Nonempirical Anharmonic Vibrational Perturbation Theory Applied to Biomolecules: Free-Base Porphin

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

Vibrational spectroscopy of tolane; Coriolis coupling between Raman-active modes of <i>g</i> symmetry

<p>Vibrational spectroscopy of tolane (diphenylacetylene), which has 66 normal modes, has been advanced. Anharmonic wavenumber predictions were made with the quartic potential energy surface obtained with B3LYP/cc-pVTZ model and the second-order perturbation theory (VPT2). Infrared (IR) intensity and Raman activities were computed at the harmonic level. The IR spectrum of the crystal and Raman spectra of the liquid and the crystal tolane were newly recorded. The lingering problem of an excess of polarised Raman bands at wavenumbers appropriate for fundamentals, other than <i>a_g</i> modes, has now been attributed to Coriolis coupling within modes of <i>g</i> symmetry species. Consequently, <i>D_2h</i> point symmetry group has been confirmed for a planar tolane molecule. Assignments for almost all fundamentals of tolane are now secure. The assignment for ν₃₂ remains questionable. Remaining unassigned fundamentals are: ν₃₄ and ν₃₅, which, as <i>a_u</i> symmetry species, are IR- and Raman-inactive transitions, and ν₅₉(<i>b_2u</i>), which is predicted to have a very low wavenumber.</p

Anharmonic Vibrational Analysis of the Gas-Phase Infrared Spectrum of 1,1-Difluoroethylene Using the Operator Van Vleck Canonical Perturbation Theory

Anharmonic vibration frequencies of 1,1-difluoroethylene (11DFE) in the gas phase are predicted by means of the numerical-analytic operator version of the canonical van Vleck perturbation theory in the second and fourth orders (CVPT2 and CVPT4). The full quartic and “semi-diagonal” sextic rectilinear normal coordinate potential energy surfaces, needed for CVPT2 and CVPT4, respectively, were obtained with the MP2/cc-pVTZ quantum-mechanical model. CVPT2 is superior to the traditional second-order vibrational perturbation theory approach (VPT2) because of the uniform general treatment of the Fermi and second-order Darling–Dennison resonances. The fourth-order version, CVPT4, provides a more refined solution and proves convergence of the perturbative treatment. Labeling of the basis functions by polyad numbers breaks down the infinite Hamiltonian matrix into a block-diagonal form. The polyad expression for 11DFE has been determined as P = 14(ν1 + ν7) + 8ν2 + 6(ν3 + ν8) + 4(ν4 + ν9) + 3(ν6 + ν11 + ν12) + 2(ν5 + ν10), where the νi are quantum numbers. The theoretical prediction of anharmonic infrared absorption intensities corroborated an assignment of the majority of observed gas-phase bands up to 3500 cm–1. The solution was refined by iteratively fitting harmonic frequencies, until predicted fundamental anharmonic frequencies matched the observed values. The average error for about 90 observed frequencies after fitting only fundamental frequencies is ∼1.05 cm–1. The fitted “semi-experimental” harmonic frequencies agree very well the quantum-mechanical predictions based on the CCSD(T)/cc-pVTZ and CCSD(T)/cc-pVQZ models

Ab Initio Anharmonic Analysis of Vibrational Spectra of Uracil Using the Numerical-Analytic Implementation of Operator Van Vleck Perturbation Theory

The numerical-analytic implementation of the operator version of the canonical Van Vleck second-order vibrational perturbation theory (CVPT2) is employed for a purely <i>ab initio</i> prediction and interpretation of the infrared (IR) and Raman anharmonic spectra of a medium-size molecule of the diketo tautomer of uracil (2,4­(1<i>H</i>,3<i>H</i>)-pyrimidinedione), which has high biological importance as one of the four RNA nucleobases. A nonempirical, semidiagonal quartic potential energy surface (PES) expressed in normal coordinates was evaluated at the MP2/cc-pVTZ level of theory. The quality of the PES was improved by replacing the harmonic frequencies with the “best” estimated CCSD­(T)-based values taken from the literature. The theoretical method is enhanced by an accurate treatment of multiple Fermi and Darling–Dennison resonances with evaluation of the corresponding resonance constants <i>W</i> and <i>K</i> (CVPT2+<i>WK</i> method). A prediction of the anharmonic frequencies as well as IR and Raman intensities was used for a detailed interpretation of the experimental spectra of uracil. Very good agreement between predicted and observed vibrational frequencies has been achieved (RMSD ∼4.5 cm^–1). The model employed gave a theoretically robust treatment of the multiple resonances in the 1680–1790 cm^–1 region. Our new analysis gives the most reliable reassignments of IR and Raman spectra of uracil available to date

Anharmonic Vibrational Analysis of the Gas-Phase Infrared Spectrum of 1,1-Difluoroethylene Using the Operator Van Vleck Canonical Perturbation Theory

