17, 0.43386034566740667,
        2.7752524484127306e-16, -1.750984035443476e-16, 6.630593955330684e-16, 2.0085151356068553e-16,
        0.43386034566739995, -2.3284244724559463e-16, 0.021846731006765797, -0.018000510234698338,
        -1.5635705523911888e-16, 8.866653543969614e-17, -0.38269901057270467, -0.04471895461535049,
        0.2274933965530645, 3.372911701059132e-16, -2.3284244724559463e-16, 0.43286246038114506]
}

def o2_sto3g_rohf_db() -> Arr {
    return o2_sto3g_mat(o2_sto3g_rohf_db_flat(), 10, 10)
}

# Max |D' - D| after one PySCF step (get_fock, eig, get_occ, make_rdm1) from the stable density below.
O2_STO3G_ROHF_STABLE_SELF_STEP = 3.409994508984937e-12
#| Converged alpha density, stable state.
def o2_sto3g_rohf_stable_da_flat() -> Arr {
    return [1.056566973703979, -0.23995204723362532, 9.602117796808998e-18, 4.4761136056008063e-17,
        0.04457031283561652, -0.0004207095592540944, 0.020252474641285614, -1.914209509086782e-18,
        2.3211796204239686e-18, 0.021698089227032247, -0.23995204723362532, 1.0426266887586955,
        -9.736259663875581e-17, 1.3571149006174012e-16, -0.22685057396405275, 0.020252474641285406,
        -0.1650865173354893, 1.9756944574058873e-17, -1.0262327190008962e-17, -0.01735768764568897,
        9.602117796808998e-18, -9.736259663875581e-17, 1.0237922639564063, 2.444816303686112e-16,
        -2.4369836407188064e-16, -1.0061178561054265e-16, 1.1080919564473632e-16, -0.15607157262159269,
        6.42506566335344e-17, -9.471039951021519e-17, 4.4761136056008063e-17, 1.3571149006174012e-16,
        2.444816303686112e-16, 1.023792263956405, -1.741825558540212e-16, 5.812315117493529e-16,
        -3.8858728175353215e-16, 1.1817611570229167e-16, -0.15607157262159227, -2.1451164936362712e-16,
        0.04457031283561652, -0.22685057396405275, -2.4369836407188064e-16, -1.741825558540212e-16,
        0.43256418388972095, -0.021698089227032858, 0.01735768764568883, 1.1076494024618883e-17,
        -2.2458372838411202e-17, -0.38299728706413466, -0.0004207095592540944, 0.020252474641285406,
        -1.0061178561054265e-16, 5.812315117493529e-16, -0.021698089227032858, 1.0565669737039773,
        -0.23995204723362432, 3.088551842183354e-17, -1.754647747935954e-17, -0.04457031283561777,
        0.020252474641285614, -0.1650865173354893, 1.1080919564473632e-16, -3.8858728175353215e-16,
        0.01735768764568883, -0.23995204723362432, 1.042626688758692, -1.7192506648203827e-17,
        2.5050652716192096e-17, 0.22685057396405697, -1.914209509086782e-18, 1.9756944574058873e-17,
        -0.15607157262159269, 1.1817611570229167e-16, 1.1076494024618883e-17, 3.088551842183354e-17,
        -1.7192506648203827e-17, 1.0237922639564063, 5.1809639528433694e-17, 6.342951234363673e-17,
        2.3211796204239686e-18, -1.0262327190008962e-17, 6.42506566335344e-17, -0.15607157262159227,
        -2.2458372838411202e-17, -1.754647747935954e-17, 2.5050652716192096e-17, 5.1809639528433694e-17,
        1.0237922639564059, 7.473825155897822e-18, 0.021698089227032247, -0.01735768764568897,
        -9.471039951021519e-17, -2.1451164936362712e-16, -0.38299728706413466, -0.04457031283561777,
        0.22685057396405697, 6.342951234363673e-17, 7.473825155897822e-18, 0.43256418388971435]
}

def o2_sto3g_rohf_stable_da() -> Arr {
    return o2_sto3g_mat(o2_sto3g_rohf_stable_da_flat(), 10, 10)
}

