Search

A first principles quantum mechanical calculation of the vibrational energy levels and transition frequencies associated with protons in stoichiometric LiNbO3 single crystal has been carried out. The hydrogen contaminated crystal has been approximated by a model one obtains by translating a supercell, i.e., a cluster of LiNbO3 unit cells containing a single H+ and a Li+ vacancy. Based on the supercell model an approximate Hamiltonian operator describing vibrations of the proton sublattice embedded in the host crystal has been derived. It is further simplified to a sum of uncoupled Hamiltonian operators corresponding to different wave vectors (ks) and each describing vibrations of a quasi-particle (quasi-proton). The three dimensional (3D) Hamiltonian operator of k=0 has been employed to calculate vibrational levels and transition frequencies. The potential energy surface (PES) entering this Hamiltonian operator has been calculated point wise on a large set of grid points by using density functional theory, and an analytical approximation to the PES has been constructed by non-parametric approximation. Then, the nuclear motion Schrödinger equation has been solved by employing the method of discrete variable representation. It has been found that the (quasi-)H+ vibrates in a strongly anharmonic PES. Its vibrations can be described approximately as a stretching, and two orthogonal bending vibrations. The theoretically calculated transition frequencies agree within 1% with those experimentally determined, and they have allowed the assignment of one of the hitherto unassigned bands as a combination of the stretching and the bending of lower fundamental frequency. [ABSTRACT FROM AUTHOR]

We present a second-order perturbation theory based on a density matrix renormalization group self-consistent field (DMRG-SCF) reference function. The method reproduces the solution of the complete active space with second-order perturbation theory (CASPT2) when the DMRG reference function is represented by a sufficiently large number of renormalized many-body basis, thereby being named DMRG-CASPT2 method. The DMRG-SCF is able to describe non-dynamical correlation with large active space that is insurmountable to the conventional CASSCF method, while the second-order perturbation theory provides an efficient description of dynamical correlation effects. The capability of our implementation is demonstrated for an application to the potential energy curve of the chromium dimer, which is one of the most demanding multireference systems that require best electronic structure treatment for non-dynamical and dynamical correlation as well as large basis sets. The DMRG-CASPT2/cc-pwCV5Z calculations were performed with a large (3d double-shell) active space consisting of 28 orbitals. Our approach using large-size DMRG reference addressed the problems of why the dissociation energy is largely overestimated by CASPT2 with the small active space consisting of 12 orbitals (3d4s), and also is oversensitive to the choice of the zeroth-order Hamiltonian. [ABSTRACT FROM AUTHOR]

We present an efficient O(N) implementation of screened hybrid density functional for periodic systems with numerical atomic orbitals (NAOs). NAOs of valence electrons are fitted with gaussian-type orbitals, which is convenient for the calculation of electron repulsion integrals and the construction of Hartree-Fock exchange matrix elements. All other parts of Hamiltonian matrix elements are constructed directly with NAOs. The strict locality of NAOs is adopted as an efficient two-electron integral screening technique to speed up calculations. [ABSTRACT FROM AUTHOR]

Random networks of carbon nanotubes and metallic nanowires have shown to be very useful in the production of transparent, conducting films. The electronic transport on the film depends considerably on the network properties, and on the interwire coupling. Here we present a simple, computationally efficient method for the calculation of conductance on random nanostructured networks. The method is implemented on metallic nanowire networks, which are described within a single-orbital tight binding Hamiltonian, and the conductance is calculated with the Kubo formula. We show how the network conductance depends on the average number of connections per wire, and on the number of wires connected to the electrodes. We also show the effect of the inter/intrawire hopping ratio on the conductance through the network. Furthermore, we argue that this type of calculation is easily extendable to account for the upper conductivity of realistic films spanned by nanowire networks. When compared to experimental measurements, this quantity provides a clear indication of how much room is available for improving the film conductivity. [ABSTRACT FROM AUTHOR]

