Nonempirical
Anharmonic Vibrational Perturbation Theory
Applied to Biomolecules: Free-Base Porphin
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Abstract
Anharmonic
vibrational frequencies and intensities (infrared and
Raman) of an isolated free-base porphin molecule are predicted from
the quantum mechanical (QM) geometry, the “semi-diagonal”
quartic force field, and dipole moment and polarizability surfaces.
The second-order vibrational perturbation theory plus the numerical
diagonalization of the Hamiltonian matrix containing off-diagonal
Fermi and Darling–Dennison resonance couplings (VPT2+<i>WK</i>) was used. The QM calculations were carried out with
the Becke–Lee–Yang–Parr composite exchange–correlation
functional (B3LYP) and with the 6-31+G(d,p) basis set. The harmonic
force field for the equilibrium configuration was transformed into
nonredundant local symmetry internal coordinates, and normal coordinates
were defined. The semi-diagonal quartic rectilinear normal coordinate
potential energy surface (PES), as well as the cubic surfaces of dipole
moment (<i>p</i>) and polarizability (α) components,
needed for the VPT2+<i>WK</i> calculation, were constructed
by a five-point finite differentiation of Hessians (for PES) and of
the values and first derivatives of <i>p</i> and α.
They were obtained at the point of equilibrium and for 432 displaced
configurations. This theoretical approach provides very good agreement
between the predicted and experimental frequencies and intensities.
However, the favorable result can be partly attributed to error cancellation
within the B3LYP/6-31+G(d,p) QM model, as observed in earlier studies.
Reassignments of some observed bands are proposed