Mixed quantum-classical description of spectroscopy of dissipative systems

Mixed quantum-classical statistical mechanics is employed to calculate dipole moment correlation function and linear absorption spectra. A quantum two-level subsystem interacting with quantum vibrations (primary oscillators) which in turn are coupled to a classical bath composed of infinite set of harmonic oscillators is used as a dissipative system. Starting with mixed quantum-classical Liouville equation for the evaluation of the mixed quantum-classical dipole moment correlation function and using coherent states and the inverse of Baker-Campbell-Hausdorf formula to evaluate the trace over the primary oscillators, whereby, a closed analytical expression for the electronic dipole moment correlation function is obtained. Illustrations of several absorption spectra at different temperatures are provided. An approximate optical four-point correlation is obtained in the high temperature limit. A strategy for deriving an exact optical four-point correlation is suggested.     

A coherent discrete variable representation method for multidimensional systems in physics

A coherent discrete variable representation (ZDVR) is proposed for constructing a multidimensional potential-optimized DVR basis. The multidimensional quadrature pivots are obtained by diagonalizing a complex coordinate operator matrix in a finite basis set, which is spanned by the lowest eigenstates of a two-dimensional reference Hamiltonian. Here a c-norm condition is used in the diagonalization procedure. The orthonormal eigenvectors define a collocation matrix connecting the localized ZDVR basis functions and the finite basis set. The method is applied to two vibrational models for computing the lowest bound states. Results show that the ZDVR method provides exponential convergence and accurate energies. Finally, a zeroth-order approximation method is also derived.     

General calculation of 4f-5d transition rates for rare-earth ions using many-body perturbation theory

The 4f-5d transition rates for rare-earth ions in crystals can be calculated with an effective transition operator acting between model 4f(N) and 4f(N-1)5d states calculated with effective Hamiltonian, such as semiempirical crystal Hamiltonian. The difference of the effective transition operator from the original transition operator is the corrections due to mixing in transition initial and final states of excited configurations from both the center ion and the ligand ions. These corrections are calculated using many-body perturbation theory. For free ions, there are important one-body and two-body corrections. The one-body correction is proportional to the original electric dipole operator with magnitude of approximately 40% of the uncorrected electric dipole moment. Its effect is equivalent to scaling down the radial integral (5d/r/4f) to about 60% of the uncorrected HF value. The two-body correction has magnitude of approximately 25% relative to the uncorrected electric dipole moment. For ions in crystals, there is an additional one-body correction due to ligand polarization, whose magnitude is shown to be about 10% of the uncorrected electric dipole moment.     

A theoretical study of calcium monohydride, CaH: low-lying states and their permanent electric dipole moments

Potential energy curves, energy parameters, and spectroscopic values for the X (2)Sigma(+), A (2)Pi, B (2)Sigma(+), a (4)Pi, and b (4)Sigma(+), states of CaH have been calculated using the multireference configuration interaction and coupled cluster levels of theory, while employing quantitative basis sets (of augmented quintuple-zeta quality) and taking also into account core/valence correlation and one-electron relativistic effects. For the ground (X (2)Sigma(+)) and the first two following excited states (A (2)Pi, B (2)Sigma(+)) of CaH, the permanent electric dipole moments have been calculated. Our best finite field dipole moment of the A (2)Pi state of 2.425 D (upsilon = 0) is in very good agreement with the experimental literature value of 2.372(12) D. However, a discrepancy is observed in the dipole moment of the X (2)Sigma(+) state. Our most extensive calculation gives mu = 2.623 D (upsilon = 0), which is considerably smaller than the experimental value of mu = 2.94(16) D (upsilon = 0). Small van der Waals minima were found for both "repulsive" quartet states. Spectroscopic constants and energy parameters for all states are in remarkable agreement with available experimental values.     

Intrinsic optical bistability of thin films of linear molecular aggregates: the one-exciton approximation

We perform a theoretical study of the nonlinear optical response of an ultrathin film consisting of oriented linear aggregates. A single aggregate is described by a Frenkel exciton Hamiltonian with uncorrelated on-site disorder. The exciton wave functions and energies are found exactly by numerically diagonalizing the Hamiltonian. The principal restriction we impose is that only the optical transitions between the ground state and optically dominant states of the one-exciton manifold are considered, whereas transitions to other states, including those of higher exciton manifolds, are neglected. The optical dynamics of the system is treated within the framework of truncated optical Maxwell-Bloch equations, in which the electric polarization is calculated by using a joint distribution of the transition frequency and the transition dipole moment of the optically dominant states. This function contains all the statistical information about these two quantities that govern the optical response and is obtained numerically by sampling many disorder realizations. We derive a steady-state equation that establishes a relationship between the output and input intensities of the electric field and show that within a certain range of the parameter space this equation exhibits a three-valued solution for the output field. A time-domain analysis is employed to investigate the stability of different branches of the three-valued solutions and to get insight into switching times. We discuss the possibility to experimentally verify the bistable behavior.     

