Equivalence of the first-order generalized phase shift and first-order time-dependent perturbation treatments of rotational excitation

For atom-rigid rotor scattering in the limit of high initial rotor states, it is shown that the first-order approximation of the GPS treatment is equivalent to first-order time-dependent perturbation theory, with the assumption of curved, planar trajectories.     

Franck-Condon simulation of the B-A bands of BO

Franck-Condon simulation of the emission B-A band system of boron monoxide are given. The computed band origin wavenumbers are found to be in good agreement with those derived from measured band head positions. In the absence of intensity measurements for the B-A bands, the simulated intensities were tested by calculation of the relative intensities of the well known A-X bands under the assumption that the electronic transition moment function is constant. The resulting good agreement between the simulated and experimentally obtained intensity patterns for A-X bands supports the reliability of our simulated B-A spectrum.     

Equation for the direct determination of the density matrix: Time-dependent density equation and perturbation theory

The density equation proposed previously for the direct determination of the density matrix, i.e. for the wave mechanics without wave, is extended to a time-dependent case. The time-dependent density equation has been shown to be equivalent to the time-dependent Schr?dinger equation so long as the density matrix, included as a self-contained variable, is N-representable. Formally, it is obtainable from the previous time-independent equation by replacing the energy E with . The perturbation theory formulas for the density equation have also been given for both the time-dependent and time-independent cases. Received: 16 June 1998 / Accepted: 2 September 1998 / Published online: 8 February 1999     

Time-dependent wavepacket calculations of atom scattering from surfaces with impurities

Exact quantum-mechanical calculations are reported on atom scattering from a crystalline surface with isolated impurities. The calculations are for He scattering from a one-dimensional model of a Cu surface with adsorbed Ar atoms. The difficulties of carrying out calculations on scattering from extended but non-periodic structures are overcome by using a time-dependent wavepacket approach. A recently developed method for solving the time-dependent Schrödinger equation is employed. Scattering intensities are given for several energies and incidence angles. Detailed insight is obtained on impurity effects on surface scattering. The main features are: (1) Broad intensity tails are superimposed on each diffraction spike. The width of the tails decreases with increasing diffraction order; (2) Shallow rainbow peaks arise, due to impurity induced local corrugation; (3) Weak intensity maxima arise due to interference between surface and impurity scattering. The intensities are somewhat sensitive to the position of the impurity within the surface unit cell. Physical interpretation of the effects is provided from exact calculations, and from a simple sudden approximation for the scattering intensities. It is argued that He scattering can be used to determine impurity locations on surfaces.     

Infrared intensities of lattice vibrations in molecular crystals

From the dynamic multipoles model an expression is derived for the dipole moment derivative governing the intensity of infrared absorption by lattice modes in molecular crystals. The result depends on non-local susceptibilities which take proper account of the local electric field in a way consistent with dielectric theory. It is shown that the non-local rsponse follows naturally from microscopic lattice dynamical theory. It arises from dipolar coupling and is intimately connected with the delocalized exciton states produced by the same mechanism. Intensities calculated for the iodine crystal are inproved by including the local field, but a point quadrupole field proves too anisotropic to yield the measured intensity ratio. The treatment shows that infrared intensities can be used to obtain unique effective molecular polarizabilities.     

Two-dimensional infrared (2D IR) spectroscopy. A new tool for interpreting infrared spectra

Two-dimensional infrared (2D IR) spectroscopy is used to study atactic polystyrene. 2D IR is a technique based on time-resolved detection of IR signals in response to an external perturbation, such as mechanical strain. Since different chemical functional groups respond to the applied perturbation at unique and often different rates, characteristic time-dependent variations of the IR-band intensities are observed. Correlation analysis of the dynamic variation of the IR signals yields a new spectrum defined by two independent wave numbers. Peaks located on a 2D IR spectral plane imply interactions and connectivities among chemical functional groups. By spreading convoluted IR bands over two dimensions, the spectral resolution is also greatly enhanced.     