#| Converged beta density, stable state.
def o2_sto3g_rohf_stable_db_flat() -> Arr {
    return [1.056566973703979, -0.23995204723362532, -4.320934619905939e-17, 5.27265812079063e-17,
        0.04457031283561652, -0.0004207095592540944, 0.020252474641285614, 4.683052022173595e-17,
        -2.4832777852428062e-17, 0.021698089227032247, -0.23995204723362532, 1.0426266887586955,
        1.6737317714404e-16, 8.927031157374667e-17, -0.22685057396405275, 0.020252474641285406,
        -0.1650865173354893, -2.266998783782711e-16, 1.3408489697204844e-16, -0.01735768764568897,
        -4.320934619905939e-17, 1.6737317714404e-16, 0.334380678701673, -0.17652653746418873,
        -3.0205252791870956e-16, -6.972969091103355e-17, 5.4911340682830284e-17, 0.3894877647916197,
        4.936823315024086e-15, 2.1556533498964787e-16, 5.27265812079063e-17, 8.927031157374667e-17,
        -0.17652653746418873, 0.5468687307576836, -1.2503261298773941e-17, 4.709052389221047e-16,
        -1.2699748480919397e-16, 5.889289045555107e-15, 0.38948776479161323, -1.495954231984342e-16,
        0.04457031283561652, -0.22685057396405275, -3.0205252791870956e-16, -1.2503261298773941e-17,
        0.43256418388972095, -0.021698089227032858, 0.01735768764568883, 1.1440376968534812e-16,
        -2.456506617469943e-16, -0.38299728706413466, -0.0004207095592540944, 0.020252474641285406,
        -6.972969091103355e-17, 4.709052389221047e-16, -0.021698089227032858, 1.0565669737039773,
        -0.23995204723362432, -3.180960987048274e-17, 1.318629713232577e-16, -0.04457031283561777,
        0.020252474641285614, -0.1650865173354893, 5.4911340682830284e-17, -1.2699748480919397e-16,
        0.01735768764568883, -0.23995204723362432, 1.042626688758692, 1.1631550720518563e-16,
        -3.2360159891212727e-16, 0.22685057396405697, 4.683052022173595e-17, -2.266998783782711e-16,
        0.3894877647916197, 5.889289045555107e-15, 1.1440376968534812e-16, -3.180960987048274e-17,
        1.1631550720518563e-16, 0.5468687307576564, 0.17652653746418723, -1.86806078125101e-16,
        -2.4832777852428062e-17, 1.3408489697204844e-16, 4.936823315024086e-15, 0.38948776479161323,
        -2.456506617469943e-16, 1.318629713232577e-16, -3.2360159891212727e-16, 0.17652653746418723,
        0.3343806787016464, 2.5836452269234244e-17, 0.021698089227032247, -0.01735768764568897,
        2.1556533498964787e-16, -1.495954231984342e-16, -0.38299728706413466, -0.04457031283561777,
        0.22685057396405697, -1.86806078125101e-16, 2.5836452269234244e-17, 0.43256418388971435]
}

def o2_sto3g_rohf_stable_db() -> Arr {
    return o2_sto3g_mat(o2_sto3g_rohf_stable_db_flat(), 10, 10)
}

test "o2_sto3g packs" {
    assert_near(o2_sto3g_pack_bad(o2_sto3g_shells(), O2_STO3G_NSH, O2_STO3G_NPRIMTOT, O2_STO3G_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(O2_STO3G_NAO_CART - O2_STO3G_NAO_SPH, 0.0, 0.0)
    assert_near(len(o2_sto3g_fc()), O2_STO3G_NAO_CART, 0.0)
}

test "o2_sto3g unit one-electron integrals are symmetric with a unit overlap diagonal" {
    assert_near(o2_sto3g_asym(o2_sto3g_s_unit(), 10), 0.0, 1.0e-14)
    assert_near(o2_sto3g_asym(o2_sto3g_t_unit(), 10), 0.0, 1.0e-14)
    assert_near(o2_sto3g_asym(o2_sto3g_v_unit(), 10), 0.0, 1.0e-14)
    assert_near(o2_sto3g_diag_dev(o2_sto3g_s_unit(), 10), 0.0, 1.0e-14)
}

test "o2_sto3g unit packed ERIs match their checksums and the Schwarz bound" {
    assert_near(len(o2_sto3g_eri8_cart()), O2_STO3G_ERI8_CART_LEN, 0.0)
    assert_near(o2_sto3g_sumsq(o2_sto3g_eri8_cart()) / O2_STO3G_ERI8_CART_SUMSQ, 1.0, 1.0e-12)
    assert_near(o2_sto3g_wsum(o2_sto3g_eri8_cart(), O2_STO3G_SEED_WSUM), O2_STO3G_ERI8_CART_WSUM, 1.0e-12 * O2_STO3G_ERI8_CART_SUMSQ)
    assert_lt(o2_sto3g_schwarz(o2_sto3g_eri8_cart(), 10), 1.0e-12)
}