Evaluating First-Order Molecular Properties of Delocalized Ionic or Excited States in Molecular Aggregates by Renormalized Excitonic Method

In the past few years, the renormalized excitonic model (REM) approach was developed as an efficient low-scaling ab initio excited state method, which assumes the low-lying excited states of the whole system are a linear combination of various single monomer excitations and utilizes the effective Hamiltonian theory to derive their couplings. In this work, we further extend the REM calculations for the evaluations of first-order molecular properties (e.g. charge population and transition dipole moment) of delocalized ionic or excited states in molecular aggregates, through generalizing the effective Hamiltonian theory to effective operator representation. Results from the test calculations for four different kinds of one dimensional (1D) molecular aggregates (ammonia, formaldehyde, ethylene and pyrrole) indicate that our new scheme can efficiently describe not only the energies but also wavefunction properties of the low-lying delocalized electronic states in large systems.     

Electric dipole (hyper)polarizabilities of spatially confined LiH molecule

In this study we report on the electronic contributions to the linear and nonlinear static electronic electric dipole properties, namely the dipole moment (μ), the polarizability (α), and the first-hyperpolarizability (β), of spatially confined LiH molecule in its ground X (1)Σ(+) state. The finite-field technique is applied to estimate the corresponding energy and dipole moment derivatives with respect to external electric field. Various forms of confining potential, of either spherical or cylindrical symmetry, are included in the Hamiltonian in the form of one-electron operator. The computations are performed at several levels of approximation including the coupled-cluster methods as well as multi-configurational (full configuration interaction) and explicitly correlated Gaussian wavefunctions. The performance of Kohn-Sham density functional theory for the selected exchange-correlation functionals is also discussed. In general, the orbital compression effects lead to a substantial reduction in all the studied properties regardless of the symmetry of confining potential, however, the rate of this reduction varies depending on the type of applied potential. Only in the case of dipole moment under a cylindrical confinement a gradual increase of its magnitude is observed.     

Investigations on Binary Mixtures of Propan-2-ol with Methyl Benzoate and Ethyl Benzoate

The molecular interactions between the polar systems propan-2-ol with alkyl benzoates (methyl benzoate and ethyl benzoate), for various mole fractions and different temperatures, were studied by determining the dielectric permittivity using a LF impedance analyzer and Abbe’s refractometer in the static and optical frequency regions, respectively. The effective Kirkwood correlation factor, corrective Kirkwood correlation factor, dipole moment, excess dipole moment, and excess Helmholtz free energy were calculated using the experimental data. Hamiltonian quantum mechanical calculations (ab initio and semiempirical) were performed using PC Spartan and Argus lab Modeling software for both pure and equimolar binary systems of propan-2-ol with alkyl benzoates.     

N-level Li2 multiphoton rotational wave packets: alignment effects in resonant multiphoton coherent excitation

Using one color ultrafast pump-probe spectroscopy, the authors create N-level multiphoton rotational wave packets via resonant optical pumping between the A((1)Sigma(u) (+)) and E((1)Sigma(g) (+)) electronically bound states of Li(2) from a single optically state-selected rovibrational state |nu(A)=11, j(A)=28>. The authors find that excitation with a single amplitude shaped femtosecond pulse allows the direct observation of up to a six photon absorption, which generates a coherent superposition of 13 rotational states. The multilevel rotational wave packet is theoretically treated with the multipole moment formalism in order to characterize the experimentally observed time-dependent alignment. In particular, the authors find that the magnetic state distributions measured among coherently excited rotational states generated by the resonant multiphoton pumping reduces the measured coherence amplitudes by as much as 40%.     

Dielectric and Thermodynamic Studies on the Hydrogen Bonded Binary System of Isopropyl Alcohol and Aniline

The molecular interactions between the polar systems isopropyl alcohol (IPA) and aniline for various mole fractions at different temperatures were studied by determining the dielectric permittivity using an HP-LF impedance analyzer at radio frequencies, the plunger method in the microwave frequency range and Abbe’s refractometer in optical region. Kirkwood effective correlation factors, corrective Kirkwood correlation factors, excess permittivities, Bruggeman parameters, excess Helmholtz free energy, relaxation time, dipole moment and excessive dipole moment were calculated using the experimental data. Optimized geometries were calculated using Spartan Modeling software for both pure and equimolar systems of isopropyl alcohol and aniline for Hamiltonian quantum mechanical calculations. Conformational analysis of the formation of hydrogen bond between the two systems is supported by the FT-IR spectra.     

