A theoretical study of Ne3 using hyperspherical coordinates and a slow variable discretization approach

We study theoretically the ground and excited bound states of the bosonic rare gas van der Waals trimer Ne(3). A slow variable discretization approach is adopted to solve the nuclear Schro?dinger equation, in which the Schro?dinger equation in hyperangular coordinates is solved using basis splines at a series of fixed finite-element methods discrete variable representation hyper-radii. We consider not only zero total nuclear orbital angular momentum, J = 0, states but also J > 0 states. By using the best empirical neon dimer interaction potentials, all the bound state energy levels of Ne(3) will be calculated for total angular momenta up to J = 6, as well as their average root-mean-square radii. We also analyze the wave functions in hyperspherical coordinates for several selected bound states.     

Role of higher excited electronic states on high harmonic generation in H2(+)--a time-independent Hermitian Floquet approach

We have theoretically studied the role of high-lying molecular electronic states on the high harmonic generation (HHG) in H(2)(+) within the framework of a time-independent Hermitian nonperturbative three-dimensional Floquet technique for continuous wave monochromatic lasers of intensities of 2.59 × 10(13), 4.0 × 10(13), and 5.6 × 10(13) W∕cm(2), and wavelengths of 1064, 532, and 355 nm. To evaluate the HHG spectra, the resonance Floquet quasienergy and the Fourier components of the Floquet state corresponding to the initial vibrational-rotational level v = 0, J = 0 have been computed by solving the time-independent close-coupled Schro?dinger equation following the Floquet method. The calculations include seven molecular electronic states in the basis set expansion of the Floquet state. The electronic states considered, apart from the two lowest 1sσ(g) and 2pσ(u) states, are 2pπ(u), 2sσ(g), 3pσ(u), 3dσ(g), and 4fσ(u). All the concerned higher excited molecular electronic states asymptotically degenerate into the atomic state H(2 l) with l = 0, 1. The computations reveal signature of significant oscillations in the HHG spectra due to the interference effect of the higher molecular electronic states for all the considered laser intensities and wavelengths. We have attempted to explain, without invoking any ionization, the dynamics of HHG in H(2)(+) within the framework of electronic transitions due to the electric dipole moments and the nuclear motions on the field coupled ground, the first and the higher excited electronic states of this one-electron molecular ion.     

Solving the Schrödinger and Dirac equations of hydrogen molecular ion accurately by the free iterative complement interaction method

The nonrelativistic Schr?dinger equation and the relativistic four-component Dirac equation of H(2) (+) were solved accurately in an analytical expansion form by the free iterative complement interaction (ICI) method combined with the variational principle. In the nonrelativistic case, we compared the free ICI wave function with the so-called "exact" wave function as two different expansions converging to the unique exact wave function and found that the free ICI method is much more efficient than the exact method. In the relativistic case, we first used the inverse Hamiltonian to guarantee Ritz-type variational principle and obtained accurate result. We also showed that the ordinary variational calculation also gives a nice convergence when the g function is appropriately chosen, since then the free ICI calculation guarantees a correct relationship between the large and small components of each adjacent order, which we call ICI balance. This is the first application of the relativistic free ICI method to molecule. We calculated both ground and excited states in good convergence, and not only the upper bound but also the lower bound of the ground-state energy. The error bound analysis has assured that the present result is highly accurate.     

The Sigma(-) states of the molecular hydrogen

A class of doubly excited electronic states of the hydrogen molecule is reported. The states are of Sigma(-) symmetry and are located ca. 200,000 cm(-1) above the ground state and about 75,000 cm(-1) above the ionization threshold. The electronic wave functions employed to described these states have been expanded in the basis of exponentially correlated Gaussian (ECG) functions with the nonlinear parameters variationally optimized. The lowest (3)Sigma and (1)Sigma states dissociate into hydrogen atoms in the n = 2 state, whereas the lowest (3)Sigma and (1)Sigma states have H(n = 2) and H(n = 3) as the dissociation products. All the four states are attractive and accommodate vibrational levels. The location of the vibrational energy levels has been determined by solving the radial Schr?dinger equation within the Born-Oppenheimer approximation.     

