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1.
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. 相似文献
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A method is proposed for fragment calculation of electronic structures of polyatomic molecules in the ground state. The wave
function of a molecule in the ground state in single-determinantal representation of a closed shell is employed. The concise
formulation allows efficient calculation of the electronic structures of polyatomic molecules taking into account possible
charge transfer between interacting molecular fragments.
V.I. Vernadskii Institute of Geochemistry and Analytical Chemistry, Russian Academy of Sciences. Translated fromZhurnal Struktumoi Khimii, Vol. 36, No. 3, pp. 387–394, May–June, 1995.
Translated by I. Izvekova 相似文献
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Dina L. Kinoshita Luiz G. Ferreira Manoel L. De Siqueira 《International journal of quantum chemistry》1985,28(1):85-101
This is the third paper on the cellular method for polyatomic systems. We show how to deal with nonspherical Coulomb potentials. We also show how to modify the variational expression for the energy eigenvalues so as to obtain a faster convergence in the angular momentum series for the wavefunctions. We apply both techniques to the self-consistent calculation of SF6. Contrary to what we obtained in CH4 and SiH4, the cellular method cannot yield the correct equilibrium interatomic distance in the present case. The calculated ionization potentials are in the correct order but are all shifted by 2–3 eV. This shift is attributed to the wrong expression for exchange correlation. 相似文献
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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. 相似文献
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The calculation of the vibrational structure associated to electronic spectra in large molecules requires a Taylor expansion of the initial and final state potential energy surface (PES) around some reference nuclear structure. Vertical (V) and adiabatic (A) approaches expand the final state PES around the initial-state (V) or final-state (A) equilibrium structure. Simplest models only take into account displacements of initial- and final-state minima, intermediate ones also allow for difference in frequencies and more accurate models introduce the Dushinsky effect through the computation of the Hessians of both the initial and final state. In this contribution we summarize and compare the mathematical expressions of the complete hierarchy of V and A harmonic models and we implement them in a numerical code, presenting a detailed comparison of their performance on a number of prototypical systems. We also address non-Condon effects through linear expansions of the transition dipole as a function of nuclear coordinates (Herzberg-Teller effect) and compare the results of expansions around initial and final state equilibrium geometries. By a throughout analysis of our results we highlight a number of general trends in the relative performance of the models that can provide hints for their proper choice. Moreover we show that A and V models including final state PES Hessian outperform the simpler ones and that discrepancies in their predictions are diagnostic for failure of harmonic approximation and/or of Born-Oppenheimer approximation (existence of remarkable geometry-dependent mixing of electronic states). 相似文献
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Using contact transformation perturbation method based on the Taylor expansion of the potential energy function in terms of dimensionless normal coordinates up to sixth‐order, the vibrational energy levels in terms of force constants are derived. The contact transformation theory has been applied to simplify the calculation of perturbation effects. To calculate the second‐order vibrational energy correction, the third and fourth‐order terms of potential function have been placed in the first‐order perturbation Hamiltonian and the second‐order Hamiltonian contains hexatic ones. We present expressions which give relations between the fourth‐ and sixth‐order terms in dimensionless normal coordinates of the potential and the anharmonicity coefficients. For illustration, a set of vibrational energies levels of SO2, and H2O molecules including anharmonic effects has been calculated. © 2013 Wiley Periodicals, Inc. 相似文献
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Quantum chemical predictions of the vibrational spectra of polyatomic molecules. The uracil molecule and two derivatives 总被引:1,自引:0,他引:1
Palafox MA Rastogi VK 《Spectrochimica acta. Part A, Molecular and biomolecular spectroscopy》2002,58(3):411-440
This work describes the different scaling procedures used to correct the quantum-chemical theoretical predictions of the IR and Raman vibrational wavenumbers. Examples of each case are shown, with special attention to the uracil molecule and some derivatives. The results obtained with different semiempirical and ab initio methods, and basis sets, are compared and discussed. A comprehensive compendium of the main scale factors and scaling equations available to obtain the scaled wavenumbers is also shown. 相似文献
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A. I. Pavlyuchko 《Journal of Structural Chemistry》1995,36(2):204-209
A method of variational solution of anharmonic vibration problems using a mixed Morse—anharmonic basis is proposed. The basis
functions are the products of the Morse oscillator eigenfunctions for vibrations of peripheral bonds, the harmonic oscillator
eigenfunctions for almost harmonic skeletal and deformation vibrations, and the anharmonic basis functions for essentially
anharmonic skeletal and deformation vibrations. The anharmonic basis wave functions are taken as a linear combination of the
Morse and harmonic oscillator eigenfunctions. The introduction of the combined Morse—anharmonic functions allows one to factorize
the solution of a problem into a series of individual blocks according to the fragmentary structure of molecules.
Volgograd Pedagogical University. Translated fromZhurnal Strukturnoi Khimii, Vol. 36, No. 2, pp. 231–238, March–April, 1995.
