Determining partial differential cross sections for low-energy electron photodetachment involving conical intersections using the solution of a Lippmann-Schwinger equation constructed with standard electronic structure techniques

A method for obtaining partial differential cross sections for low energy electron photodetachment in which the electronic states of the residual molecule are strongly coupled by conical intersections is reported. The method is based on the iterative solution to a Lippmann-Schwinger equation, using a zeroth order Hamiltonian consisting of the bound nonadiabatically coupled residual molecule and a free electron. The solution to the Lippmann-Schwinger equation involves only standard electronic structure techniques and a standard three-dimensional free particle Green's function quadrature for which fast techniques exist. The transition dipole moment for electron photodetachment, is a sum of matrix elements each involving one nonorthogonal orbital obtained from the solution to the Lippmann-Schwinger equation. An expression for the electron photodetachment transition dipole matrix element in terms of Dyson orbitals, which does not make the usual orthogonality assumptions, is derived.     

Two-photon dissociation of vibrationally excited H2+. Complex quasi-vibrational energy and inhomogeneous differential equation approaches

We present two practical theoretical methods — the complex quasi-vibrational energy and the inhomogeneous differential equation approaches — for numerical computation of multiphoton dissociation cross sections. The methods are applied to the study of the two-photon dissociation of H₂⁺ (1sσg). The cross sections are small for low-lying vibrational states but increase very rapidly with increasing vibrational quantum number, suggesting that experimentally accessible powerful lasers can be used to probe the highly excited vibrational states of the ground electronic state of a homonuclear diatomic molecule.     

Matrix elements of N-particle explicitly correlated Gaussian basis functions with complex exponential parameters

In this work we present analytical expressions for Hamiltonian matrix elements with spherically symmetric, explicitly correlated Gaussian basis functions with complex exponential parameters for an arbitrary number of particles. The expressions are derived using the formalism of matrix differential calculus. In addition, we present expressions for the energy gradient that includes derivatives of the Hamiltonian integrals with respect to the exponential parameters. The gradient is used in the variational optimization of the parameters. All the expressions are presented in the matrix form suitable for both numerical implementation and theoretical analysis. The energy and gradient formulas have been programmed and used to calculate ground and excited states of the He atom using an approach that does not involve the Born-Oppenheimer approximation.     

Kinetic Energy Partition Method for Competing Modes

We present a new basis set expansion method for quantum dynamics systems with two competing modes where the interaction potentials are equally dominant. The new idea introduced here is a kinetic energy partition scheme instead of the usual division of the potential energy. The partition results in two kinetic energy terms with their effective masses. By distributing each partial kinetic energy to the respective potential, the full Hamiltonian can be expressed as the sum of the two competing modes. The solution procedure is illustrated by using a system consisting of a particle under the action of two harmonic potentials with different equilibrium distances and force constants. Next we apply this method to obtain the potential energy curves for the prototype hydrogen molecule ion. This new expansion converges very fast to the exact solutions for both eigenvalues and eigenfunctions.     

Long-range interaction and the dynamics of nonadiabatic transitions in collisions of the I2(E) molecule with inert gas atoms

A special form of perturbation theory based on intermolecular interaction was used to analyze the contributions to the interaction energy between a homonuclear diatomic molecule with dipole-coupled electronic states n and n′ and a neutral particle A. At large distances, the energy of the system in both states n and n′ is determined by the induction contribution similar to the induction interaction of particle A and a polar molecule. The presence of a constant electric moment of particle A gives an electrostatic contribution to the matrix element of the nonadiabatic coupling of the states n and n′. The equations obtained were specialized to describe the interaction of the iodine molecule excited to ion-pair states with an inert gas atom and used as corrections to the potential energy surfaces of this system constructed within the diatomics-in-molecule approximation. The dynamics of transitions between the ion-pair states of the I₂ molecule induced by collisions with the Ar and He atoms was calculated. The results demonstrate the importance of correctly including long-range interaction.     