On the hypervirial relation in the random phase approximation and the sum rules for ordinary and rotatory intensities in finite bases

It is shown that a one-electron hypervirial relation for transition amplitudes in the random phase approximation (RPA) follows immediately from the double commutator RPA formulation proposed by Rowe. For the transition energy-independent expressions for the ordinary and rotatory intensities it is shown that, in finite basis calculations, the sums of these intensities are independent of whether the single-transition approximation, the Tamm—Dancoff approximation or the RPA method is used. Specific results are quoted for a ab-initio minimal basis calculations on twisted ethylene.     

On the theory of tunnelling in electron and proton transfer reactions

The concept of tunnelling in the theory of electron and proton transfer reactions has recently been questioned on the ground that the situation is a non-stationary one. It has been suggested that time-dependent perturbation theory should be applied to obtain the quantum mechanical transition probability. We have done this for a square barrier. The result for most reactions is the same as obtained by the WKB approximation.     

Resonance Raman spectra of uracil based on Kramers-Kronig relations using time-dependent density functional calculations and multireference perturbation theory

The use of time-dependent density functional calculations for the optimization of excited-state structures and the subsequent calculation of resonance Raman intensities within the transform-theory framework is compared to calculations of Hartree-Fock/configuration interaction singles-type (CIS). The transform theory of resonance Raman scattering is based on Kramers-Kronig relations between polarizability tensor components and the optical absorption. Stationary points for the two lowest excited singlet states of uracil are optimized and characterized by means of numerical differentiation of analytical excited-state gradients. It is shown that the effect of electron correlation leads to substantial modifications of the relative intensities. Calculations of vibrational frequencies for ground and excited states are carried out, which show that the neglect of Duschinsky mixing and the assumption of equal wave numbers for ground and excited state are not in all cases good approximations. We also compare the transform-theory resonance Raman intensities with those obtained within a simple approximation from excited-state gradients at the ground-state equilibrium position, and find that they are in qualitative agreement in the case of CIS, but show some important differences in calculations based on density functional theory. Since the results from CIS calculations are in better agreement with experiment, we also present approximate resonance Raman spectra obtained using excited-state gradients from multireference perturbation theory calculations, which confirm the CIS gradients.     

A vibrational CASSCF study of stretch-bend interactions and their influence on infrared intensities in the water molecule

Summary An extension of the multiconfigurational SCF approach for the resolution of the vibrational problem is presented; it follows the philosophy of the CASSCF method developed in Quantum Chemistry. The new method allows a more complete treatment of anharmonic mode couplings, converges much faster and gives a clearer physical insight of vibrational interactions. This is exemplified by the calculation of infrared transition moments in the H₂O and D₂O isotopomers of the water molecule. It is shown how this property varies with the quality of the wave function when vibrational resonances occur. A detailed analysis by means of this new VCASSCF method demonstrates the crucial importance of excited bending oscillators in the intensity of some pure stretching transitions.Boursier F.R.I.A.     

Theory and computational methods for studies of nonlinear phenomena in laser spectroscopy. I. General formalism

A general formalism will be outlined, which uses steady-state wave functions for the study of nonlinear phenomena occurring in molecular systems interacting with intense electromagnetic fields. The steady-state approach has the advantage of being free from the secular divergencies and normalization terms which appear in a perturbation expansion of the time-dependent wave function. A physical interpretation of the steady states will be given by considering the interaction between the molecule and the quantized electromagnetic field. The steady states appear as states of the combined system molecule plus electromagnetic field, with eigenvalues corresponding to the energy levels of the combined system in a semiclassical approximation. Evolution operators will be introduced and used to derive formulas for n-photon transition probabilities between molecular states both in the ordinary configuration Hilbert space and in the composite Hilbert space spanned by the steadystate wave functions.     

