lang_2026#
J. Lang, G. Garberoglio, M. Przybytek and M. Lesiuk, “Determination of fundamental properties of nitrogen from first principles. III. Temperature and frequency dependence of the molecular polarizability and magnetic susceptibility”, arXiv:2607.21261v2 [physics.chem-ph] (2026)
Source record · Catalogue · Review register
DOI: 10.48550/arxiv.2607.21261
Source kind: theory
Recorded technique: Ab initio isotropic static polarizability alpha_0(R), Cauchy coefficients alpha_2(R), alpha_4(R), alpha_6(R) (alpha(omega, R) = alpha_0 + alpha_2 omega^2 + alpha_4 omega^4 + alpha_6 omega^6, Eq. (2)) and isotropic magnetic susceptibility chi_0(R) of 14N2 (X 1Sigma_g+) on a grid of internuclear distances R = 1.75-2.60 bohr. Polarizability: composite coupled-cluster scheme, Eq. (32): frozen-core CCSD (with the Hartree-Fock part; aug-cc-pVXZ to X = 7) + CC3 (X = 6) + full CCSDT (X = 4) + CCSDTQ (aug-cc-pVDZ, 50 % uncertainty) + all-electron CC3 (aug-cc-pCVXZ, X = 4) and CCSDT (X = 3) core corrections + one-electron scalar relativistic (DKH2, all-electron CCSD, X = 4); Riemann extrapolation to the basis-set limit with random-walk uncertainty; alpha_6 at CCSD + CC3 only (flat 10 % uncertainty). QED, diagonal Born-Oppenheimer and two-electron relativistic terms neglected (p. 7). The Cauchy coefficients of the post-CC3 terms by fitting a 27-frequency grid (p. 7). Magnetic susceptibility: diamagnetic plus paramagnetic (Van Vleck) terms, Eq. (40), frozen-core CC3 response with aug-cc-pV5Z (gauge origin at the molecular centre; 5 % uncertainty; no relativistic or post-CC3 terms; frequency dependence neglected, pp. 10-11). Thermal averages 50-2000 K by rovibrational averaging over 345 levels of the Paper II potential with the 14N2 nuclear-spin weights, Eqs. (18)-(22), and independently by path integral Monte Carlo (Eqs. (24)-(31)); the two agree within the PIMC statistics (p. 13).
Materials in structured entries: N2
Dataset quantities: cauchy_moment, magnetic_susceptibility, polarizability
Contents: 9 datasets; 3 formulas.
Curation notes#
The library copy is the arXiv preprint 2607.21261v2 (dated 9 September 2026, 18 pdf pages); not peer reviewed; no journal reference. Page numbers are the preprint’s pdf pages. Atomic units throughout: polarizability and magnetic susceptibility in a0^3 (the magnetic term enters the Lorentz-Lorenz relation as alpha + chi, Eq. (1)), omega in hartree; 1 cm^3/mol = 2.675205 a.u. (p. 2; the package’s (4 pi/3) N_A a0^3 = 0.3738031 cm^3/mol gives 2.675205), CODATA 2022.
Papers I (the nitrogen atom’s polarizability, the same Cauchy expansion) and II (the N2 ground-state potential, its rovibrational levels, D_0 = 9.76 eV) of the series are referred to only as ‘Paper I’ and ‘Paper II’ (pp. 1, 2, 4-5, 7): the reference list does not cite them. Neither is in the library; neither holds a quantity of the package for N2 (Paper II’s potential enters here only through the averaging). The supplementary material (Zenodo, doi 10.5281/zenodo.22662189: alpha_n(T) and chi_0(T) on a 1 K grid, the Eq. (52) parameters, the uncertainty fits, the full R grid) is not in the library: the temperature dependence exists here only at 303 K (Eq. (53)) and, semi-empirically, at 273.16 K (p. 15). Figures 2 and 3 (alpha_n(T), chi_0(T), raster) are not digitised: the numbers are published in the supplement (TC-699).
ELECTRIC POLARIZABILITY. The alpha_n here are the electric polarizability alone; the refractive (package) polarizability is alpha + chi_0 (Eq. (54)). Every dataset below says which it holds.