Generalized relativistic effective core potential: Theoretical grounds

The generalized relativistic effective core potential (GRECP) method is analyzed from theoretical and computational points of view. The Hamiltonian in the frozen‐core approximation is compared with the Hamiltonian containing the GRECP operator. It is demonstrated that the GRECP operator can be derived from rather natural physical grounds and the procedure of the GRECP generation can be justified theoretically. The accuracy of the RECP approximations in the simulation of the interactions and densities in the valence and outer‐core regions is analyzed. The reliability of the simulation of the interaction with the inner‐core electrons removed from the calculations with the GRECP is also studied. The importance of additional nonlocal terms both with the potentials for the outer‐core pseudospinors and with the potentials depending on the occupation numbers of the outermost core shells in the expression for the GRECP operator is demonstrated in calculations on the Ag, Ba, Hg, Tl, and U atoms. The difference between the outer core and valence potentials was investigated. It is shown that in the valence region the two‐component pseudospinors coincide with the large components of four‐component spinors in calculations for the same configuration states with a very high accuracy. Problems of Gaussian approximation caused by rather singular shapes of the potentials are considered. To attain a required high accuracy of approximation of the numerical potentials by Gaussians, serious additional efforts were undertaken. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 71: 359–401, 1999     

Beyond the MNDO model: Methodical considerations and numerical results

It is suggested to improve the MNDO model by the explicit inclusion of valence-shell orthogonalization corrections, penetration integrals, and effective core potentials (ECPs) in the one-center part of the core Hamiltonian matrix. Guided by analytic formulas and numerical ab initio results, the orthogonalization corrections are expressed in terms of the resonance integrals that are represented by a new empirical parametric function. All two-center Coulomb interactions and ECP integrals are evaluated analytically in a Gaussian basis followed by a uniform Klopman–Ohno scaling. One particular implementation of the proposed NDDO SCF approach is described and parameterized for the elements H, C, N, O, and F. In a statistical evaluation of ground-state properties, this implementation shows slight but consistent improvements over MNDO, AM1, and PM3. Significant improvements are found for excited states, transition states, and strong hydrogen bonds. Possible further enhancements of the current implementation are discussed. © 1993 John Wiley & Sons, Inc.     

Quantum transport in chains with noisy off-diagonal couplings

We present a model for conductivity and energy diffusion in a linear chain described by a quadratic Hamiltonian with Gaussian noise. We show that when the correlation matrix is diagonal, the noise-averaged Liouville-von Neumann equation governing the time evolution of the system reduces to the [Lindblad, Commun. Math. Phys. 48, 119 (1976)] equation with Hermitian Lindblad operators. We show that the noise-averaged density matrix for the system expectation values of the energy density and the number density satisfies discrete versions of the heat and diffusion equations. Transport coefficients are given in terms of model Hamiltonian parameters. We discuss conditions on the Hamiltonian under which the noise-averaged expectation value of the total energy remains constant. For chains placed between two heat reservoirs, the gradient of the energy density along the chain is linear.     

Extensive theoretical study on the low-lying electronic states of silicon monofluoride cation including spin-orbit coupling

Ab initio calculations on the low-lying electronic states of SiF+ are performed using the internally contracted multireference configuration interaction method with the Davidson correction and entirely uncontracted aug-cc-pV5Z basis set. The effects of spin-orbit coupling are accounted for by the state interaction approach with the full Breit-Pauli Hamiltonian. The entire 23 Omega states generated from the 12 valence Lambda-S states, which correlate with the first dissociation channel are studied for the first time. Good agreement is found between the calculated results and the available experimental data. The spin-orbit coupling effects on the potential energy curves and spectroscopic properties are studied. Various curve crossings are revealed, which could lead to the predissociation of the a3Pi, A1Pi, and (2)3Sigma+ states and the predissociation pathways are analyzed based upon the calculated spin-orbit matrix elements. The calculated ionization potentials of the ground-state SiF to a few states of SiF+ are in good agreement with the available experimental measurements. Moreover, the transition dipole moments of the dipole-allowed transitions and the transition properties for the A3Pi0+ -X1Sigma+ 0+ and B3Pi1-X1Sigma+ 0+ transitions are predicted, including the Franck-Condon factors and the radiative lifetimes.     

Bound-state plus continuum electron densities,and Slater sum,in a bare Coulomb field

After reporting numerical studies based solely on s-states of total (s + p + d etc.) bound-state densities, which allow the range of validity of the simplest density functional theory of Thomas and Fermi to be critically assessed, two areas in which analytical progress proves possible are focused on. The first of these is the local density of states in the continuum, for which an exact formula is derived. The second concerns the Slater sum, for which an explicit differential equation is established. Prior to this, only the Bloch equation satisfied by the off-diagonal generalization of the Slater sum, namely the canonical density matrix, was available.     