A means of evaluating the action of Hamiltonian operators on functions expanded in orthogonal compact support wavelet bases is developed, avoiding the direct construction and storage of operator matrices that complicate extension to coupled multidimensional quantum applications. Application of a potential energy operator is accomplished by simple multiplication of the two sets of expansion coefficients without any convolution. The errors of this coefficient product approximation are quantified and lead to use of particular generalized coiflet bases, derived here, that maximize the number of moment conditions satisfied by the scaling function. This is at the expense of the number of vanishing moments of the wavelet function (approximation order), which appears to be a disadvantage but is shown surmountable. In particular, application of the kinetic energy operator, which is accomplished through the use of one-dimensional (1D) [or at most two-dimensional (2D)] differentiation filters, then degrades in accuracy if the standard choice is made. However, it is determined that use of high-order finite-difference filters yields strongly reduced absolute errors. Eigensolvers that ordinarily use only matrix-vector multiplications, such as the Lanczos algorithm, can then be used with this more efficient procedure. Applications are made to anharmonic vibrational problems: a 1D Morse oscillator, a 2D model of proton transfer, and three-dimensional vibrations of nitrosyl chloride on a global potential energy surface. [ABSTRACT FROM AUTHOR]

We propose a novel explicitly correlated coupled-cluster singles and doubles method CCSD(F12*), which retains the accuracy of CCSD-F12 while the computational costs are only insignificantly larger than those for a conventional CCSD calculation. [ABSTRACT FROM AUTHOR]

In Hohenberg–Kohn density functional theory, the energy E is expressed as a unique functional of the ground state density ρ(r): E=E[ρ] with the internal energy component FHK[ρ] being universal. Knowledge of the functional FHK[ρ] by itself, however, is insufficient to obtain the energy: the particle number N is primary. By emphasizing this primacy, the energy E is written as a nonuniversal functional of N and probability density p(r): E=E[N,p]. The set of functions p(r) satisfies the constraints of normalization to unity and non-negativity, exists for each N;N=1,...,∞, and defines the probability density or p-space. A particle number N and probability density p(r) functional theory is constructed. Two examples for which the exact energy functionals E[N,p] are known are provided. The concept of A-representability is introduced, by which it is meant the set of functions Ψp that leads to probability densities p(r) obtained as the quantum-mechanical expectation of the probability density operator, and which satisfies the above constraints. We show that the set of functions p(r) of p-space is equivalent to the A-representable probability density set. We also show via the Harriman and Gilbert constructions that the A-representable and N-representable probability density p(r) sets are equivalent. [ABSTRACT FROM AUTHOR]

We have developed a three-dimensional, self-consistent full-quantum transport simulator for nanowire field effect transistors based on the eight-band k·p method. We have constructed the mode-space Hamiltonian via a unitary transformation from the Hamiltonian discretized in the k-space, and reduced its size significantly by selecting only the modes that contribute to the transport. We have also devised an approximate but highly accurate method to solve the cross-sectional eigenvalue problems, thereby overcoming the numerical bottleneck of the mode-space approach. We have therefore been able to develop a highly efficient device simulator. We demonstrate the capability of our simulator by calculating the hole transport in a p-type Si nanowire field effect transistor and the band-to-band tunneling current in a InAs nanowire tunnel field effect transistor. [ABSTRACT FROM AUTHOR]

The photophysics and photochemistry of benzene is a classic example of the richness of competing pathways available to a molecule after photoexcitation. Computer simulations are one way to provide a molecular picture for the dynamics behind the experimental observations. In this paper we develop a vibronic coupling Hamiltonian prepared in a previous paper [G. A. Worth, J. Photochem. Photobiol., A 190, 190 (2007)]. Using CASPT2 we add dynamic correlation to the description of the excited states, improving their accuracy dramatically. Seven coupled states and all vibrational modes are included in the model and the parameters are obtained by fitting to points provided by the quantum chemistry calculations. The model is shown to be a good fit of the adiabatic surfaces and its accuracy is demonstrated by the calculation of three absorption bands, which compare favorably with the experimentally obtained spectra. [ABSTRACT FROM AUTHOR]