A DFT/TDDFT interpretation of the ground and excited states of porphyrin and porphyrazine complexes

A comprehensive treatment is given of the electronic excitation spectra of Mg, Zn and Ni complexes of porphyrin and porphyrazine using time-dependent density functional theory (TDDFT). It is emphasized that the Kohn–Sham (KS) molecular orbital (MO) method, which is the basis for the TDDFT calculations, affords a MO interpretation of the ground state electronic structure and of the nature of the excitations. This implies that a direct connection can be made to many previous MO treatments of the title compounds. We discuss in particular, how the original explanations of the intensity distribution over the lowest excitations (the Q and B bands) in terms of a cyclic polyene model, or even a free-electron model, can be reconciled with the actual molecular and electronic structure of these compounds being much more complicated than these simple models. A fragment approach is used, building the porphyrin ring from pyrrole rings and CH or N bridges. This leads directly to a simple interpretation of the orbitals of Gouterman's four-orbital model, which are responsible for the Q and B bands. It also leads to additional occupied π-orbitals which are absent in the cyclic polyene model and which need to be invoked to understand other features of the electronic spectra such as the origin of the N, L and M bands. Considerable attention is given to the intensities of the various transitions, explaining why the transitions within the so-called four-orbital model of Gouterman have large transition dipoles, why transitions from additional occupied π-orbitals have relatively small transition dipoles.     

Higher-order contributions to the intermolecular energy in the perturbation treatment of long-range forces in the light of spherical tensor theory

A preliminary account of the full spherical tensor theory of long-range interactions between two molecules based on a Rayleigh-Schrödinger perturbation treatment is given. The isotropic third-order interaction energy expression is then derived. Finally, the interaction between two tetrahedral molecules in the third-order of perturbation is studied as an example. It is shown that, in some cases, higher-order contributions should be taken into account.     

Glass transition in semicrystalline polycarbonate

The intensity of the glass transition in semicrystalline polycarbonate was measured by differential scanning calorimetry and by thermally stimulated discharge of electrets. Solution-cast and bulk-crystallized samples possessing widely varying crystallinities and morphologies were investigated. It is shown that the intensity of the glass transition is governed by the extent of primary crystallization and is a linear combination of intensities from the bulk amorphous regions and from noncrystalline polymer within semicrystalline aggregates such as spherulites. The intensity of the glass transition within spherulites is about 0.1–0.3 as great as that in bulk amorphous regions. A three-phase model incorporating two distinct types of noncrystalline polycarbonate is proposed to account for the properties of this polymer.     

Statistical Approach to the Description of Homogeneous Nucleation in the Vapor-Gas Medium: Effects of the Heat of Phase Transition

The effect of the heat release of phase transition is included in the formalism of the statistical approach in order to allow for the depletion of a substance comprising the metastable phase in the kinetics of the homogeneous nucleation of supersaturated vapor. The diffusion regime of the exchange of molecules between the vapor and the growing droplets is considered on the assumption of instantaneous creation of the initial vapor supersaturation. The time-dependent boundary condition on the surface of a sphere with a fixed radius and a center coinciding with the center of a growing droplet is used in the problem of heat conductivity that allowed us to provide the heat balance of phase transition. The main characteristics of the nucleation stage are calculated for the representative vapor-gas systems. It is shown that the allowance for the effects of the heat release of phase transition resulted in a rather notable change in the kinetics of nucleation even at a sufficiently high concentration of the passive gas.     

Light absorption during alkali atom-noble gas atom interactions at thermal energies: a quantum dynamics treatment

The absorption of light during atomic collisions is treated by coupling electronic excitations, treated quantum mechanically, to the motion of the nuclei described within a short de Broglie wavelength approximation, using a density matrix approach. The time-dependent electric dipole of the system provides the intensity of light absorption in a treatment valid for transient phenomena, and the Fourier transform of time-dependent intensities gives absorption spectra that are very sensitive to details of the interaction potentials of excited diatomic states. We consider several sets of atomic expansion functions and atomic pseudopotentials, and introduce new parametrizations to provide light absorption spectra in good agreement with experimentally measured and ab initio calculated spectra. To this end, we describe the electronic excitation of the valence electron of excited alkali atoms in collisions with noble gas atoms with a procedure that combines l-dependent atomic pseudopotentials, including two- and three-body polarization terms, and a treatment of the dynamics based on the eikonal approximation of atomic motions and time-dependent molecular orbitals. We present results for the collision induced absorption spectra in the Li-He system at 720 K, which display both atomic and molecular transition intensities.     