Theoretical transition probabilities for the OH Meinel system

The authors present a new potential energy curve, electric dipole moment function, and spin-orbit coupling function for OH in the X 2Pi state, based on high-level ab initio calculations. These properties, combined with a spectroscopically parametrized lambda-type doubling Hamiltonian, are used to compute the Einstein A coefficients and photoabsorption cross sections for the OH Meinel transitions. The authors investigate the effect of spin-orbit coupling on the lifetimes of rovibrationally excited states. Comparing their results with earlier ab initio calculations, they conclude that their dipole moment and potential energy curve give the best agreement with experimental data to date. The results are made available via EPAPS Document No. E-JCPSAG-017709.     

Intermediate state representation approach to physical properties of electronically excited molecules

Propagator methods provide a direct approach to energies and transition moments for (generalized) electronic excitations from the ground state, but they do not usually allow one to determine excited state wave functions and properties. Using a specific intermediate state representation (ISR) concept, we here show how this restriction can be overcome in the case of the algebraic-diagrammatic construction (ADC) propagator approach. In the ISR reformulation of the theory the basic ADC secular matrix is written as a representation of the Hamiltonian (or the shifted Hamiltonian) in terms of explicitly constructable states, referred to as intermediate (or ADC) states. Similar intermediate state representations can be derived for operators other than the Hamiltonian. Together with the ADC eigenvectors, the intermediate states give rise to an explicit formulation of the excited wave functions and allow one to calculate physical properties of excited states as well as transition moments for transitions between different excited states. As for the ground-state excitation energies and transition moments, the ADC excited state properties are size consistent so that the theory is suitable for applications to large systems. The established hierarchy of higher-order [ADC(n)] approximations, corresponding to systematic truncations of the IS configuration space and the perturbation-theoretical expansions of the ISR matrix elements, can readily be extended to the excited state properties. Explicit ISR matrix elements for arbitrary one-particle operators have been derived and coded at the second-order [ADC(2)] level of theory. As a first computational test of the method we have carried out ADC(2) calculations for singlet and triplet excited state dipole moments in H(2)O and HF, where comparison to full CI results can be made. The potential of the ADC(2) method is further demonstrated in an exploratory study of the excitation energies and dipole moments of the low-lying excited states of paranitroaniline. We find that four triplet states, T1-T4, and two singlet states, S1 and S2, lie (vertically) below the prominent charge transfer (CT) excitation, S3. The dipole moment of the S3 state (17.0D) is distinctly larger than that of the corresponding T3 triplet state (11.7D).     

Thermally activated escape rate for the Brownian motion of a fixed axis rotator in a double well potential for all values of the dissipation

The extension of the Kramers theory of the escape rate of a Brownian particle from a potential well to the entire range of damping proposed by Mel'nikov and Meshkov [J. Chem, Phys. 85, 1018 (1986)] is applied to the rotational Brownian motion of fixed axis rotators in a double well cosine potential. The procedure yields an expression for the Kramers escape rate valid for all values of the dissipation including the very low damping (VLD), very high damping (VHD), and crossover regimes. This equation provides a good asymptotic estimate of the correlation time tau per pendicular of the longitudinal dipole moment correlation function calculated by solving the underlying Langevin equation using the matrix-continued fraction method. Moreover, for low barriers, where the Mel'nikov and Meshkov approach is not applicable, analytic equations for tau in the VLD and VHD limits are derived and a simple extrapolating equation that is valid for all values of the damping is proposed.     

Stereocontrol of attosecond time-scale electron dynamics in ABCU using ultrafast laser pulses: a computational study

The attosecond time-scale electronic dynamics induced by an ultrashort laser pulse is computed using a multi configuration time dependent approach in ABCU (C(10)H(19)N), a medium size polyatomic molecule with a rigid cage geometry. The coupling between the electronic states induced by the strong pulse is included in the many electron Hamiltonian used to compute the electron dynamics. We show that it is possible to implement control of the electron density stereodynamics in this medium size molecule by varying the characteristics of the laser pulse, for example by polarizing the electric field either along the N-C axis of the cage, or in the plane perpendicular to it. The excitation produces an oscillatory, non-stationary, electronic state that exhibits localization of the electron density in different parts of the molecule both during and after the pulse. The coherent oscillations of the non-stationary electronic state are also demonstrated through the alternation of the dipole moment of the molecule.     

