Fragment calculation of electronic structures of polyatomic molecules in the ground state. II. A method of delocalized states of fragments

A fragment method is proposed to calculate the electronic structures of polyatomic molecules in the ground state. Localization and delocalization of the electronic states of molecular fragments are calculated simultaneously. The compact formulation of the method allows algorithmically efficient calculations of the electronic structures of interacting molecular fragments as well as of the whole molecules. V. I. Vernadskii Institute of Geochemistry and Analytical Chemistry, Russian Academy of Sciences. Translated fromZhurnal Struktumoi Khimii, Vol. 36, No. 3, pp. 395–400, May–June, 1995. Translated by I. Izvekova     

Variational method for the calculation of the vibrational structure of the electronic spectra of polyatomic molecules. I

A method is proposed to calculate the vibrational structures of the electronic spectra of polyatomic molecules based on the variational solution of the vibrational problem in the excited state with the vibrational wave functions of the ground state as basis set. The electrono-vibrational problem leads to an evaluated and diagonalized variational matrix. The elements of the variational matrix have a simple form which is easily evaluated, has a clear physical meaning and is directly interconnected with observed spectral effects. This allows preliminary estimation of spectral phenomena and correction of the molecular model to take account of experimental results. The use of contemporary methods of diagonalization of the variational matrix, which possesses a characteristic structure, facilitates a tenfold increase in the speed of the method in comparison with traditional methods.K. A. Timiryazev Agricultural Academy. Translated from Zhurnal Strukturnoi Khimii, Vol. 34, No. 1, pp. 141–148, January–February, 1993.     

Variational method for the calculation of the vibrational structure of the electronic spectra of polyatomic molecules. II

A variational method has been developed to solve the vibrational problem in the excited electronic state and to calculate the vibrational structure of the electronic spectrum of polyatomic molecules. The properties and structural characteristics of the variational matrix have been analyzed and an effective algorithm has been proposed for its approximate diagonalization. The effectiveness of the method and the corresponding suite of programs for the personal computer have been analyzed via the results of model calculations for a number of molecular structures. The method has high precision (errors of about 5% for frequencies and 15% for relative intensities), is an order of magnitude faster than previously used methods, and provides the possibility for the effective solution of the electrono-vibrational problem for polyatomic molecules, including the reverse problem.K. A. Timiryazev Agricultural Academy. Translated from Zhurnal Strukturnoi Khimii, Vol. 34, No. 1, pp. 149–156, January–February, 1993.     

Perturbation calculation of correlation energies for polyatomic molecules I. Initial results

The calculation of correlation energies for polyatomic molecules is discussed. Four second-order perturbation expressions are considered; only the simplest, a Rayleigh-Schroedinger expansion with the Moller-Plesset partitioning of the Hamiltonian is invariant to an arbitrary mixing of degenerate orbitals and has the correct dependence on the number of particles. In the absence of degeneracies an iterative Brillouin-Wigner method is proposed. Calculations predict that correlation effects favor the non-classical form of carbonium ions.     

Model calculation on the pump-probe measurement of ultrafast electronic population decay in polyatomic molecules

We consider the common situation of strong vibronic coupling of an optically bright (in absorption from the ground state) excited electronic state to a lower-lying dark electronic state in a polyatomic molecule. It is shown that for sufficiently short pump and probe laser pulses a time-resolved experiment measures the total time-dependent population probability P(t) of the bright state. For a realistic model problem (representing the three lowest electronic states of the benzene cation) a conical intersection of the potential energy surfaces of the bright and the dark state causes an ultrafast initial decay of P(t) on a femtosecond time scale, followed by quasiperiodic recurrences. These recurrences show up as femtosecond quantum beats in the time-resolved pump-probe signal. The beating frequency is related to the vibrational frequency of the dominant accepting mode of the system.     

Semiclassical calculation of energy transfer in polyatomic molecules. XII. Organic molecules

A semiclassical method for energy transfer to the torsional motion of polyatomic molecules is presented. It is shown that a purely classical treatment of the torsional motion is problematic due to the zero-point vibrational energy which may migrate into other modes. State-to-state cross sections for the excitation of the CH₃ torsion in CH₃OH colliding with ⁴He are presented as a function of initial kinetic energy.     

Theory of radiationless transitions in polyatomic molecules. The intermediate case

A theory of radiationless transitions that spans the intermediate case between the small “molecule” and “big molecule” limits is presented. The theory is applicable to spectra and picosecond time evolution experiments concerning states such as the vibronically perturbed second excited single state of naphtalene studied by Wessel. An important philosophy used in the paper is the “unbunding” of the time-dependent and stationary state aspects of this problem. This view has been strongly emphasized by Rhodes and allows each part of the problem to be handled separately without being limited by the approximations of the other. The single-sharp-level-embedded-in-a-continuum model is used, and the stipulation that the sharp level carries all the oscillator strength is retained. However no limiting restrictions are placed on the nature of the continuum nor the interaction matrix elements. Thus the theory encompasses both the statistical limit and the small molecule limit as well as all cases intermediate between these and should therefore be of more interest to the experimentalist. The exact Green function for this problem is obtained, allowing the observed absorption spectrum and time evolution experiments under various excitation conditions to be exactly related in a practical way. Transformation between an observed spectrum and unperturbed zero-order states is possible and should be of use to the spectroscopist when trying to analyze spectra in regions of massive perturbative mixing.     