Complete experimental rovibrational eigenenergies of HCN up to 6880 cm(-1) above the ground state

The [H,C,N] molecular system is a very important model system to many fields of chemical physics and the experimental characterization of highly excited vibrational states of this molecular system is of special interest. This paper reports the experimental characterization of all 3822 eigenenergies up to 6880 cm(-1) relative to the ground state in the HCN part of the potential surface using high temperature hot gas emission spectroscopy. The spectroscopic constants for the first 71 vibrational states including highly excited bending vibrations up to v(2) = 10 are reported. The perturbed eigenenergies for all 20 rotational perturbations in the reported eigenenergy range have been determined. The 11,070 eigenenergies up to J = 90 for the first 123 vibrational substates are included as supplement to this paper. We show that a complete ab initio rovibrational analysis for a polyatomic molecule is possible. Using such an analysis we can understand the molecular physics behind the Schro?dinger equation for problems for which perturbation theoretical calculations are no more valid. We show that the vibrational structure of the linear HCN molecule persists approximately up to the isomerization barrier and only above the barrier the accommodation of the vibrational states to the double well structure of the potential takes place.     

An adaptive pseudospectral method for wave packet dynamics

We solve the time-dependent Schro?dinger equation for molecular dynamics using a pseudospectral method with global, exponentially decaying, Hagedorn basis functions. The approximation properties of the Hagedorn basis depend strongly on the scaling of the spatial coordinates. Using results from control theory we develop a time-dependent scaling which adaptively matches the basis to the wave packet. The method requires no knowledge of the Hessian of the potential. The viability of the method is demonstrated on a model for the photodissociation of IBr, using a Fourier basis in the bound state and Hagedorn bases in the dissociative states. Using the new approach to adapting the basis we are able to solve the problem with less than half the number of basis functions otherwise necessary. We also present calculations on a two-dimensional model of CO(2) where the new method considerably reduces the required number of basis functions compared to the Fourier pseudospectral method.     

Rapid, accurate calculation of the s-wave scattering length

Transformation of the conventional radial Schro?dinger equation defined on the interval r ∈ [0, ∞) into an equivalent form defined on the finite domain y(r) ∈ [a, b] allows the s-wave scattering length a(s) to be exactly expressed in terms of a logarithmic derivative of the transformed wave function φ(y) at the outer boundary point y = b, which corresponds to r = ∞. In particular, for an arbitrary interaction potential that dies off as fast as 1/r(n) for n ≥ 4, the modified wave function φ(y) obtained by using the two-parameter mapping function r(y; ?r,β) = ?r[1 + 1/β tan(πy/2)] has no singularities, and a(s) = ?r[1 + 2/πβ 1/φ(1) dφ(1)/dy]. For a well bound potential with equilibrium distance r(e), the optimal mapping parameters are ?r ≈ r(e) and β ≈ n/2 - 1. An outward integration procedure based on Johnson's log-derivative algorithm [J. Comp. Phys. 13, 445 (1973)] combined with a Richardson extrapolation procedure is shown to readily yield high precision a(s)-values both for model Lennard-Jones (2n, n) potentials and for realistic published potentials for the Xe-e(-), Cs(2)(aΣ(u)(+)(3)), and (3, 4)He(2)(XΣ(g)(+)(1)) systems. Use of this same transformed Schro?dinger equation was previously shown [V. V. Meshkov et al., Phys. Rev. A 78, 052510 (2008)] to ensure the efficient calculation of all bound levels supported by a potential, including those lying extremely close to dissociation.     

Carbonyl vibrational wave packet circulation in Mn2(CO)10 driven by ultrashort polarized laser pulses

The excitation of the degenerate E(1) carbonyl stretching vibrations in dimanganese decacarbonyl is shown to trigger wave packet circulation in the subspace of these two modes. On the time scale of about 5 ps, intramolecular anharmonic couplings do not cause appreciable disturbance, even under conditions where the two E(1) modes are excited by up to about two vibrational quanta each. The compactness of the circulating wave packet is shown to depend strongly on the excitation conditions, such as pulse duration and field strength. Numerical results for the solution of the seven-dimensional vibrational Schro?dinger equation are obtained for a density functional theory based potential energy surface and using the multi-configuration time-dependent Hartree method.     

Calculation of the structure, potential energy surface, vibrational dynamics, and electric dipole properties for the Xe:HI van der Waals complex

We report the structure and spectroscopic characteristics for the Xe:HI van der Waals binary isomers determined from variational solutions of two-dimensional and three-dimensional (3D) vibrational Schro?dinger equations. The solutions are based on a potential energy surface computed at the coupled-cluster level of theory including single and double excitations and a non-iterative perturbation treatment of triple excitations [CCSD(T)]. The dipole moment surface was calculated using quadratic configuration interaction (QCISD). The global potential minimum is shown to be located at the anti-hydrogen-bonded Xe-IH isomer, 21 cm(-1) below the secondary local minimum associated with the hydrogen-bonded Xe-HI isomeric form. The dissociation energy from the global minimum is 245.9 cm(-1). 3D Schro?dinger equations are solved for the rotational quantum numbers J = k = 0, 1, and 2, without invoking an adiabatic separation of high- and low-frequency degrees of freedom. The vibrational ground state resides in the Xe-HI potential well, while the first excited state, 8.59 cm(-1) above the ground, occupies the Xe-IH well. We find that intra-complex dynamics exhibits a sudden transformation upon increase of the r(HI) bond length, accompanied by abrupt changes in the geometric and dipole parameters. A similar chaotic behavior is predicted to occur for Xe:DI at a shorter r(DI) bond length, which implies stronger coupling between low- and high-frequency motions in the heavier complex. Our calculations confirm a strong enhancement for the r(HI) stretch fundamental and a significant weakening for the first overtone vibrational transitions in Xe:HI, as compared to those in the free HI molecule. A qualitative explanation of this, earlier experimentally detected effect is suggested.     