Spin-orbit vibronic coupling in 3Pi states of linear triatomic molecules

The Renner-Teller vibronic-coupling problem of a 3Pi electronic state of a linear molecule is analyzed with the inclusion of the spin-orbit coupling of the 3Pi electronic state, employing the microscopic (Breit-Pauli) spin-orbit coupling operator for the two unpaired electrons. The 6x6 Hamiltonian matrix in a diabatic spin-electronic basis is obtained by an expansion of the molecular Hamiltonian in powers of the bending amplitude. The symmetry properties of the Hamiltonian with respect to the time-reversal operator and the relativistic vibronic angular momentum operator are analyzed. It is shown that there exists a linear vibronic-coupling term of spin-orbit origin, which has not been considered so far in the Renner-Teller theory of 3Pi electronic states. While two of the six adiabatic electronic wave functions do not exhibit a geometric phase, the other four carry nontrivial topological phases which depend on the radius of the integration contour. The spectroscopic effects of the linear spin-orbit vibronic-coupling mechanism have been analyzed by numerical calculations of the vibronic spectrum for selected model examples.     

Phase-sensitive stimulated Raman adiabatic passage in dipolar extended lambda systems

The authors investigate the possible phase-sensitive behavior of (multiphoton) stimulated Raman adiabatic passage population transfer in extended lambda systems, if more than one state of an anharmonic progression of target levels is accessible in transitions of different photonicities. They use a minimal model four-level system (4LS) with one initial state separated from two target states by an apex state. The parameters of the 4LS are adapted from the bend states of the HCN-HNC system. Using a dressed-state analysis within the rotating wave approximation (RWA), the authors identify phase-dependent diabatic transitions between the two dressed states contributing to the state vector as the mechanism leading to phase-sensitive target populations. The essential features giving rise to the phase dependence are found to be different (non-zero-) diagonal elements of the dipole matrix, i.e., permanent dipole moments, and the presence of a direct two-photon overtone coupling between the apex state and the lower target state which formally enters the RWA Hamiltonian upon inclusion of permanent dipole moments. Among the parameters controlling the extent of the effect are the anharmonic properties of the target progression and the absolute values of the field frequencies, so that in view of the requirement to tune the driving fields into the vicinity of resonance, details of the level structure are of importance. A comparative numerical study executed without invoking RWA shows that qualitatively there are similar trends in the appearance of phase sensitivity, although the effects are considerably more pronounced in the full treatment. In the full treatment the authors also explore off-resonance conditions and discuss the signatures of phase sensitivity in the target populations.     

Integrals and derivatives for correlated Gaussian functions using matrix differential calculus

The matrix differential calculus is applied for the first time to a quantum chemical problem via new matrix derivations of integral formulas and gradients for Hamiltonian matrix elements in a basis of correlated Gaussian functions. Requisite mathematical background material on Kronecker products, Hadamard products, the vec and vech operators, linear structures, and matrix differential calculus is presented. New matrix forms for the kinetic and potential energy operators are presented. Integrals for overlap, kinetic energy, and potential energy matrix elements are derived in matrix form using matrix calculus. The gradient of the energy functional with respect to the correlated Gaussian exponent matrices is derived. Burdensome summation notation is entirely replaced with a compact matrix notation that is both theoretically and computationally insightful. © 1996 John Wiley & Sons, Inc.     

Abnormal inversion splitting in NH2D: rotational analysis of the nu5 bending vibrational band system

A high-resolution Fourier transform infrared spectrum of the nu(5) bending vibrational band system region of the partially deuterated ammonia molecule NH(2)D has been measured and rotationally analyzed. The spectrum consists of strong a-type transitions between the states of same vibrational symmetry and weaker c-type transitions between the states of different vibrational symmetry. The Hamiltonian model used includes interaction terms between the rotational states of both upper and lower inversion doublets. The vibrational term values for the symmetric and the antisymmetric component of the upper-inversion doublet are 1,605.637 965(620) cm(-1) and 1,590.993 82(100) cm(-1), respectively, where the numbers in parentheses are one-standard deviations in the least significant digit. These figures are close to the corresponding values 1,605.62 cm(-1) and 1,590.72 cm(-1) obtained recently from results based on high-level ab initio calculations. The order of the vibrational term values is abnormal in the ammonia family, as typically the symmetric state is lower in wavenumber than the antisymmetric one.     