UNCERTAINTIES. alpha_0, alpha_2, alpha_4 at 303 K: expanded, k = 2 (‘evaluated at 2 sigma confidence level’, p. 14; ‘approximately a 95% confidence level’, p. 6), including the potential’s propagated uncertainty. alpha_6 and chi_0 carry flat 10 % and 5 % estimates (pp. 9, 11, 13), with no stated level (‘extremely unlikely to exceed 5%’, p. 11, for chi_0).
CHECKS (2026-09-29). Eq. (55) with the Eq. (53) values reproduces the paper’s theoretical molar polarizabilities 11.743(13) at 1542.383 nm and 11.875(13) at 632.9908 nm (computed 11.743019, 11.874645). The semi-empirical alpha_0 = 11.735962 and alpha_2 = 30.086359 with the theoretical alpha_4, alpha_6, chi_0 reproduce the measured 11.762120 and 11.894428 to 1e-6 (computed 11.762119, 11.894427). Eq. (50) with Table III reproduces Table I’s totals at R = 1.750, 2.070, 2.600 bohr (formula alpha_n_of_R); Eq. (51) reproduces Table II’s aug-cc-pV5Z diamagnetic + paramagnetic sums (formula chi0_of_R). Eq. (53) and the p. 15 values checked on the pdf text.
COMPARISON WITH fit/N2 (computed 2026-09-29; fit/N2 has chi0_au = 0, so its polarizability is the refractive one). Ab initio alpha + chi_0 at 303 K is 1606 ppm below the fit at the static limit, 1615, 1638 and 1656 ppm below at 1542, 800 and 633 nm (2.9-3.0 sigma of the theory’s k = 2 uncertainty halved); its GVD (d^2(omega alpha)/d omega^2) is 0.54, 0.52, 0.51 % below the fit’s at 1550, 800, 633 nm (theory sigma 0.13 %: about 4 sigma); S(-4) is 0.55 % below the fit’s 30.0938, S(-6) 0.20 % above its 100.423, S(-8) 2.8 % above its 372.66 (within the 10 %). The semi-empirical values (below) agree with the fit to +9.9 ppm (static, with chi_0), +9.3 (1542 nm), +8.0 (800 nm), +7.0 ppm (633 nm), and in GVD to -0.02 %; fit/N2 rests on data near 293 K, and the theory’s temperature coefficient (below) moves the 303 K values by -11 to -12 ppm to 293 K, leaving the fit 1.5 (1542 nm) to 4.6 ppm (633 nm) above them.
TEMPERATURE COEFFICIENT (computed from the two semi-empirical static values, p. 15): (11.735962 - 11.735585)/29.84 K = 1.263e-5 a.u./K = 1.077e-6 per K of alpha_0 = 47.2e-7 (cm^3/mol)/K, 273.16-303 K; egan_2019 lists Buldakov et al. 48(1)e-7 (optical, theory), Sharipov et al. 51e-7 (static, theory), Schmidt and Moldover 62(11)e-7 (static); Egan and Yang (2023, Int. J. Thermophys. 44, 181, p. 17; in the library, not curated) measure A_theta = 1.18(4)e-6 per K at 632.9908 nm over 293-433 K. N2’s first refractivity coefficient changes by about 30 ppm between 273 and 303 K, four times its pair term at 1 atm (Achtermann’s B_R rho/A_R = 8e-6).
MAGNETIC SUSCEPTIBILITY. chi_0(303 K) = -1.75(9) x 10^-4 a.u. (Eq. (53)), diamagnetic -3.46 x 10^-4 and paramagnetic +1.70 x 10^-4 at R = 2.07 bohr (Table II): the paramagnetic term ‘is substantial and cannot be omitted’ (p. 15). -14.9 ppm of alpha_0. The four measurements the paper quotes (datasets below) are 5-31 % smaller in magnitude; the authors ‘cannot explain the origin of this discrepancy’ (p. 15). The same measurer’s neon agrees with the ab initio neon to 1.1 % and his argon is 6.3 % low (lesiuk_2023b, Table X): scaled by argon’s 6.3 %, Havens’ N2 would still be 18 % below this theory. The centre-of-mass coupling (Eq. (49)) and the frequency dependence of chi (below 1 %, p. 11) are negligible. The conclusions (p. 16) speak of ‘the single experimental result’; p. 15 quotes four.
