TY - JOUR

T1 - Analytical second derivatives in ab initio Hartree-Fock crystal orbital theory of polymers

AU - Hirata, So

AU - Iwata, Suehiro

N1 - Funding Information:
One of the authors (S.H.) is indebted to the Japan Society for the Promotion of Science for a Research Fellowship for Young Scientists. The present work was partly supported by the Grant-in-Aids for Scientific Research (A) (No. 09304057) by the Ministry of Education, Science, and Culture, Japan.

PY - 1998/9/28

Y1 - 1998/9/28

N2 - In the framework of ab initio Hartree-Fock crystal orbital theory of polymers, the formulas for the analytical second derivatives of energy with respect to in-phase (k = 0) nuclear coordinates are derived. The coupled perturbed Hartree-Fock (CPHF) equation is iteratively solved by using the direct (recomputation of two-electron integrals) atomic-orbital-based algorithm. Frequencies of the Brillouin zone center (k = 0) vibrations of all-trans polyethylene are calculated by using the STO-3G, 3-21G and 6-31G* basis sets. The dependence of the frequencies on the number of neighbors included in the lattice summations, on the number of momentum sampling points in the first Brillouin zone, and on the convergence criterion for the CPHF solutions is examined. In our implementation, the use of analytical second derivatives is more efficient than the use of the finite differences of analytical first derivatives.

AB - In the framework of ab initio Hartree-Fock crystal orbital theory of polymers, the formulas for the analytical second derivatives of energy with respect to in-phase (k = 0) nuclear coordinates are derived. The coupled perturbed Hartree-Fock (CPHF) equation is iteratively solved by using the direct (recomputation of two-electron integrals) atomic-orbital-based algorithm. Frequencies of the Brillouin zone center (k = 0) vibrations of all-trans polyethylene are calculated by using the STO-3G, 3-21G and 6-31G* basis sets. The dependence of the frequencies on the number of neighbors included in the lattice summations, on the number of momentum sampling points in the first Brillouin zone, and on the convergence criterion for the CPHF solutions is examined. In our implementation, the use of analytical second derivatives is more efficient than the use of the finite differences of analytical first derivatives.

KW - Ab initio Hartree-Fock crystal orbital theory

KW - All-trans polyethylene

KW - Analytical second derivative method

KW - Harmonic vibrational frequencies

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U2 - 10.1016/S0166-1280(98)00165-1

DO - 10.1016/S0166-1280(98)00165-1

M3 - Article

AN - SCOPUS:0001096435

SN - 0166-1280

VL - 451

SP - 121

EP - 134

JO - Journal of Molecular Structure: THEOCHEM

JF - Journal of Molecular Structure: THEOCHEM

IS - 1-2

ER -