Some Recent Results concerning the Electronic Density and the Force Constants of Small Molecules

Bratož, Silva; Daudel, R.; Roux, Monique; Allavena, M.

doi:10.1103/revmodphys.32.412

Cited by 36 publications

(8 citation statements)

References 13 publications

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“…(3) The potential energy must approach -De as r approaches the equilibrium internuclear separation r e , where De is the bond dissociation energy.…”

Section: A General Relationshipsmentioning

confidence: 99%

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A theoretical basis for the correlation between bond length and local mode frequency

Swanton

Henry

1987

The Journal of Chemical Physics

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Articles you may be interested inOn the correlation between bond-length change and vibrational frequency shift in halogen-bonded complexes J. Chem. Phys. 134, 224303 (2011); 10.1063/1.3599050 Theoretical analysis of local attenuation approximations when calculating scatterer correlation lengthWe construct a modified Morse potential which allows us to obtain equations which relate the equilibrium internuclear distance in a Morse oscillator re to the experimental quantities {i)e and {i)eXe' The results provide a theoretical basis for the observed correlation of overtone spectral frequency shifts and changes in equilibrium bond lengths. We also use our results to discuss the basis of the many empirical and nonempirical relationships that have been proposed between re and spectral observables. We illustrate the applicability of our equations for re through calculations ofCH bond lengths for a number of poly atomic molecules. We also use our approach to determine bond lengths for a number of diatomic molecules from measured spectroscopic constants. We compare these results to results obtained from other relationships.

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“…(3) The potential energy must approach -De as r approaches the equilibrium internuclear separation r e , where De is the bond dissociation energy.…”

Section: A General Relationshipsmentioning

confidence: 99%

“…(3) The eigenvalues of the Morse oscillator, relative to the potential minimum, are ll E(v) is in joules, and.u is the reduced mass. The equivalent (truncated) expression involving spectroscopic observables is 21…”

Section: A General Relationshipsmentioning

confidence: 99%

A theoretical basis for the correlation between bond length and local mode frequency

Swanton

Henry

1987

The Journal of Chemical Physics

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“…The second derivatives of the electronic energy are the basis for the calculation of force constants, harmonic vibrational frequencies, infrared and Raman intensities, as well as for subsequent thermodynamic and kinetic property calculations. The theory of SCF energy derivatives including the first derivation of its modern formalism goes back to work of Bratoz beginning from 1958 [3,4]. Gerratt and Mills derived force constants as the analytical derivatives of the Hellmann-Feynman forces [5].…”

Section: Introductionmentioning

confidence: 99%

Efficient implementation of the analytic second derivatives of Hartree–Fock and hybrid DFT energies: a detailed analysis of different approximations

et al. 2015

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In this paper, various implementations of the analytic Hartree-Fock and hybrid density functional energy second derivatives are studied. An approximation-free four-centre implementation is presented, and its accuracy is rigorously analysed in terms of self-consistent field (SCF), coupled-perturbed SCF (CP-SCF) convergence and prescreening criteria. The CP-SCF residual norm convergence threshold turns out to be the most important of these. Final choices of convergence thresholds are made such that an accuracy of the vibrational frequencies of better than 5 cm −1 compared to the numerical noise-free results is obtained, even for the highly sensitive low frequencies (<100-200 cm −1 ). The effects of the choice of numerical grid for density functional exchange-correlation integrations are studied and various weight derivative schemes are analysed in detail. In the second step of the work, approximations are introduced in order to speed up the computation without compromising its accuracy. To this end, the accuracy and efficiency of the resolution of identity approximation for the Coulomb terms and the semi-numerical chain of spheres approximation to the exchange terms are carefully analysed. It is shown that the largest performance improvements are realised if either Hartree-Fock exchange is absent (pure density functionals) and otherwise, if the exchange terms in the CP-SCF step of the calculation are approximated by the COSX method in conjunction with a small integration grid. Default values for all the involved truncation parameters are suggested. For vancomycine (176 atoms and 3593 basis functions), the RIJCOSX Hessian calculation with the B3LYP functional and the def2-TZVP basis set takes ∼3 days using 16 Intel R Xeon R 2.60GHz processors with the COSX algorithm having a net parallelisation scaling of 11.9 which is at least ∼20 times faster than the calculation without the RIJCOSX approximation.

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“…The expression (21) was constructed to weight the unitedand separated-atom configurations in proportion to The real molecular orbital splits into two separated atomic orbitals.…”

Section: N)!'mentioning

confidence: 99%

Force Constants of Diatomic Molecules. I. A General Semitheoretical Approach

Empedocles

1967

The Journal of Chemical Physics

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A general method for calculating the quadratic, cubic, and quartic force constants of homonuclear diatomic molecules and binary hydrides is proposed. The scheme has been designed to be sufficiently simple for application to any molecule and represents an attempt to bridge the gap between atomic and molecular data. It uses as starting parameters only the orbital exponents and one-electron, one-center, kinetic-energy integrals for the united and separated atoms. A distorting operator is defined and used to generate functions of the molecular orbital type. A scaling property of wavefunctions along the three independent Cartesian axes is invoked to calculate a reasonably close approximation to the kinetic energy of the electrons and its derivatives with respect to the internuclear coordinate. The virial method is used to calculate the force constant from these quantities. The method is applied to the elements of the first and second periods.T HE empirical relationships between vibrational force constants and bond lengths which hold for a very wide variety of molecules, such as Badger's law l and other rules,2-4 and between force constants, bond lengths, and dissociation energies 5 ,6 have encouraged theoretical attempts to find a practical way of calculating force constants. These include calculation of (d2 E/dR2) Re,7-9 calculation of (dT jdR)Re lfH2 which can be related to the force constant by the virial theorem,13 calculation of the force on an atomic nucleus in the molecule and use of the Hellmann-F eynman theorem/ 4 -16 perturbation theoryl7-19 and an electrostatic approach.20--23 The principles of these methods

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Some Recent Results concerning the Electronic Density and the Force Constants of Small Molecules

Cited by 36 publications

References 13 publications

A theoretical basis for the correlation between bond length and local mode frequency

A theoretical basis for the correlation between bond length and local mode frequency

Efficient implementation of the analytic second derivatives of Hartree–Fock and hybrid DFT energies: a detailed analysis of different approximations

Force Constants of Diatomic Molecules. I. A General Semitheoretical Approach

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