The degree to which tunneling through a barrier in the N–H and N–D photodissociation channels of methylamine (CH3NH2) and its deuterated variant (CH3ND2), respectively, plays a role was investigated by time-dependent quantum wave-packet dynamics calculations. Two dimensional potential energy surfaces (PESs) of methylamine, presenting the N–H stretch and the HNC bend, were constructed employing multireference ab initio electronic-structure methods, allowing full description of the H motion on the HC–NH2 plane. The time-dependent Schrödinger equation was solved employing the Fourier method for calculating the Hamiltonian operation together with the Chebychev polynomial expansion of the evolution operator. The results show that tunneling and decay to vibrational resonant states on the first excited electronic PES are faster for the H atom than for the D. The decay into two of the resonant states found on the first PES strongly depends on the initially excited vibrational state on the ground electronic PES. [ABSTRACT FROM AUTHOR]

The degree to which tunneling through a barrier in the N–H and N–D photodissociation channels of methylamine (CH3NH2) and its deuterated variant (CH3ND2), respectively, plays a role was investigated by time-dependent quantum wave-packet dynamics calculations. Two dimensional potential energy surfaces (PESs) of methylamine, presenting the N–H stretch and the HNC bend, were constructed employing multireference ab initio electronic-structure methods, allowing full description of the H motion on the HC–NH2 plane. The time-dependent Schrödinger equation was solved employing the Fourier method for calculating the Hamiltonian operation together with the Chebychev polynomial expansion of the evolution operator. The results show that tunneling and decay to vibrational resonant states on the first excited electronic PES are faster for the H atom than for the D. The decay into two of the resonant states found on the first PES strongly depends on the initially excited vibrational state on the ground electronic PES. [ABSTRACT FROM AUTHOR]

Vibrational coupled cluster (VCC) calculations of molecular vibrational energy levels can be characterized by the number of modes coupled in the Hamiltonian operator and the number of modes simultaneously excited in the parameter space. We propose a VCC model which includes all two-mode couplings in the Hamiltonian and excitation space but only an approximate treatment of three-mode couplings. The approximation is based on a perturbational analysis and the introduced concepts can also be used for even more accurate treatments. The method is iterative and allows the use of VCC response theory to obtain excitation energies. Furthermore, the method is shown to scale with the number of vibrational modes to the third power which is no higher than the corresponding VCC model with only two-mode couplings. Encouraging benchmark calculations are given for a test set of three- and four-atomic molecules. The fundamentals of the larger ethylene oxide molecule have been calculated as well using a grid-based potential energy surface obtained from electronic coupled cluster theory with singles, doubles, and perturbative triples (CCSD(T)). [ABSTRACT FROM AUTHOR]

Based on a microscopic Hamiltonian picture where the system is coupled with the nonequilibrium environment, comprising of a set of harmonic oscillators, the Langevin equation with proper microscopic specification of Langevin force is formulated analytically. In our case, the reservoir is perturbed by an external force, either executing rapid or showing periodic fluctuations, hence the reservoir is not in thermal equilibrium. In the presence of external fluctuating force, using Shapiro–Loginov procedure, we arrive at the linear coupled first order differential equations for the two-time correlations and examine the time evolution of the same considering the system as a simple harmonic oscillator. We study the stochastic resonance phenomena of a Kubo-type oscillator (assumed to be the system) when the bath is modulated by a periodic force. The result(s) obtained here is of general significance and can be used to analyze the signature of stochastic resonance. [ABSTRACT FROM AUTHOR]

A black-box-type algorithm is presented for the variational computation of energy levels and wave functions using a (ro)vibrational Hamiltonian expressed in an arbitrarily chosen body-fixed frame and in any set of internal coordinates of full or reduced vibrational dimensionality. To make the required numerical work feasible, matrix representation of the operators is constructed using a discrete variable representation (DVR). The favorable properties of DVR are exploited in the straightforward and numerically exact inclusion of any representation of the potential and the kinetic energy including the G matrix and the extrapotential term. In this algorithm there is no need for an a priori analytic derivation of the kinetic energy operator, as all of its matrix elements at each grid point are computed numerically either in a full- or a reduced-dimensional model. Due to the simple and straightforward definition of reduced-dimensional models within this approach, a fully anharmonic variational treatment of large, otherwise intractable molecular systems becomes available. In the computer code based on the above algorithm, there is no inherent limitation for the maximally coupled number of vibrational degrees of freedom. However, in practice current personal computers allow the treatment of about nine fully coupled vibrational dimensions. Computation of vibrational band origins of full and reduced dimensions showing the advantages and limitations of the algorithm and the related computer code are presented for the water, ammonia, and methane molecules. [ABSTRACT FROM AUTHOR]

