General method for removing resonance singularities in quantum mechanical perturbation theory

Kuhler, Kathleen; Truhlar, Donald G.; Isaacson, Alan D.

doi:10.1063/1.471161

Cited by 100 publications

(106 citation statements)

References 19 publications

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“…While group theory can elucidate certain global features of energy landscapes, [6][7][8][9] quantitatively accurate potential energy surfaces are needed in many contexts. Thus, chemical reaction rates [10][11][12][13][14][15] are sensitive to energy barriers calculated for transition structures, and thermodynamic properties 16,17 depend on the accuracy of the calculated harmonic and anharmonic frequencies. 18 This demand is motivating work on ab initio methods capable of yielding the desired accuracy 4,5,[19][20][21] and the search for new methodological approaches.…”

Section: Introductionmentioning

confidence: 99%

Accurate ab initio potential energy curve of F2. III. The vibration rotation spectrum

Bytautas

Matsunaga

Nagata

et al. 2007

The Journal of Chemical Physics

134

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An analytical expression is found for the accurate ab initiopotential energy curve of the fluorine molecule that has been determined in the preceding two papers. With it, the vibrational and rotational energy levels of F2 are calculated using the discrete variable representation. The comparison of this theoretical spectrum with the experimental spectrum, which had been measured earlier using high-resolution electronic spectroscopy, yields a mean absolute deviation of about 5cm−1 over the 22 levels. The dissociation energy with respect to the lowest vibrational energy is calculated within 30cm−1 of the experimental value of 12953±8cm−1. The reported agreement of the theoretical spectrum and dissociation energy with experiment is contingent upon the inclusion of the effects of core-generated electron correlation,spin-orbit coupling, and scalar relativity. The Dunham analysis [Phys. Rev.41, 721 (1932)] of the spectrum is found to be very accurate. New values are given for the spectroscopic constants. KeywordsAb initio calculations, Dissociation energies, Polynomials, Dissociation, Electron correlation calculations Disciplines Chemistry CommentsThe following article appeared in Journal of Chemical Physics 127 (2007) An analytical expression is found for the accurate ab initio potential energy curve of the fluorine molecule that has been determined in the preceding two papers. With it, the vibrational and rotational energy levels of F 2 are calculated using the discrete variable representation. The comparison of this theoretical spectrum with the experimental spectrum, which had been measured earlier using high-resolution electronic spectroscopy, yields a mean absolute deviation of about 5 cm −1 over the 22 levels. The dissociation energy with respect to the lowest vibrational energy is calculated within 30 cm −1 of the experimental value of 12 953± 8 cm −1 . The reported agreement of the theoretical spectrum and dissociation energy with experiment is contingent upon the inclusion of the effects of core-generated electron correlation, spin-orbit coupling, and scalar relativity. The Dunham analysis ͓Phys. Rev. 41, 721 ͑1932͔͒ of the spectrum is found to be very accurate. New values are given for the spectroscopic constants.

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Section: Introductionmentioning

confidence: 99%

Accurate ab initio potential energy curve of F2. III. The vibration rotation spectrum

Bytautas

Matsunaga

Nagata

et al. 2007

The Journal of Chemical Physics

134

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“…A simple approach is to use the anharmonic frequencies in the simple ͑harmonic͒ energy expression given in Table I, where i are the anharmonic frequencies obtained from VSCF calculations, 2,4 as suggested by Truhlar and Isaacson. 7 Alternatively, one can employ the VSCF vibrational energy levels to calculate the zero point energy ͑ZPE͒. The first method is consistent with both the approach described above for calculating the thermodynamic properties and the manner in which ZPEs, are reported in the NIST database, 9 while the second method is directly related to the VSCF approach.…”