Also in the text (p. 15): Egan and Yang’s own static value 11.735909 a.u. (the yang_2025 A_eps_N2, 4.38692 cm^3/mol, with older alpha_4, alpha_6, chi_0) and ‘Egan and collaborators’ alpha_2 30.109 a.u. (yang_2025’s n2_cauchy, S(-4) = 30.1086): not extracted (in yang_2025). The kinetic-energy correction to Eq. (10), about -2 x 10^-4 a.u. for v = J = 0 from the b 1Pi_u state alone (p. 4), is neglected by the paper.
Byproduct (computed, not printed): Eq. (50) gives d alpha_0/dR = 5.98 a0^2 at R = 2.07 bohr (1.675 angstrom^2), the derivative of the mean polarizability with the bond length; murphy_1969’s reproduced N2 d alpha/dr is 1.75 angstrom^2 (4 % higher).
Not extracted: Table I’s components by R (not a quantity: a polarizability at fixed R is not the molecule’s), Table II’s basis-set sequence (its X = 5 sums are the check of chi0_of_R), Fig. 1 (the partition-function exchange ratio).
Recorded bibliographic identity status: VALIDATED. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
lang_2026/cauchy_303K#
{
"id": "cauchy_303K",
"material": "N2",
"table": "text",
"quantity": "cauchy_moment",
"unit": "au",
"abscissa": "order",
"abscissa_unit": "1",
"use": "check",
"uncertainty": {
"column": true,
"level": "2 sigma"
},
"parameters": {
"temperature_k": 303.0
}
}
4 inline points in the source record.
Eq. (53), p. 14: alpha_0 = 11.717(13), alpha_2 = 29.928(80), alpha_4 = 100.62(82), alpha_6 = 383(38) a.u. of 14N2 at 303 K, rovibrationally averaged (PIMC uncertainty propagation), stored as S(-2), S(-4), S(-6), S(-8) (alpha_2k = S(-2k-2), Eq. (6)). ELECTRIC polarizability: chi_0 not included. Uncertainties k = 2 for the first three; alpha_6’s is the flat 10 % (p. 9), level not stated (stored under the same level). A check, not fitted: a preprint; the uncertainty of S(-2), 0.11 % (k = 2), is 100 times the metrology’s; S(-2) is 1600 ppm and S(-4) 0.53 % below the semi-empirical values (2.9 and 4 sigma), which the authors themselves recommend over the ab initio ones (p. 15). S(-6) and S(-8) (100.42 and 372.66 in fit/N2) are the only ab initio N2 moments of their order in the library with uncertainties.
lang_2026/chi0_303K#
{
"id": "chi0_303K",
"material": "N2",
"table": "text",
"quantity": "magnetic_susceptibility",
"unit": "au",
"scale": 0.0001,
"abscissa": "none",
"use": "primary",
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"temperature_k": 303.0
}
}
1 inline points in the source record.
Eq. (53), p. 14 (and p. 15): chi_0 = -1.75(9) x 10^-4 a.u., the isotropic magnetic susceptibility (magnetizability) of 14N2 at 303 K, rovibrationally averaged, frozen-core CC3/aug-cc-pV5Z, static (the frequency dependence ‘most likely smaller than 1%’, p. 11). The uncertainty is the flat 5 % goal (pp. 11, 13), level not stated. -14.9 ppm of alpha_0. The only calculation of N2’s susceptibility in the library; 31 % larger in magnitude than havens_1933 (-1.338) and 5-31 % than every measurement (source notes). The temperature dependence is weak (Fig. 3; numbers in the supplement, not in the library). A preprint: primary as the value to adopt for fit/N2’s chi0_au, with the unresolved disagreement with experiment stated.
lang_2026/hector_1924#
{
"id": "hector_1924",
"material": "N2",
"table": "text",
"quantity": "magnetic_susceptibility",
"unit": "au",
"scale": 0.0001,
"abscissa": "none",
"use": "reproduced",
"reproduced_from": [
"L. G. Hector, Phys. Rev. 24, 418 (1924)"
],
"uncertainty": {
"relative": 0.02,
"level": "not stated"
}
}
1 inline points in the source record.
p. 15: Hector’s measurement as converted by Lang et al., chi_0 = -1.34 x 10^-4 a.u., ‘stating the uncertainty at 2%’ (level not stated); the value the CRC Handbook cites (-12.0 x 10^-6 cm^3/mol in cgs molar units is -1.345 x 10^-4 a.u., computed). Temperature not stated. The original is not in the library.