A new Douglas–Kroll transformation scheme up to arbitrary order is presented to study the convergence behavior of the Douglas–Kroll series and the influence of different choices of parametrization for the unitary transformation. The standard approach for evaluating the Douglas–Kroll Hamiltonian suffers from computational difficulties due to the huge number of matrix multiplications, which increase exponentially with respect to the order of truncation. This makes it prohibitively expensive to obtain results for very high order Douglas–Kroll Hamiltonians. The highest order previously presented is 14th order, but it is not enough to obtain accurate results for systems containing heavy elements, where the Douglas–Kroll series converges very slowly. In contrast, our approach dramatically reduces the number of matrix multiplications, which only increase with a polynomial scaling. With the new method, orders greater than 100 and machine accuracy are possible. This fast method is achieved by employing a special transformation to all Douglas–Kroll operators and our algorithm is very simple. We demonstrate the performance of our implementation with calculations on one-electron systems and many-electron atoms. All results show very good convergence behavior of the Douglas–Kroll series. Very small differences are found between the different parametrizations, and therefore the exponential form, which is the simplest and fastest, is recommended. [ABSTRACT FROM AUTHOR]

We present tunneling calculations using the reaction path Hamiltonian in the zero-curvature approximation and a one-dimensional Hamiltonian in the imaginary-frequency, rectilinear normal mode of a saddle point, neglecting the vibrational angular momentum terms. This latter Hamiltonian was recently introduced and applied to the tunneling splitting in full-dimensional malonaldeyde [Y. Wang et al., J. Chem. Phys. 128, 224314 (2008)]. The results using the latter method are shown to be much more accurate than those using the former one for the ground-state tunneling splittings for H and D-transfer in malonaldehyde and for the D+H2 reaction in three dimensions for zero total angular momentum. [ABSTRACT FROM AUTHOR]

We calculate the shear piezocoefficient π44 in p-type Si with a 6×6 k·p Hamiltonian model using the Boltzmann transport equation in the relaxation-time approximation. Furthermore, we fabricate and characterize p-type silicon piezoresistors embedded in a (001) silicon substrate. We find that the relaxation-time model needs to include all scattering mechanisms in order to obtain correct temperature and acceptor density dependencies. The k·p results are compared to results obtained using a recent tight-binding (TB) model. The magnitude of the π44 piezocoefficient obtained from the TB model is a factor of 4 lower than experimental values; however, the temperature and acceptor density dependencies of the normalized values agree with experiments. The 6×6 Hamiltonian model shows good agreement between the absolute value of π44 and the temperature and acceptor density dependencies when compared to experiments. Finally, we present a fitting function of temperature and acceptor density to the 6×6 model that can be used to predict the piezoresistance effect in p-type silicon. [ABSTRACT FROM AUTHOR]

An extension of the Anderson–Newns–Schmickler model for electrochemical proton-coupled electron transfer (PCET) is presented. This model describes reactions in which electron transfer between a solute complex in solution and an electrode is coupled to proton transfer within the solute complex. The model Hamiltonian is derived in a basis of electron-proton vibronic states defined within a double adiabatic approximation for the electrons, transferring proton, and bath modes. The interaction term responsible for electronic transitions between the solute complex and the electrode depends on the proton donor-acceptor vibrational mode within the solute complex. This model Hamiltonian is used to derive the anodic and cathodic rate constants for nonadiabatic electrochemical PCET. The derivation is based on the master equations for the reduced density matrix of the electron-proton subsystem, which includes the electrons of the solute complex and the electrode, as well as the transferring proton. The rate constant expressions differ from analogous expressions for electrochemical electron transfer because of the summation over electron-proton vibronic states and the dependence of the couplings on the proton donor-acceptor vibrational motion. These differences lead to additional contributions to the total reorganization energy, an additional exponential temperature-dependent prefactor, and a temperature-dependent term in the effective activation energy that has different signs for the anodic and cathodic processes. This model can be generalized to describe both nonadiabatic and adiabatic electrochemical PCET reactions and provides the framework for the inclusion of additional effects, such as the breaking and forming of other chemical bonds. [ABSTRACT FROM AUTHOR]

