bishop_1993#
D. M. Bishop, B. Kirtman, H. A. Kurtz and J. E. Rice, “Calculation of vibrational dynamic hyperpolarizabilities for H2O, CO2, and NH3”, J. Chem. Phys. 98, 8024 (1993)
Source record · Catalogue · Review register
DOI: 10.1063/1.464556
Source kind: theory
Recorded technique: Bishop-Kirtman perturbation theory for the pure vibrational beta^v and gamma^v: products of electrical-property derivatives (mu, alpha, beta with respect to normal coordinates, first and second derivatives) with harmonic frequencies and cubic force constants, orders (0,0), (1,0), (2,0), (0,1), (1,1) in electrical and mechanical anharmonicity (Eqs. 3, 4); third derivatives omitted. CO2: SCF and partial MP2 (second derivatives of beta not at MP2) with a Huzinaga-Dunning [9s6p/4s2p] basis plus diffuse and polarization functions; CADPAC; optimized geometry (pp. 8025-8027).
Materials in structured entries: CO2
Dataset quantities: hyperpolarizability
Contents: 6 datasets; 0 formulas.
Curation notes#
Identity: pdf page 1 is the publisher’s cover; journal pages 8024-8030 = pdf pages 2-8 (page = pdf page + 8022). Only CO2 is curated (H2O and NH3 skipped).
CONVENTION: ‘Our definitions of beta and gamma are in accord with those given in Refs. 14 and 15 [Bogaard and Orr 1975; Buckingham 1967], that is they are the coefficients in a Taylor series expansion of the induced dipole moment’ (p. 8025): T. Atomic units (gamma 6.23538e-65 C^4 m^4 J^-3). Processes (p. 8025): static; dc Kerr (w1 = w, w2 = w3 = 0); dc-SHG = ESHG (w1 = w2 = w, w3 = 0); THG; ‘the intensity dependent refractive index (IDRI) where w1 = w2 = w and w3 = -w’ (process kerr). ‘In all cases the circular optical frequency will be given the value defined by hbar w = 0.07 E_h’ (650.9 nm, computed here).
MEANS (p. 8027): gamma-bar^v = (gamma_xxyy + gamma_xyxy + gamma_xyyx)/15 summed (Eq. 8), the isotropic gamma_par; for the Kerr experiment gamma-bar_K^v = (3 gamma_xyxy - gamma_xxyy)/10 summed (Eq. 10), recorded as component ‘K’ (dataset dc_kerr_k). PART: pure vibrational only, ‘over and above vibrational effects emanating from zero-point vibrational averaging’ (p. 8024), which is not computed for gamma. Rotational terms are not included.
DATASETS: Table VI (p. 8028, image checked), one dataset per process, rows: ‘scf_partial’ and ‘mp2_partial’ (footnote a: ‘terms including second derivatives of beta are not included, i.e., [mu beta]^(2,0) and part of [mu beta]^(1,1)’), ‘scf’ (complete). Electron correlation matters: ‘the dc-Kerr effect exhibits a change of sign’ (p. 8028); for dc Kerr and IDRI much of the SCF-MP2 difference comes from the vibrational frequencies. The anharmonic term ‘is often larger than the harmonic term’ for the static and dc Kerr components of CO2 (p. 8029), so those are less certain. Table XI: vibrational/electronic in % at the SCF level, CO2: static 48, dc Kerr -2, ESHG -9, THG about 0, IDRI 12 (against Sekino and Bartlett’s SCF electronic values, sekino_1993): not recorded as data.
NOT EXTRACTED: Table V (SCF tensor components of gamma^v for CO2; the library’s cells print the last row label ‘zzzx’, the image ‘xzzx’), H2O and NH3 tables. The earlier CO2 treatment (Kirtman and Bishop, Chem. Phys. Lett. 175, 601 (1990); Bishop and Kirtman, J. Chem. Phys. 95, 2646 (1991)) is superseded here (p. 8028).
Recorded bibliographic identity status: VALIDATED_WITH_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
bishop_1993/static#
{
"id": "static",
"material": "CO2",
"file": "CO2/bishop_1993__static.csv",
"table": "tbl_bcd9303581c8",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "check",
"parameters": {
"process": "static",
"convention": "T",
"part": "vibrational"
}
}
Table VI, CO2 pure vibrational static gamma-bar^v(0;0,0,0); rows scf_partial, mp2_partial (without second derivatives of beta) and scf (complete). No uncertainty stated.
bishop_1993/dc_kerr#
{
"id": "dc_kerr",
"material": "CO2",
"file": "CO2/bishop_1993__dc_kerr.csv",
"table": "tbl_bcd9303581c8",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "check",
"parameters": {
"process": "dc_kerr",
"convention": "T",
"part": "vibrational",
"component": "parallel"
}
}
Table VI, CO2 pure vibrational gamma-bar^v(-w; w, 0, 0), the isotropic mean for the dc Kerr frequencies at hbar w = 0.07 E_h; rows scf_partial, mp2_partial (without second derivatives of beta) and scf (complete). No uncertainty stated.
bishop_1993/eshg#
{
"id": "eshg",
"material": "CO2",
"file": "CO2/bishop_1993__eshg.csv",
"table": "tbl_bcd9303581c8",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "check",
"parameters": {
"process": "eshg",
"convention": "T",
"part": "vibrational",
"component": "parallel"
}
}
Table VI, CO2 pure vibrational gamma-bar^v(-2w; w, w, 0) at hbar w = 0.07 E_h; rows scf_partial, mp2_partial (without second derivatives of beta) and scf (complete). No uncertainty stated.
bishop_1993/thg#
{
"id": "thg",
"material": "CO2",
"file": "CO2/bishop_1993__thg.csv",
"table": "tbl_bcd9303581c8",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "check",
"parameters": {
"process": "thg",
"convention": "T",
"part": "vibrational",
"component": "parallel"
}
}
Table VI, CO2 pure vibrational gamma-bar^v(-3w; w, w, w) at hbar w = 0.07 E_h; rows scf_partial, mp2_partial (without second derivatives of beta) and scf (complete). No uncertainty stated.
bishop_1993/kerr#
{
"id": "kerr",
"material": "CO2",
"file": "CO2/bishop_1993__kerr.csv",
"table": "tbl_bcd9303581c8",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "check",
"parameters": {
"process": "kerr",
"convention": "T",
"part": "vibrational",
"component": "parallel"
}
}
Table VI, CO2 pure vibrational gamma-bar^v(-w; w, w, -w), the intensity-dependent refractive index (IDRI) at hbar w = 0.07 E_h; rows scf_partial, mp2_partial (without second derivatives of beta) and scf (complete). No uncertainty stated.
bishop_1993/dc_kerr_k#
{
"id": "dc_kerr_k",
"material": "CO2",
"file": "CO2/bishop_1993__dc_kerr_k.csv",
"table": "tbl_bcd9303581c8",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "check",
"parameters": {
"process": "dc_kerr",
"convention": "T",
"part": "vibrational",
"component": "K"
}
}
Table VI, CO2 pure vibrational gamma-bar_K^v(-w; w, 0, 0) = (3 gamma_xyxy - gamma_xxyy)/10 (Eq. 10), the Kerr-experiment combination at hbar w = 0.07 E_h; rows scf_partial, mp2_partial (without second derivatives of beta) and scf (complete). No uncertainty stated.
Formulas#
No formulas are recorded.
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.