lang_2026/vaidyanathan_1928#
{
"id": "vaidyanathan_1928",
"material": "N2",
"table": "text",
"quantity": "magnetic_susceptibility",
"unit": "au",
"scale": 0.0001,
"abscissa": "none",
"use": "reproduced",
"reproduced_from": [
"V. Vaidyanathan, Lond. Edinb. Dubl. Phil. Mag. J. Sci. 5, 380 (1928)"
],
"uncertainty": {
"relative": 0.05,
"level": "bound"
},
"parameters": {
"temperature_k": 303.0
}
}
1 inline points in the source record.
p. 15: -1.45 x 10^-4 a.u. at 303 K, ‘estimating the error at no more than 5%’ (a bound). As converted by Lang et al.; the original is not in the library.
lang_2026/bitter_1930#
{
"id": "bitter_1930",
"material": "N2",
"table": "text",
"quantity": "magnetic_susceptibility",
"unit": "au",
"scale": 0.0001,
"abscissa": "none",
"use": "reproduced",
"reproduced_from": [
"F. Bitter, Phys. Rev. 36, 1648 (1930)"
],
"parameters": {
"temperature_k": 298.0
}
}
1 inline points in the source record.
p. 15: -1.66 x 10^-4 a.u. at 298 K, ‘without explicit uncertainty estimation’; the measurement closest to the theory (5 % smaller in magnitude). As converted by Lang et al.; the original is not in the library.
lang_2026/havens_1933#
{
"id": "havens_1933",
"material": "N2",
"table": "text",
"quantity": "magnetic_susceptibility",
"unit": "au",
"scale": 0.0001,
"abscissa": "none",
"use": "reproduced",
"reproduced_from": [
"G. G. Havens, Phys. Rev. 43, 992 (1933)"
],
"uncertainty": {
"column": true,
"level": "not stated"
}
}
1 inline points in the source record.
p. 15: -1.338(2) x 10^-4 a.u. ‘at room temperature’ (level not stated), as converted by Lang et al. The same work’s Ne and Ar values are lesiuk_2023b/havens_1933_Ne (1.1 % from theory) and havens_1933_Ar (6.3 % low). Soné (1920) and Hammar (1926), ‘roughly two times smaller’ (gas purity), print no number here. The original is not in the library.
lang_2026/semi_empirical_303K#
{
"id": "semi_empirical_303K",
"material": "N2",
"table": "text",
"quantity": "cauchy_moment",
"unit": "au",
"abscissa": "order",
"abscissa_unit": "1",
"use": "check",
"uncertainty": {
"relative_rows": {
"-2": 1e-05
},
"level": "bound"
},
"parameters": {
"temperature_k": 303.0
}
}
2 inline points in the source record.
p. 15: the static polarizability alpha_0(303 K) = 11.735962 a.u. and the second Cauchy coefficient alpha_2 = 30.086359 a.u., solved from Egan and Yang’s two molar polarizabilities (dataset egan_yang_303K) with this paper’s alpha_4, alpha_6 and chi_0 at 303 K, Eq. (55). ELECTRIC (chi_0 removed). alpha_0 ‘no worse than 10ppm’ (a bound, row -2); alpha_2 printed without uncertainty (the theory’s alpha_4 uncertainty alone moves it by 0.0025, 83 ppm; the two measurements, if uncorrelated, by 0.012, 0.04 %: computed). Not independent of the Egan and Yang measurements (the refractivities of egan_yang_303K; yang_2025’s A_eps_N2 is the same data reduced with older theory, 4.5 ppm lower): a check. Against fit/N2: S(-2) + chi_0 = 11.735787 is 9.9 ppm above the fit’s static value; S(-4) is 0.025 % below the fit’s 30.0938 (0.6 sigma), and yang_2025’s 30.1086 0.05 % above it.
lang_2026/semi_empirical_273K#
{
"id": "semi_empirical_273K",
"material": "N2",
"table": "text",
"quantity": "polarizability",
"unit": "au",
"abscissa_unit": "nm",
"use": "check",
"parameters": {
"temperature_k": 273.16
}
}
1 inline points in the source record.
