The inversion of spectroscopic data to the diatomic effective Hamiltonian containing the generalized potential energy function. Ground state of PbO

A method of inversion of spectroscopic data of a diatomic molecule to the effective Hamiltonian containing adiabatic and non-adiabatic corrections is reported. The method is based on the use of a previously suggested generalized potential energy function with correct long-range part. The potential energy function for the X¹Σ⁺ state of PbO is calculated by inversion of the infrared and microwave spectra.     

A note on excess Gibbs energy models,equations of state and the local composition concept

A density-dependent local composition expression for the residual energy is derived from a generalized NRTL expression for the excess energy and the van der Waals fluid theory. Integration of this expression yields a volume-dependent expression for the Helmholtz energy from which equations of state utilizing the local composition concept are derived and which in the high-density limit contain the well-known activity coefficient models.The local composition versions of the Carnahan—Starling—van der Waals, the Redlich—Kwong—Soave and the Peng—Robinson equations of state are derived. It is further shown that the group contribution versions of the NRTL, the Wilson and the UNIQUAC excess models may be derived from the generalized NRTL expression for the residual energy when applied to groups instead of molecules.It is thus demonstrated that all current local composition activity-coefficient models can be derived from a local composition version of the van der Waals equation of state using different sets of assumptions. In the same way the van Laar, the Scatchard—Hildebrand and the Flory—Huggins activity coefficient models are obtained from the van der Waals equation of state using the original mixing rules.     

Energy transfer via guest excitons in isotopic mixed naphthalene crystals

The temperature dependence of the fluorescence spectra of aggregates in naphthalene-perdeuteronaphthalene mixed crystals has been investigated between 1.4 and 70 K and for concentrations up to 50% naphthalene. It is shown that the most abundant traps — the monomer guest molecules — transfer energy like a guest exciton band 48 cm^?1 below the host exciton band. With increasing temperature, the excitation energy is redistributed between the different aggregate traps by thermal activation into the monomer states. The energy transfer constant within the monomer exciton band is measured as a function of concentration. It is suggested that dipole-dipole interaction between the monomer guests is responsible for the energy transfer via guest excitons.     

A generalized harmonic oscillator model of energy level particles and NNS distribution

Based on the concept of the energy level repulsion, a potential function followed by the energy level particles is suggested. By regarding the energy level fluctuation spectrum as a dynamic system which consists of the pairs of energy level particles behaving as the generalized harmonic oscillator, a generalized Schrödinger equation valid for the nearest neighbor space (NNS) distribution of the levels is established. It turns out that the different kinds of NNS distributions found so far are the solutions of this equation: Both the Poisson type and Wigner type are its eigen solutions whereas the Gaussian unitary ensemble (GUE) type and the Brody type of NNS distribution are its composite solutions. Furthermore, the influences of the small perturbation on the NNS distribution are analyzed.     

Non-markovian effects in dielectric relaxation

A generalized Nee—Zwanzig equation is proposed to describe both low and high frequency dielectric relaxation. It is shown that the inertial effect is closely related to the non-markovian character of the differential equation governing the time evolution of the dipole—dipole autocorrelation function. Comparison with experimental results is given.     

Hamiltonian for arbitrary energy states of molecules

A way how a general rovibronic Hamiltonian for a polyatomic molecule can be obtained using generalized coordinates and introducing a “well” for the potential function of nuclear oscillations has been shown. Eigenfunctions for individual types of motion have a very simple form, which makes it possible to analyze both low-and high-energy states of molecules without changing the solution algorithm and to form an energy matrix without changing the basis set.     

An ab initio effective potential for two particles in the field of the core: a reduction of (N + 2)-electron problem to two-electron problem

We have used many-body Green function theory and the two-electron Bethe—Salpeter equation to derive an approximate two-electron position space hamiltonian eigenvalue equation for two electrons in the presence of a closed shell core. The resulting effective hamiltonian is nonlocal, energy independent, hermitian and nonadiabatic. It includes all the core—valence, valence—valence exchange effects, core screening effects and electron—electron correlation effects. If a closed form solution of the equation is difficult because of the need to construct the hamiltonian, a semi-empirical approach can be taken which expresses much of the hamiltonian in terms of known properties of the core. A semi-empirical analysis of this effective hamiltonian is shown to give well-known phenomenological effective hamiltonians and the connections to them. Thus this work can also be viewed as a theoretical justification and extension of the two-electron model potential or pseudopotential theories.     

