Modeling of the time-resolved vibronic spectra of polyatomic molecules: The formulation of the problem and analysis of kinetic equations

A semiempirical parametric method is proposed for modeling three-dimensional (time-resolved) vibronic spectra of polyatomic molecules. The method is based on the use of the fragment approach in the formation of molecular models for excited electronic states and parametrization of these molecular fragments by modeling conventional (one-dimensional) absorption and fluorescence spectra of polyatomic molecules. All matrix elements that are required for calculations of the spectra can be found by the methods developed. The time dependences of the populations of a great number (>10³) of vibronic levels can be most conveniently found by using the iterative numerical method of integration of kinetic equations. Convenient numerical algorithms and specialized software for PC are developed. Computer experiments showed the possibility of the real-time modeling three-dimensional spectra of polyatomic molecules containing several tens of atoms.     

Numerical self-consistent field method for polyatomic molecules

A method for non-relativistic self-consistent field (SCF) electronic structure calculations for polyatomic molecules is described, which retains the linear combination of atomic orbitals ansatz for molecular orbitals (MO-LCAO), but replaces the usual algebraic expansion of atom-centred radial parts in terms of basis functions (usually some kind of Gauss-type functions) by a numerical representation on a set of radial grid points around each centre. The radial parts are optimized, according to the variation principle, until self-consistency is achieved. Even though Fourier integral transform techniques are used the method works completely in ordinary space. Intermediate quantities defined in momentum space are evaluated in closed form.     

Field-free three-dimensional alignment of polyatomic molecules

We experimentally demonstrate field-free, three-dimensional alignment (FF3DA) of polyatomic asymmetric top molecules. We achieve FF3DA in sulfur dioxide gas using two time-delayed, orthogonally polarized, nonresonant, femtosecond laser pulses. Our method avoids the use of rotational revivals and is therefore more robust to temperature. The alignment is probed using time-delayed coincidence Coulomb explosion imaging. FF3DA will be important for all molecular imaging, dynamics, or spectroscopy experiments for which random alignment leads to a loss of information.     

利用IEO方法求解多原子分子的振动能谱

对于线性多原子分子体系模型,借助从海森伯方程出发的不变本征算符(IEO)方法,很方便地求解了相应哈密顿量的本征能谱与振动频率,从而给出IEO方法在分子物理中的进一步应用.     

Methods for calculation of ir intensities in polyatomic molecules: A comparative study

Various methods for calculating intensities in ir spectra of polyatomic molecules are reviewed against the current theory of small vibrations of polyatomic molecules. The valence optical theory based on the representation of the molecular dipole moment as the sum of dipole moments of bonds has been shown to be erroneous. Of the two calculation procedures which use no assumptions on the molecular dipole moment, the Mayants-Averbukh method is shown to have certain advantages over the polar tensor method.     

Identification of overlapping optical lines in molecular spectra by means of the coherent population trapping of quantum levels

A new method of molecular beam spectroscopy with the ultrahigh resolution is theoretically suggested. This method is based on the phenomenon of the coherent population trapping of molecular levels and allows the identification of the overlapping optical lines in complex spectra (typical for polyatomic molecules), even when frequency intervals between the centers of given lines are less than their natural line widths. The theoretical analysis is carried out on the basis of the Schrödinger equation for the three-level molecular A-system interacting with the two-frequency laser radiation. The conditions of the practical realization and possible applications of the suggested spectroscopy method are discussed.     

The equivalent potential of water molecules for electronic structure of cysteine

In order to get more reliable electronic structure of protein in aqueous solution, it is necessary to construct a simple, easy-use equivalent potential of water molecules for protein's electronic structure calculation. The first-principles, all-electron, ab initio calculations have been performed to construct the equivalent potential of water molecules for the electronic structure of Cys. The process consists of three steps. First, the electronic structure of the cluster containing Cys and water molecules is calculated. Then, based on the structure, the electronic structure of Cys with the potential of water molecules is calculated using the self-consistent cluster-embedding method. Finally, the electronic structure of Cys with the potential of dipoles is calculated. The dipoles are adjusted so the electronic structure of Cys with the potential of dipoles is close to that of water molecules. The calculations show that the major effect of water molecules on Cys' electronic structure is lowering the occupied electronic states by about 0.032 Ry, and broadening energy gap by 16%. The effect of water molecules on the electronic structure of Cys can be simulated by dipoles potential.     

Quantum-mechanical description of the intensity distribution in two-photon absorption spectra of dihalogenated benzenes

Using molecules of dihalogenated benzenes as an example, the verification of an earlier proposed method of direct quantum-mechanical calculation of the relative intensities of lines in the two-photon absorption spectra of polyatomic molecules is continued. The method of calculation is based on the adiabatic model in the context of the Herzberg-Teller approximation. A comparative analysis of the intensity distribution in the two-photon absorption spectra of dihalogenated and monosubstituted benzenes is carried out, and the vibrational characteristics of these molecules in the lowest singlet excited electronic states are determined. A satisfactory agreement with experimental values, along with the analysis of the possibilities of the method, confirms the expediency of its use for gaining information about the intensity distribution in two-photon absorption spectra of polyatomic molecules.     

