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The electronic structure of molecules is routinely examined for static arrangements of point nuclei, which is a highly useful premise but not without certain limitations. Here, the electron-nuclear correlation energy is analysed in the context of the quantised nuclear energy associated with the chemical bond vibrations. To this end, accurate calculations of the ground state of a hydrogen atom (including basis functions in the energy continuum) whose nucleus is confined by a quadratic potential well, are performed for all values of the spring constant. The numerically exact ground state energy is compared to the results obtained within the Born–Oppenheimer approximation and within the uncorrelated product wavefunction ansatz. The electron-nuclear correlation energy is found to be smaller in magnitude than the electron correlation in two-electron atomic systems, in the limit of weak nuclear confinement, and is further reduced by at least an order of magnitude in the limit of strong confinement. In all cases, however, the electron-nuclear correlation energy is found to be significantly larger than the error of the Born–Oppenheimer approximation. Moreover, the error of the Born–Oppenheimer approximation is found to persist within the limit of infinite nuclear confinement. Insight into the electron-nuclear correlation energy from this study will help incorporate the nuclear quantum effects into the electronic structure theories. [ABSTRACT FROM AUTHOR]

The quantum trajectory approach is generalized to arbitrary coordinate systems, including curvilinear coordinates, allowing to perform an approximate quantum trajectory propagation, which scales favorably with system size, in the same framework as standard quantum wave packet dynamics. The trajectory formulation is implemented in Jacobi coordinates for a nonrotating triatomic molecule, providing an accurate description of asymptotic dynamics for the system.

A Monte Carlo simulation has been developed for electron thermalization in a liquid hydrocarbon taking n-hexane as a paradigm, both effect of the geminate cation and that of an external electric field have been included in the predicted electron thermalization distance distribution (ETDD). The distortion of the thermalization distance distribution by an external filed affects the free-ion yield in the second-order O(E2), which can be seen at very high fields.

A classical limit of quantum dynamics can be defined by compensation of the quantum potential in the time-dependent Schrödinger equation. The quantum potential is a non-local quantity, defined in the trajectory-based form of the Schrödinger equation, due to Madelung, de Broglie, and Bohm, which formally generates the quantum-mechanical features in dynamics. Selective inclusion of the quantum potential for the degrees of freedom deemed "quantum," defines a hybrid quantum/ classical dynamics, appropriate for molecular systems comprised of light and heavy nuclei. The wavefunction is associated with all of the nuclei, and the Ehrenfest, or mean-field, averaging of the force acting on the classical degrees of freedom, typical of the mixed quantum/classical methods, is avoided. The hybrid approach is used to examine evolution of light/heavy systems in the harmonic and double-well potentials, using conventional grid-based and approximate quantum-trajectory time propagation. The approximate quantum force is defined on spatial domains, which removes unphysical coupling of the wavefunction fragments corresponding to distinct classical channels or configurations. The quantum potential, associated with the quantum particle, generates forces acting on both quantum and classical particles to describe the backreaction. [ABSTRACT FROM AUTHOR]

Strong orthogonality is an important constraint placed on geminal wavefunctions in order to make variational minimization tractable. However, strong orthogonality prevents certain, possibly important, excited configurations from contributing to the ground state description of chemical systems. The presented method lifts strong orthogonality constraint from geminal wavefunction by computing a perturbative-like correction to each geminal independently from the corrections to all other geminals. The method is applied to the Singlet-type Strongly orthogonal Geminals variant of the geminal wavefunction. Comparisons of this new SSpG method are made to the non-orthogonal AP1roG and the unconstrained Geminal Mean-Field Configuration Interaction method using small atomic and molecular systems. The correction is also compared to Density Matrix Renormalization Group calculations performed on long polyene chains in order to assess its scalability and applicability to large strongly correlated systems. The results of these comparisons demonstrate that although the perturbative correction is small, it may be a necessary first step in the systematic improvement of any strongly orthogonal geminal method. [ABSTRACT FROM AUTHOR]

The electron correlation energy in a chemical system is defined as a difference between the energy of an exact energy for a given Hamiltonian, and a mean-field, or single determinant, approximation to it. A promising way to model electron correlation is through the expectation value of a linear two-electron operator for the Kohn-Sham single determinant wavefunction. For practical reasons, it is desirable for such an operator to be universal, i.e., independent of the positions and types of nuclei in a molecule. The correlation operator models the effect of electron correlation on the interaction energy in a electron pair. We choose an operator expanded in a small number of Gaussians as a model for electron correlation, and test it by computing atomic and molecular adiabatic excited states. The computations are performed within the Δ Self-Consistent Field (ΔSCF) formalism, and are compared to the time-dependent density functional theory model with popular density functionals. The simplest form of the correlation operator contains only one parameter derived from the helium atom ground state correlation energy. The correlation operator approach significantly outperforms other methods in computation of atomic excitation energies. The accuracy of molecular excitation energies computed with the correlation operator is limited by the shortcomings of the ΔSCF methodology in describing excited states. [ABSTRACT FROM AUTHOR]