New formulation for derivatives of torsion angles and improper torsion angles in molecular mechanics: Elimination of singularities

A new set of formulae is developed for the derivatives of torsion angle energy terms and is introduced into the program CHARMM. These formulae, which are based on derivatives of the torsion angle itself, avoid the singularities introduced by use of the derivatives of the torsion angle cosine. The potential energy can include any differentiable function of the torsion angle and there is no need for a special treatment for cases where planar conformations are not extrema. The resulting code is simpler than the original version and yields correct derivatives in all practical situations. Because the minimum of the torsion energy can be at any angle, the functionality of the existing energy routines is generalized. © 1996 by John Wiley & Sons, Inc.     

On the role of dissipation on the Casimir-Polder potential between molecules in dielectric media

An expression for the Casimir-Polder potential between molecules in a homogeneous dispersive and absorptive dielectric medium is derived. The effect of retardation on the interaction energy is discussed by examining the wave-zone and nonretarded limits of the potential. Unlike Lifshitz theory, the interaction energy is not derived from the potential between macroscopic bodies. In this work, a Green function that explicitly accounts for absorption in the medium is obtained. This function leads to possible dissipation effects and presents a near-zone form that vanishes in the limit of nonabsorptive medium. Employing a two-level model, it is shown that the retarded van der Waals dispersion potential in a medium may become repulsive as a consequence of absorption by the medium. It is suggested that the repulsive dispersion force may delay precipitation of nonpolar molecules from a dielectric solvent or even inhibit chemical reaction between them.     

Exploiting rotational and translational invariance of the energy in derivative calculations in quantum chemistry

It is shown how the invariance of the Born—Oppenheimer potential energy to overall translations and rotations of a molecule can be used to reduce the computational labor required for derivative evaluations at various orders.     

Optimal control theory with continuously distributed target states: An application to NaK

Laser pulse control of molecular dynamics is studied theoretically by using optimal control theory. The control theory is extended to target states which are distributed in time as well as in a space of parameters which are responsible for a change of individual molecular properties. This generalized treatment of a control task is first applied to wave packet formation in randomly oriented diatomic systems. Concentrating on an ensemble of NaK molecules which are not aligned the control yield decreases drastically when compared with an aligned ensemble. Second, we demonstrate for NaK the maximization of the probe pulse transient absorption in a pump–probe scheme with an optimized pump pulse. These computations suggest an overall optical control scheme, whereby a flexible technique is suggested to form particular wave packets in the excited state potential energy surface. In particular, it is shown that considerable wave packet localization at the turning points of the first-excited Σ-state potential energy surfaces of NaK may be achieved. The dependency of the control yield on the probe pulse parameters is also discussed.     

Theoretic quantum information entropies for the generalized hyperbolic potential

The Shannon entropy (S) and the Fisher Information (I) entropies are investigated for a generalized hyperbolic potential in position and momentum spaces. First, the Schrodinger equation is solved exactly using the Nikiforov-Uvarov-Functional Analysis method to obtain the energy spectra and the corresponding wave function. By Fourier transforming the position space wave function, the corresponding momentum wave function was obtained for the low-lying states corresponding to the ground and first excited states. The positions and momentum of Shannon entropy and Fisher Information entropies were calculated numerically. Finally, the Bialynicki-Birula and Mycielski and the Stam-Cramer-Rao inequalities for the Shannon entropy and Fisher Information entropies, respectively, were tested and were found to be satisfied for all cases considered.     

Solute-solvent interaction in liquids. I. Long-range forces and vibrational solvent shifts

The model of solute— solvent interaction based on dipole-induced-dipole forces (Kirkwood-Bauer-Magat) has been generalized, yielding an expression for the energy as a function of solute position and orientalion within a spherical cavity in a dielectric medium. An analogous relation has been derived for the dispersion energy. Barriers to rotation of the solute molecule and shifts in its vibrational frequency are calculated as functions of cavity radius and eccentricity for the case of dilute solutions of HCl in CCl₄. It is found that the effect of dispersion forces on the vibrational frequency of HCl is two-to-three times more important than the traditional dipole-induced-dipole contribution.     