Anharmonic vibration frequencies of 1,1-difluoroethylene (11DFE) in the gas phase are predicted by means of the numerical-analytic operator version of the canonical van Vleck perturbation theory in the second and fourth orders (CVPT2 and CVPT4). The full quartic and “semi-diagonal” sextic rectilinear normal coordinate potential energy surfaces, needed for CVPT2 and CVPT4, respectively, were obtained with the MP2/cc-pVTZ quantum-mechanical model. CVPT2 is superior to the traditional second-order vibrational perturbation theory approach (VPT2) because of the uniform general treatment of the Fermi and second-order Darling–Dennison resonances. The fourth-order version, CVPT4, provides a more refined solution and proves convergence of the perturbative treatment. Labeling of the basis functions by polyad numbers breaks down the infinite Hamiltonian matrix into a block-diagonal form. The polyad expression for 11DFE has been determined as <i>P</i> = 14­(ν₁ + ν₇) + 8ν₂ + 6­(ν₃ + ν₈) + 4­(ν₄ + ν₉) + 3­(ν₆ + ν₁₁ + ν₁₂) + 2­(ν₅ + ν₁₀), where the ν_<i>i</i> are quantum numbers. The theoretical prediction of anharmonic infrared absorption intensities corroborated an assignment of the majority of observed gas-phase bands up to 3500 cm^–1. The solution was refined by iteratively fitting harmonic frequencies, until predicted fundamental anharmonic frequencies matched the observed values. The average error for about 90 observed frequencies after fitting only fundamental frequencies is ∼1.05 cm^–1. The fitted “semi-experimental” harmonic frequencies agree very well the quantum-mechanical predictions based on the CCSD­(T)/cc-pVTZ and CCSD­(T)/cc-pVQZ models

Anharmonic Vibrational Analysis of the Infrared and Raman Gas-Phase Spectra of s-trans - and s-gauche -1,3-Butadiene

A quantum-mechanical (hybrid MP2/cc-pVTZ and CCSD(T)/cc-pVTZ) full quartic potential energy surface (PES) in rectilinear normal coordinates and the second-order operator canonical Van Vleck perturbation theory (CVPT2) are employed to predict the anharmonic vibrational spectra of s-trans- and s-gauche-butadiene (BDE). These predictions are used to interpret their infrared and Raman scattering spectra. New high-temperature Raman spectra in the gas phase are presented in support of assignments for the gauche conformer. The CVPT2 solution is based on a PES and electro-optical properties (EOP; dipole moment and polarizability) expanded in Taylor series. Higher terms than those routinely available from Gaussian09 software were calculated by numerical differentiation of quadratic force fields and EOP using the MP2/cc-pVTZ model. The integer coefficients of the polyad quantum numbers were derived for both conformers of BDE. Replacement of harmonic frequencies by their counterparts from the CCSD(T)/cc-pVTZ model significantly improved the agreement with experimental data for s-trans-BDE (root-mean-square deviation approximate to 5.5 cm(-1)). The accuracy in predicting the rather well-studied spectrum of fundamentals of s-trans-BDE assures good predictions of the spectrum of s-gauche-BDE. A nearly complete assignment of fundamentals was obtained for the gauche conformer. Many nonfundamental transitions of the BDE conformers were interpreted as well. The predictions of multiple Fermi resonances in the complex CH-stretching region correlate well with experiment. It is shown that solving a vibrational anharmonic problem through a numerical-analytic implementation of CVPT2 is a straightforward and computationally advantageous approach for medium-size molecules in comparison with the standard second-order vibrational perturbation theory (VPT2) based on analytic expressions

Disentangling the IR spectra of 2,3,3,3-tetrafluoropropene using an ab initio description of vibrational polyads by means of canonical Van Vleck perturbation theory

The vibrational spectra of 2,3,3,3-tetrafluoropropene (2333TFP) are studied in the infrared experimentally and theoretically by the canonical second-order Van Vleck operator perturbation theory (CVPT2) and full quartic potential energy surface (PES). 2333TFP belongs to hydrofluoroolefins (HFOs) considered among the most promising alternatives to the hydrofluorocarbons presently in use in refrigeration. The medium resolution infrared spectra of gaseous 2333TFP were recorded in the range 9500–30 cm-1. The integrated IR intensities for all bands falling between 6300–400 cm-1 were accurately determined. Theoretical descriptions of up to four-quanta anharmonic vibrational states of 2333TFP are performed using the state-of-the-art numerical-analytic implementation of CVPT2. High quality harmonic frequencies, obtained at different coupled-cluster levels of theory up to the CCSD(T*)-F12c/VTZ-F12 model were combined with the full quartic MP2/cc-pVTZ anharmonic force field to form the hybrid PES. All Fermi and Darling-Dennison resonances were detected using a universal criterion and treated with the variational CVPT2/VCI stage by using two-, three-, and four-quanta harmonic oscillator basis sets. General recommendations for choosing such basis sets in future studies are formulated. In addition to all fundamentals and their resonance satellites, the vibrational analysis led to the assignment of virtually all observed first/second overtone and binary/ternary combination bands. Computed dipole moment first derivatives in the principal axis system yielded reliable predictions of band shapes for fundamental transitions in good agreement with observed counterparts. Computed anharmonic IR intensities showed an excellent agreement with observed data in the measured ranges. The fundamental spectroscopic effect of excited resonances is observed experimentally and explained theoretically as a universal mechanism of formation of vibrational polyads. The efficiency of the CVPT2/VCI approach employed is clearly demonstrated and can be considered as a benchmark for modeling vibrational states and interpretation of vibrational spectra of semi-rigid molecules

Molecular structure and conformation of nitrobenzene reinvestigated by combined analysis of gas-phase electron diffraction, rotational constants, and theoretical calculations

Dorofeeva OV, Vishnevskiy YV, Vogt N, et al. Molecular structure and conformation of nitrobenzene reinvestigated by combined analysis of gas-phase electron diffraction, rotational constants, and theoretical calculations. Structural Chemistry. 2007;18(6):739-753