N. F. Stepanov

Ar–I2 interactions: The models based on the diatomics‐in‐molecule approach

Semiempirical model is developed for studying the electronic structure of the rare gas atom–halogen molecule systems. It is formulated in the frame of diatomics‐in‐molecule (DIM) approach and takes explicitly into account strong spin–orbit coupling pertinent to heavy halogen molecules. The consistent DIM scheme is realized for intermolecular interactions, whereas the description of valence electronic states of halogen molecule is more approximate being based on the asymptotic wave functions. The corresponding perturbation theory is also put forward. The model is applied to analysis of several features of the Ar...I2 van der Waals complex. First, the calculations on the spectroscopic constants of the B←X transition in the complex reveal the quantitative performance of the model. Second, mechanisms of nonadiabatic dynamics are examined. The results are qualitatively consistent with the current view on the Ar...I2 electronic predissociation and one‐atom cage effect. Third, the prediction is made on the valen...

Numerical-Analytic Implementation of the Higher-Order Canonical Van Vleck Perturbation Theory for the Interpretation of Medium- Sized Molecule Vibrational Spectra

Anharmonic vibrational states of semirigid polyatomic molecules are often studied using the second-order vibrational perturbation theory (VPT2). For efficient higher-order analysis, an approach based on the canonical Van Vleck perturbation theory (CVPT), the Watson Hamiltonian and operators of creation and annihilation of vibrational quanta is employed. This method allows analysis of the convergence of perturbation theory and solves a number of theoretical problems of VPT2, e.g., yields anharmonic constants y(ijk), z(ijkl), and allows the reliable evaluation of vibrational IR and Raman anharmonic intensities in the presence of resonances. Darling-Dennison and higher-order resonance coupling coefficients can be reliably evaluated as well. The method is illustrated on classic molecules: water and formaldehyde. A number of theoretical conclusions results, including the necessity of using sextic force field in the fourth order (CVPT4) and the nearly vanishing CVPT4 contributions for bending and wagging modes. The coefficients of perturbative Dunham-type Hamiltonians in high-orders of CVPT are found to conform to the rules of equality at different orders as earlier proven analytically for diatomic molecules. The method can serve as a good substitution of the more traditional VPT2.

Criteria for first- and second-order vibrational resonances and correct evaluation of the Darling-Dennison resonance coefficients using the canonical Van Vleck perturbation theory

The second-order vibrational Hamiltonian of a semi-rigid polyatomic molecule when resonances are present can be reduced to a quasi-diagonal form using second-order vibrational perturbation theory. Obtaining exact vibrational energy levels requires subsequent numerical diagonalization of the Hamiltonian matrix including the first- and second-order resonance coupling coefficients. While the first-order Fermi resonance constants can be easily calculated, the evaluation of the second-order Darling-Dennison constants requires more complicated algebra for seven individual cases with different numbers of creation-annihilation vibrational quanta. The difficulty in precise evaluation of the Darling-Dennison coefficients is associated with the previously unrecognized interference with simultaneously present Fermi resonances that affect the form of the canonically transformed Hamiltonian. For the first time, we have presented the correct form of the general expression for the evaluation of the Darling-Dennison constants that accounts for the underlying effect of Fermi resonances. The physically meaningful criteria for selecting both Fermi and Darling-Dennison resonances are discussed and illustrated using numerical examples.

ArHF vibrational predissociation dynamics using the diatomics-in-molecule potential energy surface

Vibrational predissociation dynamics of ArHF and ArDF complexes is investigated theoretically for the first time owing to the use of three-dimensional potential energy surfaces (PES’s) based on the diatomics-in-molecule approach [J. Chem. Phys. 104, 5510 (1996)]. The original PES is improved empirically to yield a reasonable description of the lowest vibrational energy levels of the ArHF complex at J=0. Predissociation dynamics is studied by means of line shape and diabatic Fermi Golden Rule methods. The latter is found to provide excellent results for the total decay widths but only a qualitative estimate for the product rotational distributions. It is shown that predissociation dynamics is governed by vibrational to rotational energy transfer. The decay proceeds almost entirely into the highest accessible rotational product channel. This propensity manifests itself in the decrease of the predissociation lifetime upon increasing vibrational excitation of the diatomic fragment when the highest rotational ...