Translated by I. Izvekova 相似文献
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The potential function of some molecules of type XHn has been obtained by a priori calculations of the total energy, within the Born Oppenheimer approximation, for several geometrical configurations. These functions have been used to calculate the simply excited vibrational levels. The calculated values of the electric dipole moment for the different geometrical configurations has enabled the computation of its derivative with respect to the nuclear coordinates. The results reported are critically discussed and some explanations are presented to justify the discrepancies found with the experimental data.
Zusammenfassung Mittels einer apriorischen Berechnung der Gesamtenergie nach der Born-Oppenheimer-Methode ist die Potentialfunktion für einige Moleküle der Art XHn in verschiedenen Konfigurationen erhalten worden. Diese Funktionen sind für die Berechnung der monoerregten SchwingungszustÄnde gebraucht worden. Die berechneten Werte des elektrischen Dipolmoments für verschiedene Geometrien haben die Berechnung der Ableitungen des Dipolmoments nach den Kernkoordinaten erlaubt. Die erhaltenen Resultate werden diskutiert und einige ErklÄrungen vorgeführt, um die gefundenen Unterschiede von den experimentellen Ergebnissen zu klÄren.
Résumé La fonction potentiel de quelques molécules XHn a été obtenue par le calcul a priori de l'énergie moléculaire, dans l'approximation de Born et Oppenheimer, pour plusieures configurations géométriques. Ces fonctions ont été utilisées pour calculer les vibrations monoexcitées. Les valeurs calculées du moment de dipole électrique pour différentes configurations donnent la possibilité de calculer ses dérivées par rapport aux coordonées nucléaires. On donne des justifications a l'accord peu satisfaisant entre les résultats et l'expérience.相似文献
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Antonio Hidalgo Jos Zúiga Jos M. Francs Adolfo Bastida Alberto Requena 《International journal of quantum chemistry》1991,40(5):685-694
A self-consistent field optimization of the vibrational coordinates for nonlinear triatomic molecules is presented. The optimal coordinates are obtained by making a three-dimensional rotational transformation of the normal modes and determining the rotation angles as those for which the SCF energy is stationary. The utility of the optimized coordinates in full variational calculations of vibrational energies is studied for the molecules of H2O, O3, H2D+, H2T+, and D2T+. For H2O and O3, the optimization procedure leads to the local mode representation. It is shown that the use of the optimal coordinates in variational calculations allows a large reduction of the dimension of the Hamiltonian matrix to be diagonalized in order to reach convergence. 相似文献
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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 相似文献
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An approximate method to calculate overlap integrals of vibrational wave functions of combined electron states is proposed.
It uses reducibility of the general transformation of normal coordinates and quasiorthogonality of the Dushinsky matrix. Simple
analytical expressions and convenient recurrent relations for the desired integrals of Franck-Condon and Herzberg-Teller types
are found. The errors of calculation are of the same order as those of the existing “accurate” methods (≤5%), and the speed
of calculation is higher by more than two orders.
The study was carried out under financial support of the Russian Fundamental Research Fund (93-02-3405).
K. A. Timiryazev Moscow Agricultural Academy. Translated fromZhurnal Strukturnoi Khimii, Vol. 35, No. 2, pp. 16–23, March–April, 1994.
Translated by L. Chernomorskaya 相似文献
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《Chemical physics letters》1987,140(2):133-141
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. 相似文献
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An ab initio method is developed for variational grand-canonical molecular electronic structure of open systems based on the Gibbs-Peierls-Boguliobov inequality. We describe the theory and a practical method for performing the calculations within standard quantum chemistry codes using Gaussian basis sets. The computational effort scales similarly to the ground-state Hartree-Fock method. The quality of the approximation is studied on a hydrogen molecule by comparing to the exact Gibbs free energy, computed using full configuration-interaction calculations. We find the approximation quite accurate, with errors similar to those of the Hartree-Fock method for ground-state (zero-temperature) calculations. A further demonstration is given of the temperature effects on the bending potential curve for water. Some future directions and applications of the method are discussed. Several appendices give the mathematical and algorithmic details of the method. 相似文献
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A semiempirical parametric method for calculating the vibrational structure of the electronic spectra of polyatomic molecules
is developed; the method is based on the adiabatic molecular model and uses a single parametric system for all excited states.
Within the model approach, simplified analytical expressions for potential surface variation during molecular excitation are
derived; the expressions include the principal terms according to the order of magnitude. The first and second derivatives
of Coulomb and resonance one-electron integrals with respect to natural coordinates in a basis set of hybrid atomic orbitals
are used as parameters. It is shown that the parameters possess distinct locality, are transferable in molecular series, and
may be easily ranked according to absolute values; describing a molecular model requires few most significant parameters.
Excitation-induced variations of potential surfaces and absorption spectra of some molecules (butadiene, hexatriene, octatetraene)
are calculated using only two parameters, which are the same for all molecules. The results of calculations are in good agreement
with the experimental data.
Supported by RFFR grant No. 95-03-08808.
V.I. Vernadskii Institute of Geochemistry and Analytical Chemistry, Russian Academy of Sciences. Translated fromZhumal Struckturnoi Khimii, Vol. 37, No. 3, pp. 419–431, May–June, 1996. 相似文献
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《Chemical physics》1986,104(1):19-28
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. 相似文献