First ultraviolet absorption band of methane: an ab initio study

Quantum mechanical calculations of the cross sections for photodissociation of CH4 and CD4 in the 1t2-->3s band are presented. The potential energy surfaces for the three states correlating with the 1 1T2 state at tetrahedral geometries are calculated. The elements of the (3x3) matrix representing the electronic Hamiltonian in the diabatic basis are expanded in powers of nuclear coordinates, up to the second order. The expansion coefficients are based on accurate multireference configuration interaction calculations. The electronically nonadiabatic dynamics is treated with the multiconfiguration time-dependent Hartree approach. All nine internal degrees of methane are included in the quantum dynamics simulations. The calculated cross section agrees well with experiment. Semiclassical calculations using the reflection principle suggest that the peaks in the spectrum correspond to the three adiabatic electronic states correlating with the 1 1T2 state at Td geometries. However, the non-Born-Oppenheimer terms in the Hamiltonian have a strong effect on the positions of the peaks in the absorption spectrum. The results of semiclassical calculations, which neglect these terms, are therefore quite different from the accurate quantum results and experiment.     

Solvent configuration-interaction calculations of intermolecular states in molecule-(atom)N clusters: application to Br2-4HeN

We describe variational calculations of J=0 intermolecular states in Br(2)-(4)He(N) clusters. The method employed is analogous to configuration-interaction calculations in electronic-structure work and relies on the ability to express the intermolecular Hamiltonian H(v) as a sum of one- and two-body terms. A basis set is built up from solutions to the Schr?dinger equation in which only the one-body terms of H(v) are included. These configurations are products of N=1 eigenstates. The matrix of H(v) in a symmetry-adapted configuration basis is then computed, the two-body terms of H(v) serving to couple different configurations. This computation involves integrals of dimension five or less. Filter diagonalization is then used to obtain energies and eigenfunctions within a selected energy range. Results on clusters having N=2-5 are reported.     

Ab initio study including spin-orbit effects on the B-X transition of AgI

The lowest Omega = 0-,0+,1,2 fine-structure potential energy curves arising from the two lowest-lying singlet (X 1Sigma+ and 2 1Sigma+) and the first 3Pi electronic states of AgI were obtained through an effective Hamiltonian; the purely electronic LambdaSSigma energies were used as diagonal elements, which were calculated through extensive complete active space self-consistent field + averaged coupled pair functional calculations, with relativistic effective core potentials and optimized Gaussian basis sets for both atoms. The spin-orbit interactions were included using the Stuttgart effective spin-orbit potentials. For the excited Omega = 0+ states, very strong mixtures were found of the 2 1Sigma+ and 3Pi parents that lead to the fine-structure (0+) single B state (dominated by the 2 1Sigma+ parent at long distance), that explains the B <-- X transitions. The present results also explain the presence of a second long-distance minimum for the B0+ state, experimentally Rydberg-Klein-Rees fitted. These calculations produced, as a byproduct, a new lower-lying Omega = 0+ yet unobserved fine-structure state predicted to exist around 22,000 cm(-1). Our theoretical results are compared and discussed in the light of the experimental data for the B-X transitions in silver halides [J. Chem. Phys. 109, 9831 (1998)].     

Nonlinear wave-packet interferometry and molecular state reconstruction in a vibrating and rotating diatomic molecule

We formulate two-color nonlinear wave-packet interferometry (WPI) for application to a diatomic molecule in the gas phase and show that this form of heterodyne-detected multidimensional electronic spectroscopy will permit the reconstruction of photoinduced rovibrational wave packets from experimental data. Using two phase-locked pulse pairs, each resonant with a different electronic transition, nonlinear WPI detects the quadrilinear interference contributions to the population of an excited electronic state. Combining measurements taken with different phase-locking angles isolates various quadrilinear interference terms. One such term gives the complex overlap between a propagated one-pulse target wave packet and a variable three-pulse reference wave packet. The two-dimensional interferogram in the time domain specifies the complex-valued overlap of the given target state with a collection of variable reference states. An inversion procedure based on singular-value decomposition enables reconstruction of the target wave packet from the interferogram without prior detailed characterization of the nuclear Hamiltonian under which the target propagates. With numerically calculated nonlinear WPI signals subject to Gaussian noise, we demonstrate the reconstruction of a rovibrational wave packet launched from the A state and propagated in the E state of Li2.     

Symmetric double-well potential model and its application to vibronic spectra: studies of inversion modes of ammonia and nitrogen-vacancy defect centers in diamond

In this paper, we have studied the vibronic transitions between two symmetric double-well potentials by proposing a model Hamiltonian consisting of a harmonic oscillator and a parturition described by a Gaussian function that leads to a double minima potential with a barrier between the two energy minima. Making use of the contour integral form of Hermite polynomials, we present a new formula that can calculate Franck-Condon factors of the system rigorously. The simulated vibronic spectra of ammonia and the negatively charged nitrogen-vacancy center in diamond are presented as an application of the formula.