Structural properties and energetics of diffuse 87Rb clusters in three-dimension

A correlated two-body basis function is used to describe the three-dimensional bosonic clusters interacting via two-body van der Waals potential. We calculate the ground state and the zero orbital angular momentum excited states for Rb(N) clusters with up to N = 40. We solve the many-particle Schro?dinger equation by potential harmonics expansion method, which keeps all possible two-body correlations in the calculation and determines the lowest effective many-body potential. We study energetics and structural properties for such diffuse clusters both at dimer and tuned scattering length. The motivation of the present study is to investigate the possibility of formation of N-body clusters interacting through the van der Waals interaction. We also compare the system with the well studied He, Ne, and Ar clusters. We also calculate correlation properties and observe the generalised Tjon line for large cluster. We test the validity of the shape-independent potential in the calculation of the ground state energy of such diffuse cluster. These are the first such calculations reported for Rb clusters.     

On the calculations of the variational correlation energy using Møller—Plesset first-order wavefunctions

A method is developed, based on first-order symmetry-adapted pair functions obtained within the framework of the Rayleigh—Schrödinger Hartree—Fock perturbation theory, for obtaining a variational upper bound to the correlation energy in the form of pair increments. The correlation-energy functional obtained is written in terms of second- and third-order energy increments of Møller—Plesset perturbation theory. Application of the procedure to the ground states of the Ne-like systems yields energies of greater accuracy than those obtained from CI calculations using very extensive sets of singly and doubly excited configurations. Our pair energies and the total correlation energy obtained for Zn²⁺ represent the most accurate variational results reported so far for atomic systems containing 3d-electrons.     

Multi-configuration electron-hole potential method for excited states

The recently proposed electron-hole potential (EHP) method for excited states is extended to the multi-configurational case. The variation equation is solved using the quadratic convergence method. The EHP methods are shown to be approximations to the complete singly excited configuration interaction (CSECI) in the variational sense. Extended Brillouin theorems are proved for the EHP methods. The excitation energies and wave functions obtained by one and two configurational EHP methods agree well with those of the CSECI method. The EHP methods have clear advantage in the computer time requirement over the CI method and are especially suited for a calculation of approximate excited states of large molecules. The EHP methods are applicable to excited states which belong to the same irreducible representation as the ground state.     

Supersymmetric solutions of <Emphasis Type="Italic">PT</Emphasis>-/non-<Emphasis Type="Italic">PT</Emphasis>-symmetric and non-Hermitian screened Coulomb potential via Hamiltonian hierarchy inspired variational method

The supersymmetric solutions of PT -symmetric and Hermitian/non-Hermitian forms of quantum systems are obtained by solving the Schr?dinger equation for the Exponential-Cosine Screened Coulomb potential. The Hamiltonian hierarchy inspired variational method is used to obtain the approximate energy eigenvalues and corresponding wave functions.      