Probing orbital structure of polyatomic molecules by high-order harmonic generation

The effects of electronic structure and symmetry are observed in laser driven high-order harmonic generation for laser aligned conjugated polyatomic molecular systems. The dependence of the harmonic yield on the angle between the molecular axis and the polarization of the driving laser field is seen to contain the fingerprint of the highest occupied molecular orbitals in acetylene and allene, a good quantitative agreement with calculations employing the strong field approximation was found. These measurements support the extension of the recently proposed molecular orbital imaging techniques beyond simple diatomic molecules to larger molecular systems.     

Theoretical ROVibrational Energies (TROVE): A robust numerical approach to the calculation of rovibrational energies for polyatomic molecules

We present a new computational method with associated computer program TROVE (Theoretical ROVibrational Energies) to perform variational calculations of rovibrational energies for general polyatomic molecules of arbitrary structure in isolated electronic states. The (approximate) nuclear kinetic energy operator is represented as an expansion in terms of internal coordinates. The main feature of the computational scheme is a numerical construction of the kinetic energy operator, which is an integral part of the computation process. Thus the scheme is self-contained, i.e., it requires no analytical pre-derivation of the kinetic energy operator. It is also general, since it can be used in connection with any internal coordinates. The method represents an extension of our model for pyramidal XY₃ molecules reported previously [S.N. Yurchenko, M. Carvajal, P. Jensen, H. Lin, J.J. Zheng, W. Thiel, Mol. Phys. 103 (2005) 359]. Non-rigid molecules are treated in the Hougen-Bunker-Johns approach [J.T. Hougen, P.R. Bunker, J.W.C. Johns, J. Mol. Spectrosc. 34 (1970) 136]. In this case, the variational calculations employ a numerical finite basis representation for the large-amplitude motion using basis functions that are generated by Numerov-Cooley integration of the appropriate one-dimensional Schrödinger equation.     

Visualization of chemical reaction dynamics: Toward understanding complex polyatomic reactions

Polyatomic molecules have several electronic states that have similar energies. Consequently, their chemical dynamics often involve nonadiabatic transitions between multiple potential energy surfaces. Elucidating the complex reactions of polyatomic molecules is one of the most important tasks of theoretical and experimental studies of chemical dynamics. This paper describes our recent experimental studies of the multidimensional multisurface dynamics of polyatomic molecules based on two-dimensional ion/electron imaging. It also discusses ultrafast photoelectron spectroscopy of liquids for elucidating nonadiabatic electronic dynamics in aqueous solutions.     

Dynamic and geometric alignment of molecules induced by intense laser fields

We present a method to discuss simultaneously the relative importance of molecular dynamic and geometric alignment induced by intense laser fields in theoretical view. This method divides the process of molecular alignment into three steps, which are tightly correlated with that of molecular multielectron dissociative ionization and Coulomb explosion. A fourth-order Runge-Kutta algorithm and a developed counting approach are used to calculate the angular distribution of molecules in the first and second steps of molecular alignment. The last step is described by a field-ionization, Coulomb explosion model. The angular distribution of molecules at the critical distance originated from geometric alignment is obtained by calculating the volume of shells associated with a series of particular angle. The final angular distributions of molecules are obtained by properly weighting the results of three steps. The numerical results of distinguishing between dynamic and geometric alignment for certain conditions are presented and discussed. Our computational results show that the alignment mechanism, which dominates the observed anisotropy of angular distributions of ionic fragments for a given condition, is determined by the dependences of the extent of dynamic and geometric alignment on laser parameters and molecular parameters.     

Rapid proton transfer mediated by a strong laser field

Kinetic energy distributions of ejected from a polyatomic molecule, anthraquinone, subjected to 60 fs, 800 nm laser pulses of intensity between 0.2 and 4.0 x 10(14) W x cm(-2), reveal field-driven restructuring of the molecule prior to Coulomb explosion. Calculations demonstrate fast intramolecular proton migration into a field-dressed metastable potential energy minimum. The proton migration occurs in the direction perpendicular to the polarization of the laser field. Rapid field-mediated isomerization is an important new phenomenon in coupling of polyatomic molecules with intense lasers.     

The equivalent potential of water molecules for electronic structure of lysine

In order to get more reliable electronic structures of proteins in aqueous solution, it is necessary to construct a potential of water molecules for protein’s electronic structure calculation. The lysine is a hydrophilic amino acid. It is positively charged (Lys+) in neutral water solution. The first-principles, all-electron, ab initio calcula-tions, based on the density functional theory, have been performed to construct such an equivalent potential of water molecules for lysine (Lys+). The process consists of three parts. First, the electronic structure of the cluster containing Lys+ and water molecules is calculated. By adjusting the positions of water molecules, the geometric structure of the cluster having minimum total energy is determined. Then, based on the structure, the electronic structure of Lys+ with the potential of water molecules is calculated using the self-consistent cluster-embedding (SCCE) method. Finally, the electronic structure of Lys+ with the potential of dipoles is calculated. The dipoles are adjusted so that the electronic structure of Lys+ with the potential of dipoles is close to that of water molecules. Thus the equivalent potential of water molecules for the electronic structure of lysine is obtained. The major effect of water molecules on lysine’s electronic structure is raising the occupied eigenvalues about 0.5032 eV, and broadening energy gap 89%. The effect of water molecules on the electronic structure of lysine can be simulated by dipoles potential.     