Photochemistry in the electronic ground state. Isotope separation by infrared multiphoton isomerization of complex molecules

Isotope selective isomerization of hexafluorocyclobutene to hexafluorobutadiene by multiphoton absorption of infrared laser light has been studied. All the three possible isotopomers were separated. The wavelength dependence of the reactions, saturation of absorption and the role of inert gas in retaining the selectivity are described.     

Non-adiabatic unimolecular dissociation of polyatomic molecules. I. General theory

A golden-rule expression for the rate constant for unimolecular dissociation of a polyatomic molecule via a non-adiabatic process is expressed, in the harmonic oscillator approximation, in terms of a diatomic-like predissociation rate constant (k^diat), which contains all the electronic part of the dynamics of the process, and in terms of a product of (3N - 7) Frank—Condon factors. The influence of a difference in the equilibrium geometries of the initial and final electronic states is pointed out. A suitably averaged rate constant is defined, and it is shown that the shortcomings of the separable hamonic oscillator model can be usefully corrected by appropriate rate constant averaging, which allows for the effect of anharmonicity as well as for the non-separability and possibly poor choice of normal coordinates. The theory presented is suitable for calculating rate constants in cases where information regarding enery partitioning among fragments is not required.     

Localized electron pair theory for the calculation of ground state energies of large molecules

The quantum mechanical energy is examined in which groups of one, two, three, and four localized electron pairs found within a molecule are separately computed. From these results, the interaction energies of the electron pairs taken one, two, three, and four at a time form the terms of a convergent molecular mechanics like expansion of the molecular ground state energy. This procedure can be used with any size consistent quantum mechanical method. The computational time for large molecules depends chiefly upon the order needed in the energy expansion to obtain sufficient convergence and not on the particular quantum mechanical method used. Preliminary results within the framework of a semiempirical CNDO/2 model Hamiltonian show at the Hartree–Fock and Møller–Plesset perturbation levels that relative energies converge to within a few tenths of a kcal/mol of the exact values at the four body level for molecules that have little delocalization. In strained ring and aromatic systems, convergence is however not nearly as rapid. Results can be improved somewhat by using larger interacting fragments containing two or more electron pairs over three or more atomic centers. © 1992 by John Wiley & Sons, Inc.     

On the vibronic level structure in the NO3 radical. I. The ground electronic state

The model Hamiltonian approach of Koppel et al. [Adv. Chem. Phys. 57, 59 (1984)] is used to analyze the electronic spectroscopy of the nitrate radical (NO3). Simulations of negative ion photodetachment of NO3-, the X 2A2'<--B 2E' dispersed fluorescence spectrum of NO3, and the B 2E'<--X 2A2' absorption spectrum are all in qualitative agreement with experiment, indicating that the model Hamiltonian contains most or all of the essential physics that govern the strongly coupled X 2A2' and B 2E' electronic states of the radical. All 14 bands seen in the dispersed fluorescence spectrum below 2600 cm-1 are assigned based on the simulations, filling in a few gaps left by previous work, and 7 additional bands below 4000 cm-1 are tentatively assigned. The assignment is predicated on the assumption that the nu3 level of NO3 is near 1000 cm-1 rather than 1492 cm-1 as is presently believed. Support for this reassignment (which associates the 1492 cm-1 band with the nu1+nu4 level) comes from both the model Hamiltonian spectrum and a Fourier-transform infrared feature at 2585 cm-1 that is consistent with the large and positive cross anharmonicity between nu1 and nu4 needed for the alternative 1492 cm-1 assignment. An apparent systematic deficiency exists in the treatment of the model Hamiltonian for levels involving nu4. A discussion of the correlation between energy levels in the rigid D3h and C2v limits is illustrative, and provides insight into just how hard it is to treat the degenerate bending coordinate (q4) of NO3 accurately.     

The calculation of excited state and ground state properties of conjugated heteroatomic molecules using a single SCF-LCAO-CI method including σ-polarization

An SCF-π method including variable π-electronegativity and σ-polarization is described and applied to the calculation of electronic transitions and ionization potentials of a large variety of heteroatomic molecules containing boron, nitrogen, oxygen, fluorine, chlorine, and sulfur. The necessary atomic parameters are the Slater effective nuclear charges and published ionization potentials, electron affinities and σ-orbital electronegativities for trigonally hybridized atoms. The program automatically adjusts the initial atomic parameters to reflect the molecular environment without the intervention of the user. The agreement between calculated and observed transition energies, oscillator strengths and ionization potentials is very good.     

Large amplitude vibration in polyatomic molecules. I. A polar representation of orthogonal relative coordinates

A general expression for the rovib kinetic energy operator in a system of orthogonal internal coordinates is derived for arbitrary amplitudes of motion. Plots of the molecular potential in such coordinates serve to determine coordinate subsets in which the potential approaches separability. A revision of previous theory for the three-body problem is presented. A rovib hamiltonian for non-branched four-atom molecules (such as C₂H₂) is derived. Certain features of application to polyatomic (five-atom) molecules are considered.     

A method for the calculation of transition moments between electronic states of molecules using a different one-electron basis set for each state

A state-specific approach to the calculation of transition moments between molecular electronic states requires that the wavefunction for each state is expanded in its optimum one-electron basis and that nonorthonormal basis techniques are used for the calculation of the transition moment integrals. A method has been developed for carrying out such nonorthonormal basis calculations, based on the corresponding orbitals transformation and appropriately defined density matrices, which may be used with configuration interaction (CI ) wavefunctions. Further improvements of the method have resulted in a decrease in the time required for the calculations and thus allow its application with moderately large CI expansions for each state. Nonorthonormal basis calculations on transition moments in H₂O have been carried out using the above method. The results are in agreement with those of large MRD -CI calculations.