On the ab initio determination of higher-order force constants at nonstationary reference geometries

Wesley D. Allen, A. Császár

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141 Citations (Scopus)

Abstract

Several complementary analyses have been performed in an investigation of the use of reference geometric structures which are not stationary at a given level of theory in the prediction of improved equilibrium anharmonic molecular force fields. Diatomic paradigms for the procedure were established by constructing empirical potential energy functions for the nitrogen and fluorine molecules which not only reproduce the available Rydberg-Klein-Rees data but also provide reliable derivatives through fourth order for ranges of 0.4 Å or greater around the equilibrium bond distance. For comparison, analogous curves were determined at the double-ζ plus polarization (DZP) restricted Hartree-Fock (RHF) level of theory, and the quartic force fields for N 2 and F2 were also obtained at the experimental r e structures using a (8s5p3d2f1g) basis set and the coupled-cluster singles and doubles method augmented by a perturbative contribution from connected triple excitations [CCSD(T)]. The results substantiate the ability of RHF theory to predict correlation-quality, higher-order force constants if an accurate reference geometry from experiment or a higher level of theory is employed. The theoretical foundations of this technique as applied to polyatomic molecular systems have been systematically explored. Mechanisms were analyzed which address the nonzero force dilemma by using various choices of internal coordinates to shift the equilibrium point of theoretical potential energy surfaces. Examples are presented in which the variations in predicted spectroscopic constants arising from different shift coordinate sets are non-negligible. A Cartesian projection scheme for higher-order force fields was developed and implemented to avert internal-coordinate dependences; formulas for higher-order projection matrices and higher-order derivatives of the external variables of a molecular system were concurrently derived. A formalism for the transformation of force fields between internal and Cartesian representations was also constructed which is applicable to arbitrary order. In addition to N2 and F2, case studies were performed on the F 2O and N2O molecules, for which electron correlation effects are of unusual importance. Quartic force fields are reported for F 2O and N2O at the DZP and TZ(2d1f) CCSD(T) levels of theory, respectively, which provide the best data sets currently available and facilitate the assessment of experimental force constants. The CCSD(T) results are reproduced remarkably well by RHF predictions at the experimental equilibrium structures of these molecules but not at the corresponding RHF optimum geometries. Finally, practical recommendations are made for predictions of higher-order force constants at nonstationary points.

Original languageEnglish
Pages (from-to)2983-3015
Number of pages33
JournalThe Journal of Chemical Physics
Volume98
Issue number4
Publication statusPublished - 1993

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field theory (physics)
Molecules
Geometry
geometry
Potential energy functions
Derivatives
Electron correlations
Potential energy surfaces
Fluorine
predictions
projection
potential energy
Nitrogen
molecules
Polarization
shift
recommendations
fluorine
formalism
nitrogen

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

Cite this

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title = "On the ab initio determination of higher-order force constants at nonstationary reference geometries",
abstract = "Several complementary analyses have been performed in an investigation of the use of reference geometric structures which are not stationary at a given level of theory in the prediction of improved equilibrium anharmonic molecular force fields. Diatomic paradigms for the procedure were established by constructing empirical potential energy functions for the nitrogen and fluorine molecules which not only reproduce the available Rydberg-Klein-Rees data but also provide reliable derivatives through fourth order for ranges of 0.4 {\AA} or greater around the equilibrium bond distance. For comparison, analogous curves were determined at the double-ζ plus polarization (DZP) restricted Hartree-Fock (RHF) level of theory, and the quartic force fields for N 2 and F2 were also obtained at the experimental r e structures using a (8s5p3d2f1g) basis set and the coupled-cluster singles and doubles method augmented by a perturbative contribution from connected triple excitations [CCSD(T)]. The results substantiate the ability of RHF theory to predict correlation-quality, higher-order force constants if an accurate reference geometry from experiment or a higher level of theory is employed. The theoretical foundations of this technique as applied to polyatomic molecular systems have been systematically explored. Mechanisms were analyzed which address the nonzero force dilemma by using various choices of internal coordinates to shift the equilibrium point of theoretical potential energy surfaces. Examples are presented in which the variations in predicted spectroscopic constants arising from different shift coordinate sets are non-negligible. A Cartesian projection scheme for higher-order force fields was developed and implemented to avert internal-coordinate dependences; formulas for higher-order projection matrices and higher-order derivatives of the external variables of a molecular system were concurrently derived. A formalism for the transformation of force fields between internal and Cartesian representations was also constructed which is applicable to arbitrary order. In addition to N2 and F2, case studies were performed on the F 2O and N2O molecules, for which electron correlation effects are of unusual importance. Quartic force fields are reported for F 2O and N2O at the DZP and TZ(2d1f) CCSD(T) levels of theory, respectively, which provide the best data sets currently available and facilitate the assessment of experimental force constants. The CCSD(T) results are reproduced remarkably well by RHF predictions at the experimental equilibrium structures of these molecules but not at the corresponding RHF optimum geometries. Finally, practical recommendations are made for predictions of higher-order force constants at nonstationary points.",
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T1 - On the ab initio determination of higher-order force constants at nonstationary reference geometries

AU - Allen, Wesley D.