p. 15: alpha_0(273.16 K) = 11.735585 a.u., semi_empirical_303K’s alpha_0 moved to the triple point of water with this paper’s theoretical alpha_0(303 K) - alpha_0(273.16 K) (the supplement’s grid, not in the library): 32.1 ppm lower than at 303 K. ELECTRIC (static). No uncertainty printed. Schmidt and Moldover’s capacitance A_eps at 273.16 K (schmidt_2003/A_eps_tau_N2, 4.38748 cm^3/mol = 11.73731 a.u.) is 147 ppm higher (their budget about 60 ppm).
lang_2026/egan_yang_303K#
{
"id": "egan_yang_303K",
"material": "N2",
"table": "text",
"quantity": "polarizability",
"unit": "au",
"abscissa_unit": "nm",
"wavelength_medium": "vacuum",
"use": "reproduced",
"reproduced_from": [
"egan_2023",
"P. F. Egan and Y. Yang, Int. J. Thermophys. 45, 120 (2024)",
"yang_2025"
],
"uncertainty": {
"column": true,
"level": "1 sigma"
},
"parameters": {
"temperature_k": 303.0
}
}
2 inline points in the source record.
p. 15: ‘the corresponding experimental results’, the molar polarizability alpha + chi (the package’s refractive polarizability) of N2 at 303 K from the NIST refractometry of Egan and Yang (Refs. 85-87, not assigned per wavelength), standard uncertainties (1 sigma, p. 15). The 632.9908 nm value is Egan and Yang 2023’s A_303 = 4.446175(14) cm^3/mol (p. 17 of that paper; in the library as Egan_2023_Optical90Measurement, not curated), 11.894429 a.u. by the paper’s factor; the 1542.383 nm value’s original (presumably Egan and Yang 2024) is not in the library (yang_2025 prints only the reduced A_eps and A_2; its laser is 194.36862 THz = 1542.3912 nm, 0.008 nm from the wavelength quoted here, 1e-9 of alpha). Against fit/N2: -9.4 ppm (1542 nm) and -7.1 ppm (633 nm); moved to 293 K with the theory’s temperature coefficient, +1.5 and +4.6 ppm (source notes). The best copy in the library of these two numbers.
Formulas#
lang_2026/cauchy_theory_303K#
{
"id": "cauchy_theory_303K",
"form": "alpha_series",
"terms": {
"c": [
"11.717",
"29.928",
"100.62",
"383"
]
},
"range_nm": [
455.6,
"inf"
],
"material": "N2",
"equation": "Eq. (2) with Eq. (53), p. 14",
"printed": "alpha(omega, T) = alpha_0(T) + alpha_2(T) omega^2 + alpha_4(T) omega^4 + alpha_6(T) omega^6; T = 303 K: alpha_0 = 11.717(13), alpha_2 = 29.928(80), alpha_4 = 100.62(82), alpha_6 = 383(38)",
"variable": "omega: angular frequency in atomic units (hartree); alpha in a0^3",
"state": "none (per molecule, 303 K)",
"density": "none",
"range": "'wavelengths longer than 400nm or omega < 0.1 in atomic units' (p. 2): the two limits differ (0.1 a.u. is 455.6 nm); range_nm takes the stricter.",
"coefficients": {
"alpha_0": "11.717",
"alpha_2": "29.928",
"alpha_4": "100.62",
"alpha_6": "383"
},
"check": "With chi_0 = -1.75e-4 added (Eq. (55)) the series gives 11.743019 at 1542.383 nm and 11.874645 at 632.9908 nm (omega = 0.0295409, 0.0719811 a.u.): the paper's 11.743(13) and 11.875(13) (p. 15). Checked 2026-09-29."
}
The paper’s ab initio series at 303 K. ELECTRIC polarizability: chi_0 = -1.75(9)e-4 a.u. (15 ppm) is not included; add it for the refractive index (Eq. (54)). 1600 ppm below the measured values; the semi-empirical alpha_0, alpha_2 (dataset semi_empirical_303K) with this series’ alpha_4, alpha_6 reproduce the measurements.