Density scaling and exchange-correlation energy

The exchange-correlation energy is studied using the density scaling proposed by Chan and Handy [G. K.-L. Chan and N. C. Handy, Phys. Rev. A 59, 2670 (1999)]. It is shown that there exists a value of the scaling factor for which the correlation energy disappears. The optimized potential method and the Krieger-Li-Iafrate approach are generalized to incorporate correlation.     

Approximate analytical solutions of a two-term diatomic molecular potential with centrifugal barrier

Approximate analytical bound state solutions of the radial Schr?dinger equation are studied for a two-term diatomic molecular potential in terms of the hypergeometric functions for the cases where q?≥?1 and q?=?0. The energy eigenvalues and the corresponding normalized wave functions of the Manning–Rosen potential, the ‘standard’ Hulthén potential and the generalized Morse potential are briefly studied as special cases. It is observed that our analytical results are the same with the ones obtained before.     

Optimal grids for generalized finite basis and discrete variable representations: definition and method of calculation

The method of optimal generalized finite basis and discrete variable representations (FBR and DVR) generalizes the standard, Gaussian quadrature grid-classical orthonormal polynomial basis-based FBR/DVR method to general sets of grid points and to general, nondirect product, and/or nonpolynomial bases. Here, it is shown how an optimal set of grid points can be obtained for an optimal generalized FBR/DVR calculation with a given truncated basis. Basis set optimized and potential optimized grids are defined. The optimized grids are shown to minimize a function of grid points derived by relating the optimal generalized FBR of a Hamiltonian operator to a non-Hermitian effective Hamiltonian matrix. Locating the global minimum of this function can be reduced to finding the zeros of a function in the case of one dimensional problems and to solving a system of D nonlinear equations repeatedly in the case of D>1 dimensional problems when there is an equal number of grid points and basis functions. Gaussian quadrature grids are shown to be basis optimized grids. It is demonstrated by a numerical example that an optimal generalized FBR/DVR calculation of the eigenvalues of a Hamiltonian operator with potential optimized grids can have orders of magnitude higher accuracy than a variational calculation employing the same truncated basis. Nevertheless, for numerical integration with the optimal generalized FBR quadrature rule basis optimized grids are the best among grids of the same number of points. The notions of Gaussian quadrature and Gaussian quadrature accuracy are extended to general, multivariable basis functions.     

Liquid—gas transition for hard spheres with attractive Yukawa tail interactions

We describe the liquid-gas transition in the hard sphere system with Yukawa tail interactions in the mean spherical approximation. The dependence of critical temperature and density on the range of the interaction is shown and the spinodal curve for a short-ranged potential and a long—ranged potential is presented. The compressibility, energy and virial pressures are presented for a long-ranged potential. Liquid phase pressures are calculated by integrating round the coexistence region, rather than through it.     

The ground-state potential energy function of PO+

The ground-state potential energy function of PO⁺ has been calculated from the set of molecular constants B _e, ω_e, a _i (i = 1, … , 5), R _e, D _e and C₄ in the form of generalized potential energy function previously suggested by us for solving the inverse spectroscopic problem.     

Inversion-free formulation of the direct recursion (transfer matrix) method

The transfer matrix or direct recursion methods (DRM), the indirect (exact) perturbation methods (IPM) and the indirect recursion methods (IRM) — the latter two commonly called resolvent or Green function methods — are briefly discussed. Lee and Joannopoulos have shown the very computational advantages of a traditional DRM. For its further improvement, a new inversion-free DRM (IF DRM) is proposed which is based on the application of generalized eigenvalue equations. In the present formulation, the IF DRM is applicable to study surface electronic problems of bounded perfect crystals. The method of the framework translation is also described which avoids the Schmidt—Hori—Asahi-type transfer matrix trick. It is convenient to study layered structures. Finally, the advantages of a new IRM are stressed which also avoids the inversion difficulty.