An appealing way to model electron correlation within the single determinant wave function formalism is through the expectation value of a linear two-electron operator. For practical reasons, it is desirable for such an operator to be universal, i.e., not depend on the positions and types of nuclei in a molecule. We show how a perturbation theory applied to a hookium atom provides for a particular form of a correlation operator, hence called the harmonic correlation operator. The correlation operator approach is compared and contrasted to the traditional ways to describe electron correlation. To investigate the two-electron approximation of this operator, we apply it to many-electron hookium systems. To investigate the harmonic approximation, we apply it to the small atomic systems. Directions of future research are also discussed. [ABSTRACT FROM AUTHOR]

The concept of the correlation operator, introduced 10 years ago as a possible method to model the electron correlation effects with single determinant wave functions [Rassolov, J. Chem. Phys. 110, 3672 (1999)], is revisited. We derive a semiclassical limit of the correlation operator in weakly correlated systems and give its coordinate space representation. Application of this operator to the atomic systems, such as computations of energies of the neutral atoms, energies of the cations, and spin states energy gaps, demonstrates capabilities and limitations of this concept. [ABSTRACT FROM AUTHOR]

Semiclassical implementation of the quantum trajectory formalism [J. Chem. Phys. 120, 1181 (2004)] is further developed to give a stable long-time description of zero-point energy in anharmonic systems of high dimensionality. The method is based on a numerically cheap linearized quantum force approach; stabilizing terms compensating for the linearization errors are added into the time-evolution equations for the classical and nonclassical components of the momentum operator. The wave function normalization and energy are rigorously conserved. Numerical tests are performed for model systems of up to 40 degrees of freedom. [ABSTRACT FROM AUTHOR]

An augmented valence triple-zeta basis set, referred to as G3Large, is reported for the first-row transition metal elements Sc through Zn. The basis set is constructed in a manner similar to the G3Large basis set developed previously for other elements (H–Ar, K, Ca, Ga–Kr) and used as a key component in Gaussian-3 theory. It is based on a contraction of a set of 15s13p5d Gaussian primitives to 8s7p3d, and also includes sets of f and g polarization functions, diffuse spd functions, and core df polarization functions. The basis set is evaluated with triples-augmented coupled cluster [CCSD(T)] and Brueckner orbital [BD(T)] methods for a small test set involving energies of atoms, atomic ions, and diatomic hydrides. It performs well for the low-lying s→d excitation energies of atoms, atomic ionization energies, and the dissociation energies of the diatomic hydrides. The Brueckner orbital-based BD(T) method performs substantially better than Hartree–Fock–based CCSD(T) for molecules such as NiH, where the starting unrestricted Hartree–Fock wavefunction suffers from a high degree of spin contamination. Comparison with available data for geometries of transition metal hydrides also shows good agreement. A smaller basis set without core polarization functions, G3MP2Large, is also defined. [ABSTRACT FROM AUTHOR]

We present a computationally inexpensive method that yields ground state wave functions of pure spin symmetry. The method is variational and rigorously size consistent, free from adjustable parameters, and has a favorable scaling with system size. It is based on the recently introduced partially spin restricted geminal wave functions with limited spin contamination. Computations of a bond breaking, a transition metal compound, and a symmetric hydrogen cluster confirm the properties of this method. [ABSTRACT FROM AUTHOR]

The authors define an ab initio electronic structure model that uses partial spin restriction. It is an intermediate case between the so-called spin-restricted and spin-unrestricted formulations, which are popular in electronic structure methodology. Partial spin restriction arises naturally when the wave function is represented as an antisymmetrized product of two-electron functions, as it is done in generalized valence bond and antisymmetrized product of strongly orthogonal geminal theories. The authors show that the new model is size consistent, and it improves the description of transition metal compounds. [ABSTRACT FROM AUTHOR]

The O(3P,1D)+H2→OH+H reaction is studied using trajectory dynamics within the approximate quantum potential approach. Calculations of the wave-packet reaction probabilities are performed for four coupled electronic states for total angular momentum J=0 using a mixed coordinate/polar representation of the wave function. Semiclassical dynamics is based on a single set of trajectories evolving on an effective potential-energy surface and in the presence of the approximate quantum potential. Population functions associated with each trajectory are computed for each electronic state. The effective surface is a linear combination of the electronic states with the contributions of individual components defined by their time-dependent average populations. The wave-packet reaction probabilities are in good agreement with the quantum-mechanical results. Intersystem crossing is found to have negligible effect on reaction probabilities summed over final electronic states. [ABSTRACT FROM AUTHOR]

Nonadiabatic effects in quantum dynamics are described using a mixed polar/coordinate space representation of the wave function. The polar part evolves on dynamically determined potential surfaces that have diabatic and adiabatic potentials as limiting cases of weak localized and strong extended diabatic couplings. The coordinate space part, generalized to a matrix form, describes transitions between the surfaces. Choice of the effective potentials for the polar part and partitioning of the wave function enables one to represent the total wave function in terms of smooth components that can be accurately propagated semiclassically using the approximate quantum potential and small basis sets. Examples are given for two-state one-dimensional problems that model chemical reactions that demonstrate the capabilities of the method for various regimes of nonadiabatic dynamics. [ABSTRACT FROM AUTHOR]