Interpretation of light-scattering spectra in terms of particle displacements

Quasielastic light-scattering spectroscopy is regularly used to examine the dynamics of dilute solutions of diffusing mesoscopic probe particles in fluids. For probes in a simple liquid, the light-scattering spectrum is a simple exponential; the field correlation function g(1)(q,tau) of the scattering particles is related to their mean-square displacements X2 identical with [(delta x(tau))2] during tau via g(1)(q,tau) = exp(-1/2 q2X2). However, demonstrations of this expression refer only to identical Brownian particles in simple liquids and show that if the form is correct then it is also true for all tau that g(1)(q,tau) = exp(-gamma tau), a pure exponential in tau. In general, g(1)(q,tau) is not a single exponential in time. A correct general form for g(1)(q,tau) in terms of the X(2n), replacing the incorrect exp(-1/2 q2X2), is obtained. A simple experimental diagnostic determining when the field correlation function gives the mean-square displacement is identified, namely, g(1)(q,tau) only reveals X2 if g(1)(q,tau) is a single exponential in tau. Contrariwise, if g(1)(q,tau) is not a single exponential, then g(1)(q,tau) depends not only on X2 but on all higher moments X(2n). Corrections to the crude approximation g(1)(q,tau) = exp(-1/2 q2X2) closely resemble the higher spectral cumulants from a cumulant expansion of g(1)(q,tau).     

Ab initio calculation of the rotational spectrum of methane vibrational ground state

In a previous article we have introduced an alternative perturbation scheme to the traditional one starting from the harmonic oscillator, rigid rotator Hamiltonian, to find approximate solutions of the spectral problem for rotation-vibration molecular Hamiltonians. The convergence of our method for the methane vibrational ground state rotational energy levels was quicker than that of the traditional method, as expected, and our predictions were quantitative. In this second article, we study the convergence of the ab initio calculation of effective dipole moments for methane within the same theoretical frame. The first order of perturbation when applied to the electric dipole moment operator of a spherical top gives the expression used in previous spectroscopic studies. Higher orders of perturbation give corrections corresponding to higher centrifugal distortion contributions and are calculated accurately for the first time. Two potential energy surfaces of the literature have been used for solving the anharmonic vibrational problem by means of the vibrational mean field configuration interaction approach. Two corresponding dipole moment surfaces were calculated in this work at a high level of theory. The predicted intensities agree better with recent experimental values than their empirical fit. This suggests that our ab initio dipole moment surface and effective dipole moment operator are both highly accurate.     

Untersuchung des UV. Spektrums von Acenaphtylen durch Beobachtung des durch ein elektrisches Feld induzierten Dichroismus

The absolute direction of transition moments and the change of the dipole moment upon transition to excited states of acenaphthylene are determined from the influence of an electric field on the optical density of a solution. The results agree well with predictions from PPP-calculations. In the lowest excited state the dipole moment is antiparallel to the ground state dipole moment.     

Quantum initial value representation simulation of water trimer far infrared absorption spectrum

We extend the technique of quantum propagation on a grid of trajectory guided coupled coherent states to simulate experimental absorption spectra. The approach involves calculating the thermally averaged dipole moment autocorrelation function by means of quantum propagation in imaginary time. The method is tested on simulation of the far infrared spectrum of water trimer based on a three-dimensional model potential. Results are in good agreement with experiment and with other calculations.     

Atomic partition of the optical rotatory power of methylhydroperoxide

We applied a methodology capable of resolving the optical rotatory power into atomic contributions. The individual atomic contributions to the optical rotatory power and molecular chirality of the methylhydroperoxide are obtained via a canonical transformation of the Hamiltonian by which the electric dipolar moment operator is transformed to the acceleration gauge formalism and the magnetic dipolar moment operator to the torque formalism. The gross atomic isotropic contributions have been evaluated for the carbon, the nonequivalent oxygen, and the nonequivalent hydrogen atoms of methylhydroperoxide, employing a very large Gaussian basis set which is close to the Hartree-Fock limit.     

The complex coordinate scattering theroy and its application to the study of the surface asymmetry effect in helium diffraction from copper

The Complex Coordinate Scattering Theory is reformulated for the general case of a time-independent Hamiltonian. It is applied to scattering of He atoms from a Cu(115) crystal surface by constracting the Green operator for the T-matrix from the eigenvectors of both the complex scaled Hamiltonian and its transposed (“right” and “left” eigenvectors), which are different in this case. The weakly asymmetric corrugation function describing the (115) face of Cu is shown to cause a strong dependence of the calculated diffraction intensities upon the direction of the incident atomic beam. The calculated transition probabilities are in excellent agreement with the experimentally measured ones, previously obtained by Perreau and Lapujoulade. We show that additional information about the gas atom/surface physisorption interaction potential can be obtained if the incident angle of the atomic beam (the angles between the beam and the surface normal) is changed from γ to ?γ. © 1993 John Wiley & Sons, Inc.