Lie algebra, Zassenhaus, and parameter differentiation techniques are utilized to break up the exponential of a bilinear Hamiltonian operator into a product of noncommuting exponential operators by the virtue of the theory of Wei and Norman [J. Math. Phys. 4, 575 (1963); Proc. Am. Math. Soc., 15, 327 (1964)]. There are about three different ways to find the Zassenhaus exponents, namely, binomial expansion, Suzuki formula, and q-exponential transformation. A fourth, and most reliable method, is provided. Since linearly displaced and distorted (curvature change upon excitation/emission) Hamiltonian and spin-boson Hamiltonian may be classified as bilinear Hamiltonians, the presented algebraic algorithm (exponential operator disentanglement exploiting six-dimensional Lie algebra case) should be useful in spin-boson problems. The linearly displaced and distorted Hamiltonian exponential is only treated here. While the spin-boson model is used here only as a demonstration of the idea, the herein approach is more general and powerful than the specific example treated. The optical linear dipole moment correlation function is algebraically derived using the above mentioned methods and coherent states. Coherent states are eigenvectors of the bosonic lowering operator a and not of the raising operator a+. While exp(a+) translates coherent states, exp(a+a+) operation on coherent states has always been a challenge, as a+ has no eigenvectors. Three approaches, and the results, of that operation are provided. Linear absorption spectra are derived, calculated, and discussed. The linear dipole moment correlation function for the pure quadratic coupling case is expressed in terms of Legendre polynomials to better show the even vibronic transitions in the absorption spectrum. Comparison of the present line shapes to those calculated by other methods is provided. Franck–Condon factors for both linear and quadratic couplings are exactly accounted for by the herein calculated linear absorption spectra. This new methodology should easily pave the way to calculating the four-point correlation function, F(τ1,τ2,τ3,τ4), of which the optical nonlinear response function may be procured, as evaluating F(τ1,τ2,τ3,τ4) is only evaluating the optical linear dipole moment correlation function iteratively over different time intervals, which should allow calculating various optical nonlinear temporal/spectral signals. [ABSTRACT FROM AUTHOR]

No compact expression of the evolution operator is known when the Hamiltonian operator is time dependent, like when Hamiltonian operators describe, in a semiclassical limit, the interaction of a molecule with an electric field. It is well known that Magnus [N. Magnus, Commun. Pure Appl. Math. 7, 649 (1954)] has derived a formal expression where the evolution operator is expressed as an exponential of an operator defined as a series. In spite of its formal simplicity, it turns out to be difficult to use at high orders. For numerical purposes, approximate methods such as “Runge-Kutta” or “split operator” are often used usually, however, to a small order (<5), so that only small time steps, about one-tenth or one-hundredth of the field cycle, are acceptable. Moreover, concerning the latter method, split operator, it is only very efficient when a diagonal representation of the kinetic energy operator is known. The Taylor expansion of the evolution operator or the wave function about the initial time provides an alternative approach, which is very simple to implement and, unlike split operator, without restrictions on the Hamiltonian. In addition, relatively large time steps (up to the field cycle) can be used. A two-level model and a propagation of a Gaussian wave packet in a harmonic potential illustrate the efficiency of the Taylor expansion. Finally, the calculation of the time-averaged absorbed energy in fluoroproprene provides a realistic application of our method. [ABSTRACT FROM AUTHOR]