AU - Császár, A.

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N2 - Several complementary analyses have been performed in an investigation of the use of reference geometric structures which are not stationary at a given level of theory in the prediction of improved equilibrium anharmonic molecular force fields. Diatomic paradigms for the procedure were established by constructing empirical potential energy functions for the nitrogen and fluorine molecules which not only reproduce the available Rydberg-Klein-Rees data but also provide reliable derivatives through fourth order for ranges of 0.4 Å or greater around the equilibrium bond distance. For comparison, analogous curves were determined at the double-ζ plus polarization (DZP) restricted Hartree-Fock (RHF) level of theory, and the quartic force fields for N 2 and F2 were also obtained at the experimental r e structures using a (8s5p3d2f1g) basis set and the coupled-cluster singles and doubles method augmented by a perturbative contribution from connected triple excitations [CCSD(T)]. The results substantiate the ability of RHF theory to predict correlation-quality, higher-order force constants if an accurate reference geometry from experiment or a higher level of theory is employed. The theoretical foundations of this technique as applied to polyatomic molecular systems have been systematically explored. Mechanisms were analyzed which address the nonzero force dilemma by using various choices of internal coordinates to shift the equilibrium point of theoretical potential energy surfaces. Examples are presented in which the variations in predicted spectroscopic constants arising from different shift coordinate sets are non-negligible. A Cartesian projection scheme for higher-order force fields was developed and implemented to avert internal-coordinate dependences; formulas for higher-order projection matrices and higher-order derivatives of the external variables of a molecular system were concurrently derived. A formalism for the transformation of force fields between internal and Cartesian representations was also constructed which is applicable to arbitrary order. In addition to N2 and F2, case studies were performed on the F 2O and N2O molecules, for which electron correlation effects are of unusual importance. Quartic force fields are reported for F 2O and N2O at the DZP and TZ(2d1f) CCSD(T) levels of theory, respectively, which provide the best data sets currently available and facilitate the assessment of experimental force constants. The CCSD(T) results are reproduced remarkably well by RHF predictions at the experimental equilibrium structures of these molecules but not at the corresponding RHF optimum geometries. Finally, practical recommendations are made for predictions of higher-order force constants at nonstationary points.

AB - Several complementary analyses have been performed in an investigation of the use of reference geometric structures which are not stationary at a given level of theory in the prediction of improved equilibrium anharmonic molecular force fields. Diatomic paradigms for the procedure were established by constructing empirical potential energy functions for the nitrogen and fluorine molecules which not only reproduce the available Rydberg-Klein-Rees data but also provide reliable derivatives through fourth order for ranges of 0.4 Å or greater around the equilibrium bond distance. For comparison, analogous curves were determined at the double-ζ plus polarization (DZP) restricted Hartree-Fock (RHF) level of theory, and the quartic force fields for N 2 and F2 were also obtained at the experimental r e structures using a (8s5p3d2f1g) basis set and the coupled-cluster singles and doubles method augmented by a perturbative contribution from connected triple excitations [CCSD(T)]. The results substantiate the ability of RHF theory to predict correlation-quality, higher-order force constants if an accurate reference geometry from experiment or a higher level of theory is employed. The theoretical foundations of this technique as applied to polyatomic molecular systems have been systematically explored. Mechanisms were analyzed which address the nonzero force dilemma by using various choices of internal coordinates to shift the equilibrium point of theoretical potential energy surfaces. Examples are presented in which the variations in predicted spectroscopic constants arising from different shift coordinate sets are non-negligible. A Cartesian projection scheme for higher-order force fields was developed and implemented to avert internal-coordinate dependences; formulas for higher-order projection matrices and higher-order derivatives of the external variables of a molecular system were concurrently derived. A formalism for the transformation of force fields between internal and Cartesian representations was also constructed which is applicable to arbitrary order. In addition to N2 and F2, case studies were performed on the F 2O and N2O molecules, for which electron correlation effects are of unusual importance. Quartic force fields are reported for F 2O and N2O at the DZP and TZ(2d1f) CCSD(T) levels of theory, respectively, which provide the best data sets currently available and facilitate the assessment of experimental force constants. The CCSD(T) results are reproduced remarkably well by RHF predictions at the experimental equilibrium structures of these molecules but not at the corresponding RHF optimum geometries. Finally, practical recommendations are made for predictions of higher-order force constants at nonstationary points.

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