Phase control over decaying molecular states in intense laser pulses

A time-dependent approach to study phase control over molecular photoabsorption, provided by intense laser pulses, is elaborate. The method allows for the decay linewidth of molecular states and frequency bandwidth of the controlling laser field, and can be applied in weak and strong laser fields where the perturbation theory is invalid. It is shown that a frequency mismatch between the fundamental laser wave and its third harmonic can destroy control. For the example of the one-photon versus three-photon control a simple picture of interference from two monochromatic absorption pathways is not enough to explain phase control and one needs to consider a nonlinear temporal interference of multiquantum transitions. In the perturbation-theory limit an elegant generalization of the famous Shapiro-Hepburn-Brumer equation for the one-photon versus three-photon control is derived. Various numerical calculations illustrate the dependence of phase control on molecular linewidth, fundamental laser wavelength, pulse duration, and peak intensity. It is obtained, that the one-photon versus three-photon control is productive if the molecular state populations, individually produced by each laser wave, have beats of approximately the same frequency. The calculations demonstrate that an enough intense optical pulse can suppress molecular decay and may be used in order to keep stable the state population of a decaying molecule for a long time. The available experimental results for the one-photon versus three-photon control over simple and large polyatomic molecules are analyzed and recommendations for the experimental improvement of control are formulated.     

A theoretical study of the chiroptical properties of molecules with isotopically engendered chirality

There has been a considerable interest in the chiroptical properties of molecules whose chirality is exclusively due to an isotopic substitution and numerous examples for the electronic circular dichroism (CD) spectra of isotopically chiral systems have been reported in literature. Four different explanations have been proposed for the mechanism as to how the isotopic substitution induces a chiral perturbation of the otherwise achiral electronic wave function; however, up to now no conclusive answer has been given about the dominating effect responsible for the experimental observations. In this study we will present, for the first time, fully quantum-mechanical calculations of the CD spectra of three different molecular systems with isotopically engendered chirality. As examples, we consider the spectra of organic molecules with ketone and alpha-diketone carbonyl and diene chromophores. The effect of vibronic couplings for the reorientation of the electric and magnetic transition dipole moments is taken into account within the Herzberg-Teller approximation. The ground and excited state geometries and vibrational normal modes are obtained with (time-dependent) density functional theory [(TD)DFT], while the vibronic coupling effects are calculated at the TDDFT and density functional theory/multireference configuration interaction (DFT/MRCI) levels of theory. Generally, the band shapes of the experimental CD spectra are reproduced very well, and also the absolute CD intensities from the simulations are of the right order of magnitude. The sign and the intensity of the CD band are determined by a delicate balance of the contributions of a large number of individual vibronic transitions, and it is found that the vibrational normal modes with a large displacement are dominant. The separation of the calculated CD spectrum into the different contributions due to the overlap of the in-plane and out-of-plane components (regarding the symmetry plane of the unsubstituted molecule) of the electric and magnetic transition dipole moments yields information about the influence of the vibronic coupling effects for the reorientation of the corresponding transition dipole moments. In conclusion, the calculations clearly show that vibronic effects are responsible or at least dominant for the chiroptical properties of isotopically chiral organic molecules.     

Perturbation theory in large order for some elementary systems

Reasons for understanding the general problem of perturbation theory in large order are discussed. It is shown that the behavior of perturbation theory in larger order is generally very simple because it reflects just the semiclassical content of the theory. Many simple examples are given, including some graph-counting problems. The behavior of mass-renormalized perturbation series for some very simple field-theory models is examined. It is shown that mass renormalization hardly affects the large-order behavior of a weak-coupling perturbation series. However, in a strong-coupling perturbation series mass renormalization has a dramatic effect.