Local effective potential theory: nonuniqueness of potential and wave function

In local effective potential energy theories such as the Hohenberg-Kohn-Sham density functional theory (HKS-DFT) and quantal density functional theory (Q-DFT), electronic systems in their ground or excited states are mapped to model systems of noninteracting fermions with equivalent density. From these models, the equivalent total energy and ionization potential are also obtained. This paper concerns (i) the nonuniqueness of the local effective potential energy function of the model system in the mapping from a nondegenerate ground state, (ii) the nonuniqueness of the local effective potential energy function in the mapping from a nondegenerate excited state, and (iii) in the mapping to a model system in an excited state, the nonuniqueness of the model system wave function. According to nondegenerate ground state HKS-DFT, there exists only one local effective potential energy function, obtained as the functional derivative of the unique ground state energy functional, that can generate the ground state density. Since the theorems of ground state HKS-DFT cannot be generalized to nondegenerate excited states, there could exist different local potential energy functions that generate the excited state density. The constrained-search version of HKS-DFT selects one of these functions as the functional derivative of a bidensity energy functional. In this paper, the authors show via Q-DFT that there exist an infinite number of local potential energy functions that can generate both the nondegenerate ground and excited state densities of an interacting system. This is accomplished by constructing model systems in configurations different from those of the interacting system. Further, they prove that the difference between the various potential energy functions lies solely in their correlation-kinetic contributions. The component of these functions due to the Pauli exclusion principle and Coulomb repulsion remains the same. The existence of the different potential energy functions as viewed from the perspective of Q-DFT reaffirms that there can be no equivalent to the ground state HKS-DFT theorems for excited states. Additionally, the lack of such theorems for excited states is attributable to correlation-kinetic effects. Finally, they show that in the mapping to a model system in an excited state, there is a nonuniqueness of the model system wave function. Different wave functions lead to the same density, each thereby satisfying the sole requirement of reproducing the interacting system density. Examples of the nonuniqueness of the potential energy functions for the mapping from both ground and excited states and the nonuniqueness of the wave function are provided for the exactly solvable Hooke's atom. The work of others is also discussed.     

Variational solution of the three-dimensional Schrödinger equation using plane waves in adaptive coordinates

A series of improvements for the solution of the three-dimensional Schr?dinger equation over a method introduced by Gygi [F. Gygi, Europhys. Lett. 19, 617 (1992); F. Gygi, Phys. Rev. B 48, 11692 (1993)] are presented. As in the original Gygi's method, the solution (orbital) is expressed by means of plane waves in adaptive coordinates u, where u is mapped from Cartesian coordinates, u=f(r). The improvements implemented are threefold. First, maps are introduced that allow the application of the method to atoms and molecules without the assistance of the supercell approximation. Second, the electron-nucleus singularities are exactly removed, so that pseudo-potentials are no longer required. Third, the sampling error during integral evaluation is made negligible, which results in a true variational, second-order energy error procedure. The method is tested on the hydrogen atom (ground and excited states) and the H(2)(+) molecule, resulting in milli-Hartree accuracy with a moderate number of plane waves.     

Conical intersection of the ground and first excited states of water: energies and reduced density matrices from the anti-Hermitian contracted Schrödinger equation

A conical intersection between the ground and first-excited states of water is computed through the direct calculation of two-electron reduced density matrices (2-RDMs) from solutions of the anti-Hermitian contracted Schr?dinger equation (ACSE). This study is an extension of a previous study in which the ACSE was used to compute the energies around a conical intersection in the triplet excited states of methylene [Snyder, J. W., Jr.; Rothman, A. E.; Foley, J. J.; Mazziotti, D. A. J. Chem. Phys. 2010, 132, 154109]. We compute absolute energies of the 1(1)A' and 2(1)A' states of water (H(2)O) and the location of the conical intersection. The ACSE energies are compared to those from ab initio wave function methods. To treat multireference correlation, we seed the ACSE with an initial 2-RDM from a multiconfiguration self-consistent field (MCSCF) calculation. Unlike the situation for methylene, the two states in the vicinity of the conical intersection of water both have the same spatial symmetry. Hence, the study demonstrates the ability of the ACSE to resolve states of the same spatial symmetry that are nearly degenerate in energy. The 2-RDMs from the ACSE nearly satisfy necessary N-representability conditions. Comparison of the results from double-ζ and augmented double-ζ basis sets demonstrates the importance of augmented (or diffuse) functions for determining the location of the conical intersection.     

Non-Born-Oppenheimer variational calculation of the ground-state vibrational spectrum of LiH+

Very accurate, rigorous, variational, non-Born-Oppenheimer (non-BO) calculations have been performed for the fully symmetric, bound states of the LiH(+) ion. These states correspond to the ground and excited vibrational states of LiH(+) in the ground (2)Sigma(+) electronic state. The non-BO wave functions of the states have been expanded in terms of spherical N-particle explicitly correlated Gaussian functions multiplied by even powers of the internuclear distance and 5600 Gaussians were used for each state. The calculations that, to our knowledge, are the most accurate ever performed for a diatomic system with three electrons have yielded six bound states. Average interparticle distances and nucleus-nucleus correlation function plots are presented.     

Quantum-dynamical study in three-dimensional space of the exchange reaction H+ClH'→HCl+H' with zero total angular momentum $ \left( {\overrightarrow J = 0} \right) $

The 3D quantum dynamics of the exchange reaction H + ClH′→HCl+H′ with zero angular momentum was studied. The nonstationary Schr?dinger equation was solved by expansion into a basis set using discrete variable representation. The probabilities of the reaction were determined in relation to the total energy for the ground and first excited vibrational states.