test "o2_sto3g uhf energies, labels and densities" {
    assert_lt(O2_STO3G_E_UHF_STABLE, O2_STO3G_E_UHF_DEFAULT + 1.0e-12)
    assert_lt(2.0 - 1.0e-10, O2_STO3G_UHF_S2)
    assert_lt(2.0 - 1.0e-10, O2_STO3G_UHF_S2_STABLE)
    assert_lt(O2_STO3G_UHF_SELF_STEP, 1.0e-10)
    assert_near(o2_sto3g_asym(o2_sto3g_uhf_da(), 10) + o2_sto3g_asym(o2_sto3g_uhf_db(), 10), 0.0, 1.0e-12)
    assert_near(o2_sto3g_trace2(o2_sto3g_uhf_da(), o2_sto3g_s_unit(), 10) + o2_sto3g_trace2(o2_sto3g_uhf_db(), o2_sto3g_s_unit(), 10), 16.0, 1.0e-10)
    assert_near(o2_sto3g_e_elec(o2_sto3g_t_unit() + o2_sto3g_v_unit(), o2_sto3g_eri8_cart(), o2_sto3g_uhf_da(), o2_sto3g_uhf_db(), 10) + O2_STO3G_E_NUC, O2_STO3G_E_UHF_DEFAULT, 1.0e-10)
    assert_lt(O2_STO3G_UHF_STABLE_SELF_STEP, 1.0e-10)
    assert_near(o2_sto3g_asym(o2_sto3g_uhf_stable_da(), 10) + o2_sto3g_asym(o2_sto3g_uhf_stable_db(), 10), 0.0, 1.0e-12)
    assert_near(o2_sto3g_trace2(o2_sto3g_uhf_stable_da(), o2_sto3g_s_unit(), 10) + o2_sto3g_trace2(o2_sto3g_uhf_stable_db(), o2_sto3g_s_unit(), 10), 16.0, 1.0e-10)
    assert_near(o2_sto3g_e_elec(o2_sto3g_t_unit() + o2_sto3g_v_unit(), o2_sto3g_eri8_cart(), o2_sto3g_uhf_stable_da(), o2_sto3g_uhf_stable_db(), 10) + O2_STO3G_E_NUC, O2_STO3G_E_UHF_STABLE, 1.0e-10)
}

test "o2_sto3g rohf energies, labels and densities" {
    assert_lt(O2_STO3G_E_ROHF_STABLE, O2_STO3G_E_ROHF_DEFAULT + 1.0e-12)
    assert_lt(O2_STO3G_ROHF_SELF_STEP, 1.0e-10)
    assert_near(o2_sto3g_asym(o2_sto3g_rohf_da(), 10) + o2_sto3g_asym(o2_sto3g_rohf_db(), 10), 0.0, 1.0e-12)
    assert_near(o2_sto3g_trace2(o2_sto3g_rohf_da(), o2_sto3g_s_unit(), 10) + o2_sto3g_trace2(o2_sto3g_rohf_db(), o2_sto3g_s_unit(), 10), 16.0, 1.0e-10)
    assert_near(o2_sto3g_e_elec(o2_sto3g_t_unit() + o2_sto3g_v_unit(), o2_sto3g_eri8_cart(), o2_sto3g_rohf_da(), o2_sto3g_rohf_db(), 10) + O2_STO3G_E_NUC, O2_STO3G_E_ROHF_DEFAULT, 1.0e-10)
    assert_lt(O2_STO3G_ROHF_STABLE_SELF_STEP, 1.0e-10)
    assert_near(o2_sto3g_asym(o2_sto3g_rohf_stable_da(), 10) + o2_sto3g_asym(o2_sto3g_rohf_stable_db(), 10), 0.0, 1.0e-12)
    assert_near(o2_sto3g_trace2(o2_sto3g_rohf_stable_da(), o2_sto3g_s_unit(), 10) + o2_sto3g_trace2(o2_sto3g_rohf_stable_db(), o2_sto3g_s_unit(), 10), 16.0, 1.0e-10)
    assert_near(o2_sto3g_e_elec(o2_sto3g_t_unit() + o2_sto3g_v_unit(), o2_sto3g_eri8_cart(), o2_sto3g_rohf_stable_da(), o2_sto3g_rohf_stable_db(), 10) + O2_STO3G_E_NUC, O2_STO3G_E_ROHF_STABLE, 1.0e-10)
}

test "o2_sto3g E_uhf <= E_rohf" {
    assert_lt(O2_STO3G_E_UHF_DEFAULT, O2_STO3G_E_ROHF_DEFAULT + 1.0e-12)
    assert_lt(O2_STO3G_E_UHF_STABLE, O2_STO3G_E_ROHF_STABLE + 1.0e-12)
}