Dynamics of quantum trajectories provides an efficient framework for description of various quantum effects in large systems, but it is unstable near the wave function density nodes where the quantum potential becomes singular. A mixed coordinate space/polar representation of the wave function is used to circumvent this problem. The resulting modified trajectory dynamics associated with the polar representation is nonsingular and smooth. The interference structure and the nodes of the wave function density are described, in principle, exactly in the coordinate representation. The approximate version of this approach is consistent with the semiclassical linearized quantum force method [S. Garashchuk and V. A. Rassolov, J. Chem. Phys. 120, 1181 (2004)]. This approach is exact for general wave functions with the density nodes in a locally quadratic potential.© 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We introduce and investigate a chemical model based on perturbative corrections to the product of singlet-type strongly orthogonal geminals wave function. Two specific points are addressed (i) Overall chemical accuracy of such a model with perturbative corrections at a leading order; (ii) Quality of strong orthogonality approximation of geminals in diverse chemical systems. We use the Epstein—Nesbet form of perturbation theory and show that its known shortcomings disappear when it is used with the reference Hamiltonian based on strongly orthogonal geminals. Application of this model to various chemical systems reveals that strongly orthogonal geminals are well suited for chemical models, with dispersion interactions between the geminals being the dominant effect missing in the reference wave functions. [ABSTRACT FROM AUTHOR]

In the de Broglie–Bohm formulation of quantum mechanics the time-dependent Schrödinger equation is solved in terms of quantum trajectories evolving under the influence of quantum and classical potentials. For a practical implementation that scales favorably with system size and is accurate for semiclassical systems, we use approximate quantum potentials. Recently, we have shown that optimization of the nonclassical component of the momentum operator in terms of fitting functions leads to the energy-conserving approximate quantum potential. In particular, linear fitting functions give the exact time evolution of a Gaussian wave packet in a locally quadratic potential and can describe the dominant quantum-mechanical effects in the semiclassical scattering problems of nuclear dynamics. In this paper we formulate the Bohmian dynamics on subspaces and define the energy-conserving approximate quantum potential in terms of optimized nonclassical momentum, extended to include the domain boundary functions. This generalization allows a better description of the non-Gaussian wave packets and general potentials in terms of simple fitting functions. The optimization is performed independently for each domain and each dimension. For linear fitting functions optimal parameters are expressed in terms of the first and second moments of the trajectory distribution. Examples are given for one-dimensional anharmonic systems and for the collinear hydrogen exchange reaction. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Solution of the Schrödinger equation within the de Broglie–Bohm formulation is based on propagation of trajectories in the presence of a nonlocal quantum potential. We present a new strategy for defining approximate quantum potentials within a restricted trial function by performing the optimal fit to the log-derivatives of the wave function density. This procedure results in the energy-conserving dynamics for a closed system. For one particular form of the trial function leading to the linear quantum force, the optimization problem is solved analytically in terms of the first and second moments of the weighted trajectory distribution. This approach gives exact time-evolution of a correlated Gaussian wave function in a locally quadratic potential. The method is computationally cheap in many dimensions, conserves total energy and satisfies the criterion on the average quantum force. Expectation values are readily found by summing over trajectory weights. Efficient extraction of the phase-dependent quantities is discussed. We illustrate the efficiency and accuracy of the linear quantum force approximation by examining a one-dimensional scattering problem and by computing the wavepacket reaction probability for the hydrogen exchange reaction and the photodissociation spectrum of ICN in two dimensions. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We present a time-dependent semiclassical method based on quantum trajectories. Quantum-mechanical effects are described via the quantum potential computed from the wave function density approximated as a linear combination of Gaussian fitting functions. The number of the fitting functions determines the accuracy of the approximate quantum potential (AQP). One Gaussian fit reproduces time-evolution of a Gaussian wave packet in a parabolic potential. The limit of the large number of fitting Gaussians and trajectories gives the full quantum-mechanical result. The method is systematically improvable from classical to fully quantum. The fitting procedure is implemented as a gradient minimization. We also compare AQP method to the widely used semiclassical propagator of Herman and Kluk by computing energy-resolved transmission probabilities for the Eckart barrier from the wave packet time-correlation functions. We find the results obtained with the Herman-Kluk propagator to be essentially equivalent to those of AQP method with a one-Gaussian density fit for several barrier widths. [ABSTRACT FROM AUTHOR]

We modify the existing model of the antisymmetrized product of strongly orthogonal geminals to define a size consistent variational theory free from any adjustable parameters apart from the usual choice of a basis set. The new theory is only slightly more computationally expensive than HartreeFock, gives an exact solution for an ensemble of noninteracting singlet two electron systems, and is applicable to open- and closed-shell systems. We use it to calculate equilibrium geometries, vibrational frequencies, and dipole moments of diatomic molecules from G2/97 database. We find excellent agreement with experimental values for covalently bound molecules, and overstretched bonds of molecules formed by atoms with extreme electronegativity. [ABSTRACT FROM AUTHOR]