Simple and accurate method to evaluate tunneling splitting in polyatomic molecules

A practical and accurate semiclassical method for calculating the tunneling splitting of the ground state in polyatomic molecules is presented based on a recent version of the instanton theory [J. Chem. Phys. 115, 6881 (2001)]. The method uses ab initio quantum chemical data for the potential energy surface without any concomitant extrapolation and requires only a small number of ab initio data points to get convergence even for large molecules. This enables one to use an advanced level of electronic structure theory and achieve a high accuracy of the result. The method is applied to the 9-atomic malonaldehyde molecule by making use of the potential energy surface at the level of CCSD(T) with the hybrid basis set of aug-cc-pVTZ (for oxygen atoms and the transferred hydrogen atom) and cc-pVTZ (for other atoms).     

Ab initio molecular dynamics approach to tunneling splitting in polyatomic molecules

An ab initio molecular dynamics approach is combined with the semiclassical tunneling method of Makri and Miller, which is applied to estimations of tunneling splitting in the umbrella inversion of ammonia and the intramolecular hydrogen transfer in malonaldehyde. In the application to malonaldehyde, effects of multidimensionality are examined by assigning quantum zero-point energies only to significant vibrational modes and changing the amount of energy given to other degrees of freedom. The calculated tunneling splitting values are in good agreement with the corresponding experimental values for both molecules.     

Quantum theory of photodissociation of polyatomic molecules: Application to HCN

A theory of direct collinear photodissociation is presented wherein the correct and different normal modes appropriate to the initial molecular state and the photofragments are employed. This remedies a serious deficiency in previous theories which assume that the reaction coordinates for the photodissociation is also a normal mode in the initial electronic state and that the remaining normal modes are the same for both. The theory provides an analytical expression for the vibrational energy distribution of the photofragments, and provides simple criteria for the occurrence of population inversions. Calculated vibrational distributions for HCN photodissociation are in agreement with experiment.     

Peculiarities of the non-radiative decay of a single vibronic level in polyatomic molecules

Optical selection experiments in the first excited singlet state of the benzophenone molecule in solution confirm a theoretical prediction concerning the retardation of the electronic relaxation rate with increasing the excess vibrational energy in excited electronic states of a large molecule characterized by a small electronic energy gap.     

To the theory of electron scattering by polyatomic molecules

Within the Born-Oppenheimer adiabatic perturbation theory, an equation was obtained for the intensity of fast electron scattering by polyatomic molecules. All of its parameters are explicitly defined by vibronic interaction in a molecule; due to this, quantum chemical calculations are fully applicable to electron diffraction studies of molecular geometries. Engels Anti-Aircraft Missile Higher Military School. Translated fromZhurmal Strukturnoi Khimii, Vol. 35, No. 2, pp. 40–45, March–April, 1994. Translated by L. Smolina     

On the theory of processes in reaction centers of polyatomic molecules

Based on general principles of quantum theory of chemical transformations for polyatomic molecules, the notion of the reaction center (RC) was revised. The presence of RCs is a necessary condition for occurrence of all types of chemical transformations in complex systems. The physical picture of processes in RCs, conditions for maximum probability of transformations, the local character of a chemical reaction and its relation to the characteristic vibrations, and the methods of a priori search for RCs based on normal coordinate analysis of coupled states and on calculations of overlap integrals between vibrational wave functions were studied. Specific features of manifestation of characteristic vibrations in vibrational and vibronic spectra were investigated and the possibility of search for RCs using optical spectroscopy was considered. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 8, pp. 1267–1273, August, 2006.     

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.     

On the theory of collision-induced vibrational transitions in polyatomic molecules: The mode-matching model

A modification of the SSH theory for collision-induced vibrational transitions in polyatomic molecules is proposed. The breathing-sphere model assumptions are avoided by considering the angular relation between the direction of approach and the normal modes displacements of the atoms involved in the contract (mode-matching). The results, as compared to the breathing-sphere model, indicate a considerable, mode specific reduction of the transition probabilities. Intramolecular transitions of CH₃Cl are studied as an example.     