lang_2026/alpha_n_of_R#
{
"id": "alpha_n_of_R",
"material": "N2",
"equation": "Eq. (50), p. 13, with Table III, p. 12",
"printed": "alpha_n(R) = exp(-a_n^(1) R) sum_{i=-1}^{1} c_in^(1) R^i + exp(-a_n^(2) R) sum_{i=0}^{2} c_in^(2) R^i, n = 0, 2, 4, 6",
"variable": "R: internuclear distance in bohr; alpha_n in atomic units (a0^3 hartree^-n)",
"state": "none (per molecule, clamped nuclei)",
"density": "none",
"range": "R in [1.75, 2.60] bohr only (p. 13: not to be extrapolated)",
"coefficients": {
"c_m1_0": "3973.239843",
"c_0_0": "-2550.566901",
"c_1_0": "480.40394",
"d_0_0": "-17636.209308",
"d_1_0": "6178.632412",
"d_2_0": "-7984.197341",
"a1_0": "0.72712153",
"a2_0": "3.06212416",
"c_m1_2": "3121512.910661",
"c_0_2": "-1565760.084872",
"c_1_2": "213071.693344",
"d_0_2": "-12511573.39832",
"d_1_2": "4306441.860778",
"d_2_2": "-4591578.708124",
"a1_2": "1.57852725",
"a2_2": "3.56319374",
"c_m1_4": "2.9522897",
"c_0_4": "-1.06250446",
"c_1_4": "0.10234389",
"d_0_4": "-8.65155509",
"d_1_4": "2.18269184",
"d_2_4": "-1.76012369",
"a1_4": "-6.04767072",
"a2_4": "-4.59332841",
"c_m1_6": "19.85061337",
"c_0_6": "-7.34704556",
"c_1_6": "0.72912448",
"d_0_6": "-59.44131003",
"d_1_6": "15.28369979",
"d_2_6": "-12.65835287",
"a1_6": "-5.57635061",
"a2_6": "-4.08555911"
},
"check": "At R = 1.750, 2.070, 2.600 bohr: alpha_0 = 9.8260, 11.6427, 14.8590 (Table I totals 9.8255(80), 11.642(12), 14.856(40)); alpha_2 = 21.1215, 29.4793, 50.6091 (21.118(21), 29.471(70), 50.58(41)); alpha_4 = 60.414, 97.999, 242.65 (60.43(19), 98.09(57), 242.5(51)); within the printed uncertainties. Table III image checked against the cells. Computed 2026-09-29."
}
Coefficient names: c_i_n = c_in^(1) (c_m1 for i = -1), d_i_n = c_in^(2), a1_n = a_n^(1), a2_n = a_n^(2), n the Cauchy order. The purely electronic, clamped-nucleus alpha_n(R) that the thermal averages are built from; not a molecular polarizability. Its slope, d alpha_0/dR = 5.98 a0^2 at 2.07 bohr (computed), is the bond-length derivative of the mean polarizability (source notes). The uncertainty fits are in the supplement (not in the library).
lang_2026/chi0_of_R#
{
"id": "chi0_of_R",
"material": "N2",
"equation": "Eq. (51), p. 13, parameters in the text, p. 13",
"printed": "chi_0(R) = exp(-b^(1) R) sum_{i=0}^{1} d_i^(1) R^i + exp(-b^(2) R^2) sum_{i=0}^{1} d_i^(2) R^i; d_0^(1) = -0.0022528, d_1^(1) = 0.0012629, d_0^(2) = 0.0012288, d_1^(2) = -0.0008785, b^(1) = 0.729884, b^(2) = 0.195461 (atomic units)",
"variable": "R: internuclear distance in bohr; chi_0 in a0^3",
"state": "none (per molecule, clamped nuclei)",
"density": "none",
"range": "R in [1.75, 2.60] bohr only",
"coefficients": {
"d1_0": "-0.0022528",
"d1_1": "0.0012629",
"d2_0": "0.0012288",
"d2_1": "-0.0008785",
"b1": "0.729884",
"b2": "0.195461"
},
"check": "At R = 1.750, 2.070, 2.600 bohr: -1.815e-4, -1.754e-4, -1.270e-4 a.u.; Table II aug-cc-pV5Z diamagnetic + paramagnetic: -1.82e-4, -1.76e-4, -1.28e-4 (to the printed digits). Checked 2026-09-29 against the pdf text (the superscripts are lost in the text layer; the order is that of the equation)."
}
Note the Gaussian R^2 in the second exponent. The thermal average at 303 K, -1.75e-4 (dataset chi0_303K), is close to the value at R = 2.07 bohr.
Corrections#
No dataset errata are recorded in this source record.
Formula corrections, where recorded, appear with their formulas above. Curation notes may also discuss corrections or unresolved interpretation. Consult the review register for the checks and decisions.