Modern methods for calculating photoionization and electron-impact ionization of two-electron atoms and molecules

A number of recently developed methods for calculating multifold differential cross sections for photoionization and electron impact ionization of atoms and molecules with two active electrons are reviewed. The methods are based on unique approaches to the calculation of three-body Coulomb wave functions. The exterior scaling method and the driven Schrödinger equation formalism are considered. The effectiveness of the time-dependent approaches to the scattering problem, such as the paraxial approximation and the time-dependent scaling, is demonstrated. A novel numerical method is formulated, which has been developed by the authors to solve the six-dimensional Schrödinger equation for an atom with two active electrons on the basis of the Chang-Fano transformation and the discrete variable representation. The threshold behavior manifested by the angular distributions of the two-electron photoionization of a negative hydrogen ion and a helium atom and the multifold differential cross sections for the electronimpact ionization of hydrogen and nitrogen molecules are analyzed on the basis of numerical simulations. The Wannier law for the angular distribution of double ionization is demonstrated to be incorrect even at very low energies.     

Local molecular dynamics with coulombic interactions

We propose a local, O(N) molecular dynamics algorithm for the simulation of charged systems. The long ranged Coulomb potential is generated by a propagating electric field that obeys modified Maxwell equations. On coupling the electrodynamic equations to an external thermostat we show that the algorithm produces an effective Coulomb potential between particles. On annealing the electrodynamic degrees of freedom the field configuration converges to a solution of the Poisson equation much like the electronic degrees of freedom approach the ground state in ab initio molecular dynamics.     

Experimental evidence of excited multicharged atomic fragments coming from laser-induced coulomb explosion of molecules

Direct experimental evidence is presented for the production of excited multicharged atomic fragments in the laser-induced Coulomb explosion of molecules. The comparison of the fluorescence signals of several atomic and molecular species shows that the excited fragments come from transient excited multicharged molecules. The atomic fluorescence spectra recorded with NH3, N2, and N2O, in the 50-120 nm wavelength range, show that the excitation increases noticeably from NH3 to N2O. This effect is interpreted in terms of the initial electronic configuration, which favors a stronger excitation when the electronic density is more delocalized on the molecular nuclear structure.     

Coulomb explosion of large polyatomic molecules assisted by nonadiabatic charge localization

The electron-nuclear dynamics of the Coulomb explosion of a large polyatomic molecule, anthracene, is probed using kinetic energy distributions of produced H+ ions. The kinetic energy release of ejected protons exceeds 30 eV for anthracene exposed to 10(14) W cm(-2), 800 nm pulses of 60 fs duration. We propose a strong-field charge localization model, based on nonadiabatic dynamics of charge distribution in a (multiply) ionized molecule; the charge localization lasts many laser periods and is sustained through successive ionizations of the molecular ion. The model explains quantitatively the dependence of the H+ kinetic energy on the laser intensity. Dissociative ionization of a polyatomic molecule enabled by long-lived charge localization is a new type of electron-nuclear dynamics and is essential for understanding the pathways of molecular or ionic fragmentation in strong fields.     

Electronic correlations in oligo-acene and -thiopene organic molecular crystals

From first-principles calculations we determine the Coulomb interaction between two holes on oligo-acene and -thiophene molecules in a crystal, as a function of the oligomer length. The electronic polarization of the molecules that surround the charged oligomer reduces the bare Coulomb repulsion between the holes by approximately a factor of 2. The effects of relaxing the molecular geometry in the presence of holes is found to be significantly smaller. In all cases the effective hole-hole repulsion is much larger than the valence bandwidth, which implies that at high doping levels the properties of these organic semiconductors are determined by electron-electron correlations.     

基于多组态含时Hartree-Fock方法研究电子关联对于H_2分子强场电离的影响

发展了三维的处理双原子分子非微扰电子动力学的多组态含时Hartree-Fock方法,并利用该方法研究了电子关联对于H_2分子强场电离概率的影响.该方法采用能够精确处理双中心库仑势的椭球坐标系,以及减小双电子积分计算量的有限元-离散变量基函数方法.利用多组态含时Hartree-Fock方法计算了H_2分子随分子取向角度变化的XUV光电离结果,并通过与单组态结果的对比研究了电子关联对于单电离和双电离概率的不同影响.研究表明,电子关联对于单电离过程影响很小,而在双电离过程中则发挥了重要作用,导致了电离概率的减小.该方法为进一步研究强场物理过程中的电子关联效应奠定了基础.