Semiempirical parametric method in the theory of vibronic spectra of polyatomic molecules

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.     

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.     

Perturbation theory for excited states of molecules

Components of the electric polarizability tensor are calculated for a number of conjugated hydrocarbons. The methods of calculation used were the configuration interaction perturbation theory and the single configuration perturbation theory introduced in paper 1. The results obtained are compared with experiment and with Hückel calculations. It is found that there is some ambiguity in the experimental evidence. The - separability approximations are discussed and the relationship between Hückel theory and the single configuration method is examined.

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Zusammenfassung Die Komponenten des elektrischen Polarisierbarkeitstensor werden für eine Anzahl konjugierter Moleküle mittels a) einer CI-Störungstheorie und b) einer auf einer einzelnen Konfiguration basierenden Störungstheorie berechnet. Die Resultate werden sowohl mit denen der Hückeltheorie als auch mit dem Experiment verglichen, wobei der letztere Vergleich nicht ganz eindeutig ist. Die -- Separabilität wird diskutiert und die Relation zwischen der Hückeltheorie und der durchgeführten Störungsrechnung untersucht.

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Résumé Les composantes du tenseur de polarisabilité électrique sont calculées pour un certain nombre d'hydrocarbures conjugés. Les méthodes de calcul utilisées ont été celles présentées dans l'article 1: théorie des perturbations multi ou mono configurationnelles. Les résultats obtenus sont comparés à l'expérience et aux calculs par la méthode de Hückel. Une certaine ambiguité se dégage des faits expérimentaux. Les approximations de séparabilité - sont discutées et l'on examine la relation entre la théorie de Hückel et la méthode mono configurationnelle.

     

Perturbation theory for excited states of molecules

Components of the electric polarizability tensor are calculated for the three lowest singlet and three lowest triplet excited states of a number of conjugated molecules. The method used is the configuration interaction perturbation theory described in the first two papers of this series. A simpler method based on Hückel theory is examined and found to be unsatisfactory.     

Theory of ultrafast nonresonant multiphoton transitions in polyatomic molecules: basics and application to optimal control theory

A systematic approach is presented to describe nonresonant multiphoton transitions, i.e., transitions between two electronic states without the presence of additional intermediate states resonant with the single-photon energy. The method is well suited to describe femtosecond spectroscopic experiments and, in particular, attempts to achieve laser pulse control of molecular dynamics. The obtained effective time-dependent Schrodinger equation includes effective couplings to the radiation field which combine powers of the field strength and effective transition dipole operators between the initial and final states. To arrive at time-local equations our derivation combines the well-known rotating wave approximation with the approximation of slowly varying amplitudes. Under these terms, the optimal control formalism can be readily extended to also account for nonresonant multiphoton events. Exemplary, nonresonant two- and three-photon processes, similar to those occurring in the recent femtosecond pulse-shaping experiments on CpMn(CO)(3), are treated using related ab initio potential energy surfaces.     

Identification of unavoided crossings in nonadiabatic photoexcited dynamics involving multiple electronic states in polyatomic conjugated molecules

Radiationless transitions between electronic excited states in polyatomic molecules take place through unavoided crossings of the potential energy surfaces with substantial non-adiabatic coupling between the respective adiabatic states. While the extent in time of these couplings are large enough, these transitions can be reasonably well simulated through quantum transitions using trajectory surface hopping-like methods. In addition, complex molecular systems may have multiple "trivial" unavoided crossings between noninteracting states. In these cases, the non-adiabatic couplings are described as sharp peaks strongly localized in time. Therefore, their modeling is commonly subjected to the identification of regions close to the particular instantaneous nuclear configurations for which the energy surfaces actually cross each other. Here, we present a novel procedure to identify and treat these regions of unavoided crossings between non-interacting states using the so-called Min-Cost algorithm. The method differentiates between unavoided crossings between interacting states (simulated by quantum hops), and trivial unavoided crossings between non-interacting states (detected by tracking the states in time with Min-Cost procedure). We discuss its implementation within our recently developed non-adiabatic excited state molecular dynamics framework. Fragments of two- and four-ring linear polyphenylene ethynylene chromophore units at various separations have been used as a representative molecular system to test the algorithm. Our results enable us to distinguish and analyze the main features of these different types of radiationless transitions the molecular system undertakes during internal conversion.     

