Force Constants and Dipole‐Moment Derivatives of Molecules from Perturbed Hartree–Fock Calculations. I

1968 ◽  
Vol 49 (4) ◽  
pp. 1719-1729 ◽  
Author(s):  
J. Gerratt ◽  
I. M. Mills
Keyword(s):  
Dipole Moment ◽  
Force Constants ◽  
Hartree Fock ◽  
Derivatives Of

Analytic derivative theory based on the Hellmann–Feynman theorem

1992 ◽  
Vol 70 (2) ◽  
pp. 434-442 ◽  
Author(s):  
K. Hirao
Keyword(s):  
Present Theory ◽  
Basis Functions ◽  
Force Constants ◽  
Basis Set ◽  
Energy Derivatives ◽  
First Order ◽  
Hartree Fock ◽  
Derivative Method ◽  
Derivatives Of ◽  
Feynman Theorem

General formulae for the second, third, and fourth derivatives of the energy with respect to the nuclear coordinates of a molecule are derived from the Hellmann–Feynman theorem. Hurley's condition is used to obtain approximations to the first-order wavefunction, from which the second, third, and fourth energies can be obtained, leading to quadratic, cubic, and quartic force constants. The procedure is equivalent to minimizing the derivative energy by perturbed variation techniques. The expressions for these higher energy derivatives are much simpler than those of the direct analytic derivative method. The electrostatic calculation involves only one-electron integrals. The coupled Hartree–Fock equations to obtain the wavefunction derivatives become much simpler. The present theory provides a great conceptual simplification. However, the theory is correct only if the basis set is complete or basis functions are independent of the perturbation. Keywords: analytic derivative theory, Hellmann–Feynman theorem, force constants, the curvature theorem.

Theoretical dipole moment derivatives and force constants for HCN

1978 ◽  
Vol 69 (4) ◽  
pp. 1425-1428 ◽  
Author(s):  
B. Liu ◽  
K. M. Sando ◽  
C. S. North ◽  
H. B. Friedrich ◽  
D. M. Chipman
Keyword(s):  
Dipole Moment ◽  
Force Constants

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

2015 ◽  
Vol 113 (13-14) ◽  
pp. 1961-1977 ◽  
Author(s):  
Dmytro Bykov ◽  
Taras Petrenko ◽  
Róbert Izsák ◽  
Simone Kossmann ◽  
Ute Becker ◽  
...  
Keyword(s):  
Detailed Analysis ◽  
Efficient Implementation ◽  
Hartree Fock ◽  
Second Derivatives ◽  
Derivatives Of
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