Section: A Thermodynamic Functionsmentioning

confidence: 81%

“…The rotational and translational partition functions were obtained using the usual rigid rotor-ideal gas approximations. Although vibrational thermodynamic functions apply rigorously only within the harmonic approximation, anharmonic frequencies can, as noted by Truhlar and Isaacson, 7 be used to construct a simple approximation to the correct vibrational partition functions. This approximation has been shown to provide good agreement with more rigorous calculations.…”

Section: A Thermodynamic Functionsmentioning

confidence: 99%

“…This approximation has been shown to provide good agreement with more rigorous calculations. 7,8 Among all thermodynamic properties entropy is, as shown in Appendix A, particularly sensitive to changes in low vibrational frequencies, which are frequently the most heavily affected by anharmonicity and coupling. One can calculate the zero point vibrational energy in more than one way.…”

Section: A Thermodynamic Functionsmentioning

confidence: 99%

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Exploring the effect of anharmonicity of molecular vibrations on thermodynamic properties

Njegic

Gordon

2006

The Journal of Chemical Physics

116

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Thermodynamic properties of selected small and medium size molecules were calculated using harmonic and anharmonic vibrational frequencies. Harmonic vibrational frequencies were obtained by normal mode analysis, whereas anharmonic ones were calculated using the vibrational self-consistent field (VSCF) method. The calculated and available experimental thermodynamic data for zero point energy, enthalpy,entropy, and heat capacity are compared. It is found that the anharmonicity and coupling of molecular vibrations can play a significant role in predicting accurate thermodynamic quantities. Limitations of the current VSCF method for low frequency modes have been partially removed by following normal mode displacements in internal, rather than Cartesian, coordinates. KeywordsNormal modes, Thermodynamic properties, Entropy, Enthalpy, Potential energy surfaces Thermodynamic properties of selected small and medium size molecules were calculated using harmonic and anharmonic vibrational frequencies. Harmonic vibrational frequencies were obtained by normal mode analysis, whereas anharmonic ones were calculated using the vibrational self-consistent field ͑VSCF͒ method. The calculated and available experimental thermodynamic data for zero point energy, enthalpy, entropy, and heat capacity are compared. It is found that the anharmonicity and coupling of molecular vibrations can play a significant role in predicting accurate thermodynamic quantities. Limitations of the current VSCF method for low frequency modes have been partially removed by following normal mode displacements in internal, rather than Cartesian, coordinates.

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“…This formula was tested for molecules [96] and polymers [98]. It has also been compared to other, non-perturbative formulae [100][101][102][103]. Imaginary shifts in multireference PT have also been considered [99].…”

Section: Complex Level Shiftsmentioning

confidence: 99%

Appendix to “Studies in Perturbation Theory”: The Problem of Partitioning

Śurján

Szabados

2004

Fundamental World of Quantum Chemistry

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The problem of partitioning in perturbation theory is reviewed starting from the classical works by Epstein and Nesbet or by Møller and Plesset, up to optimized partitionings introduced recently. Equations for optimal sets of level shift parameters are presented. Attention is paid to the specific problems appearing if the zero order solution is not a single Slater determinant. A special formalism for multi-configurational perturbation theories is outlined. It is shown that divergent perturbation series, like that of an anharmonic oscillator, can be converted to a convergent series by an appropriate redefinition of the zero order Hamiltonian via level shifts. The possible use of effective one-particle energies in many-body perturbation theory is also discussed. Partitioning optimization in a constant denominator perturbation theory leads to second order correction familiar from connected moment expansion techniques. Ionization potentials, computed perturbatively, are found sensitive to the choice of partitioning, and ordinary approximations are improved upon level shift optimization.

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General method for removing resonance singularities in quantum mechanical perturbation theory

Cited by 100 publications

References 19 publications

Accurate ab initio potential energy curve of F2. III. The vibration rotation spectrum

Accurate ab initio potential energy curve of F2. III. The vibration rotation spectrum

Exploring the effect of anharmonicity of molecular vibrations on thermodynamic properties

Appendix to “Studies in Perturbation Theory”: The Problem of Partitioning

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