Geometric phase and gauge connection in polyatomic molecules

Geometric phase is an interesting topic that is germane to numerous and varied research areas: molecules, optics, quantum computing, quantum Hall effect, graphene, and so on. It exists only when the system of interest interacts with something it perceives as exterior. An isolated system cannot display geometric phase. This article addresses geometric phase in polyatomic molecules from a gauge field theory perspective. Gauge field theory was introduced in electrodynamics by Fock and examined assiduously by Weyl. It yields the gauge field A(μ), particle-field couplings, and the Aharonov-Bohm phase, while Yang-Mills theory, the cornerstone of the standard model of physics, is a template for non-Abelian gauge symmetries. Electronic structure theory, including nonadiabaticity, is a non-Abelian gauge field theory with matrix-valued covariant derivative. Because the wave function of an isolated molecule must be single-valued, its global U(1) symmetry cannot be gauged, i.e., products of nuclear and electron functions such as χ(n)ψ(n) are forbidden from undergoing local phase transformation on R, where R denotes nuclear degrees of freedom. On the other hand, the synchronous transformations (first noted by Mead and Truhlar): ψ(n)→ψ(n)e(iζ) and simultaneously χ(n)→χ(n)e(-iζ), preserve single-valuedness and enable wave functions in each subspace to undergo phase transformation on R. Thus, each subspace is compatible with a U(1) gauge field theory. The central mathematical object is Berry's adiabatic connection i, which serves as a communication link between the two subsystems. It is shown that additions to the connection according to the gauge principle are, in fact, manifestations of the synchronous (e(iζ)/e(-iζ)) nature of the ψ(n) and χ(n) phase transformations. Two important U(1) connections are reviewed: qA(μ) from electrodynamics and Berry's connection. The gauging of SU(2) and SU(3) is reviewed and then used with molecules. The largest gauge group applicable in the immediate vicinity of a two-state intersection is U(2), which factors to U(1) × SU(2). Gauging SU(2) yields three fields, whereas U(1) is not gauged, as the result cannot be brought into registry with electronic structure theory, and there are other problems as well. A parallel with spontaneous symmetry breaking in electroweak theory is noted. Loss of SU(2) symmetry as the energy gap between adiabats increases yields the inter-related U(1) symmetries of the upper and lower adiabats, with spinor character imprinted in the vicinity of the degeneracy.     

Formation of quasistationary states in polyatomic systems

Conclusions The results from our analysis of quasistationary states in real molecules and solid clusters provide us with grounds for stating that the proposed method can be used successfully to predict the number of resonances of form in molecules and to obtain approximate estimates of their characteristics.In studies in this area at the qualitative level, it is easy to establish the genealogy of the resonances (i.e., from which atomic states they have proceeded) and the effective value of the quantum number characterizing one resonance or another. In qualitative analysis, the mutual positions of the resonances are indicated approximately; with increasing number of atoms, the inaccuracy increases. Moreover, without carrying out the calculation, it is impossible to estimate the resonance energy, as it is impossible to distinguish reliably between resonances from collective free states of the discrete spectrum and from the rudiments of resonances.Nonetheless, it is possible to use the proposed method to judge trends in the change of resonances from one compound to another. Particularly valuable, in our view, is the possibility that is offered here for the use of very nearly the entire arsenal of the qualitative LCAO-MO theory.In order to obtain semiquantitative estimates of the characteristics of resonances, a model with potential wells is applicable. In simple cases, calculations using this model can be performed on a microcalculator.Rostov Institute of Agricultural Machinery Construction. Translated from Zhurnal Strukturnoi Khimii, Vol. 32, No. 5, pp. 3–8, September–October, 1991.     

Vibronic coupling and line broadening in polyatomic molecules

The vibronic coupling between quasi-degenerate adiabatic Born-Oppenheimer states is calculated without using the Herzberg-Teller perturbation expansion, and is shown to be strongly dependent on the model chosen.