Diatomics-in-molecules description of the Rg–Hal2 rare gas–halogen van der Waals complexes with applications to He–Cl2

The diatomics-in-molecules (DIM) technique is applied for a description of the low-lying states of the Rg–Hal2 van der Waals complexes correlating with the lowest states of constituent atoms Rg(1S)+Hal(2Pj)+Hal(2Pj). The important feature of this approach is the construction of polyatomic basis functions as products of the Hal2 diatomic eigenstates classified within the Hund “c” scheme and the atomic rare gas wave function. Necessary transformations to the other basis set representations are described, and finally all the matrix elements are expressed in terms of nonrelativistic adiabatic energies of Hal2 and Rg Hal fragments and spin-orbit splitting constant of the halogen atom. Our main concern is to test the DIM-based approximations of different levels taking the He–Cl2 system as an example. Namely, we have compared the results obtained within a hierarchy of approaches: (1) the simplest pairwise potential scheme as a far extreme of the DIM model, (2) the same as (1) but with the different components (Σ...

Polyad quantum numbers and multiple resonances in anharmonic vibrational studies of polyatomic molecules

In the theory of anharmonic vibrations of a polyatomic molecule, mixing the zero-order vibrational states due to cubic, quartic and higher-order terms in the potential energy expansion leads to the appearance of more-or-less isolated blocks of states (also called polyads), connected through multiple resonances. Such polyads of states can be characterized by a common secondary integer quantum number. This polyad quantum number is defined as a linear combination of the zero-order vibrational quantum numbers, attributed to normal modes, multiplied by non-negative integer polyad coefficients, which are subject to definition for any particular molecule. According to Kellmans method [J. Chem. Phys. 93, 6630 (1990)], the corresponding formalism can be conveniently described using vector algebra. In the present work, a systematic consideration of polyad quantum numbers is given in the framework of the canonical Van Vleck perturbation theory (CVPT) and its numerical-analytic operator implementation for reducing the Hamiltonian to the quasi-diagonal form, earlier developed by the authors. It is shown that CVPT provides a convenient method for the systematic identification of essential resonances and the definition of a polyad quantum number. The method presented is generally suitable for molecules of significant size and complexity, as illustrated by several examples of molecules up to six atoms. The polyad quantum number technique is very useful for assembling comprehensive basis sets for the matrix representation of the Hamiltonian after removal of all non-resonance terms by CVPT. In addition, the classification of anharmonic energy levels according to their polyad quantum numbers provides an additional means for the interpretation of observed vibrational spectra.

First-order intermolecular diatomics-in-molecule potentials. Potential energy surfaces, spectra, and fragmentation dynamics of the Ne⋯Cl2 complex

First-order perturbative approximations to the diatomics-in-molecule (DIM) approach are implemented for studying interactions between the neon atom and chlorine molecule in the X 1Σg+(0+) and B 3Πu(0+) states. Intermolecular DIM perturbation theory (IDIM PT1) [J. Chem. Phys. 104, 9913 (1996)], which accounts for the atomic component of spin-orbit interaction, is compared to the anisotropic model by Naumkin and Knowles [J. Chem. Phys. 103, 3392 (1995)] which is proven to be a first-order approximation to the nonrelativistic DIM approach. An importance of the spin-orbit effects for the ground-state potential energy surface (PES) is demonstrated. Semiempirical PESs are used in the accurate quantum calculations on the vibrationally averaged geometry, B←X vibronic spectra, and vibrational predissociation dynamics of the Ne⋯Cl2 van der Waals complex. The IDIM PT1 model is shown to provide good agreement with available experimental data. The effects of interaction potential topology on the spectroscopic and dyna...

Anharmonic Force Fields and Perturbation Theory in the Interpretation of Vibrational Spectra of Polyatomic Molecules

The problem of describing real vibrational spectra of large molecules in terms of perturbation theory is considered. Equations necessary for presenting theoretical anharmonic force fields in various coordinate systems (Cartesian, normal, and internal curvilinear) are discussed. A review of second-order perturbation theory equations necessary for calculating certain spectroscopic values (anharmonicity constants, rotational-vibrational interaction, etc.) is given. A scheme for including resonances based on the construction of the interaction matrix between vibrational transitions of various types is described. This scheme can be used as a basis for anharmonic calculations of vibrations of medium-sized molecules.

Structure and interaction energies of the Ar…Cl2 complex. Application of first-order intermolecular potentials

Abstract The first-order intermolecular perturbation theory developed in the frame of a diatomics-in-molecule approach is used to calculate the potential energy surfaces for the Ar…Cl 2 complex in the states which correlate with the X 0 g + ( 1 Σ + ) and B 0 u + ( 3 Π) states of the Cl 2 fragment. Accurate vibrational calculations performed directly with these surfaces reveal close agreement with spectroscopic data.

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 ≈ 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.