The Dirac operator in a matrix representation in a kinetically balanced basis is transformed to the matrix representation of a quasirelativistic Hamiltonian that has the same electronic eigenstates as the original Dirac matrix (but no positronic eigenstates). This transformation involves a matrix X, for which an exact identity is derived and which can be constructed either in a noniterative way or by various iteration schemes, not requiring an expansion parameter. Both linearly convergent and quadratically convergent iteration schemes are discussed and compared numerically. The authors present three rather different schemes, for each of which even in unfavorable cases convergence is reached within three or four iterations, for all electronic eigenstates of the Dirac operator. The authors present the theory both in terms of a non-Hermitian and a Hermitian quasirelativistic Hamiltonian. Quasirelativistic approaches at the matrix level known from the literature are critically analyzed in the frame of the general theory. [ABSTRACT FROM AUTHOR]

The authors present a new potential energy curve, electric dipole moment function, and spin-orbit coupling function for OH in the X 2Π state, based on high-level ab initio calculations. These properties, combined with a spectroscopically parametrized lambda-type doubling Hamiltonian, are used to compute the Einstein A coefficients and photoabsorption cross sections for the OH Meinel transitions. The authors investigate the effect of spin-orbit coupling on the lifetimes of rovibrationally excited states. Comparing their results with earlier ab initio calculations, they conclude that their dipole moment and potential energy curve give the best agreement with experimental data to date. The results are made available via EPAPS Document No. E-JCPSAG-017709. [ABSTRACT FROM AUTHOR]

We study three wave function optimization methods based on energy minimization in a variational Monte Carlo framework: the Newton, linear, and perturbative methods. In the Newton method, the parameter variations are calculated from the energy gradient and Hessian, using a reduced variance statistical estimator for the latter. In the linear method, the parameter variations are found by diagonalizing a nonsymmetric estimator of the Hamiltonian matrix in the space spanned by the wave function and its derivatives with respect to the parameters, making use of a strong zero-variance principle. In the less computationally expensive perturbative method, the parameter variations are calculated by approximately solving the generalized eigenvalue equation of the linear method by a nonorthogonal perturbation theory. These general methods are illustrated here by the optimization of wave functions consisting of a Jastrow factor multiplied by an expansion in configuration state functions (CSFs) for the C2 molecule, including both valence and core electrons in the calculation. The Newton and linear methods are very efficient for the optimization of the Jastrow, CSF, and orbital parameters. The perturbative method is a good alternative for the optimization of just the CSF and orbital parameters. Although the optimization is performed at the variational Monte Carlo level, we observe for the C2 molecule studied here, and for other systems we have studied, that as more parameters in the trial wave functions are optimized, the diffusion Monte Carlo total energy improves monotonically, implying that the nodal hypersurface also improves monotonically. [ABSTRACT FROM AUTHOR]

In literature ladder operators of different nature exist. The most famous are those obeying canonical (anti-) commutation relations, but they are not the only ones. In our knowledge, all ladder operators have a common feature: the lowering operators annihilate a non zero vector, the vacuum. This is connected to the fact that operators of these kind are often used in factorizing some positive operators, or some operators which are bounded from below. This is the case, of course, of the harmonic oscillator, but not only. In this paper we discuss what happens when considering lowering operators with no vacua. In particular, after a general analysis of this situation, we propose a possible construction of coherent states, and we apply our construction to graphene. • We consider ladder operators with no vacuum state. • We use these ladder operators to factorize an Hamiltonian with energy eigenvalues with no bounds. • We construct coherent states for these ladder operators. • We apply our construction to Graphene. [ABSTRACT FROM AUTHOR]

Nonadiabatic effects in the two lowest electronic states of the ethoxy radical, the 1 2A and 2 2A states, are considered, using multireference configuration interaction (MRCI) wave functions comprised of over 15×106 configuration state functions. The lowest point on the seam of conical intersection is located. Using this point as the origin, a quasidiabatic Hamiltonian suitable for use in a multimode vibronic coupling treatment of the coupled 1 2A and 2 2A electronic states is determined. The Hamiltonian includes all contributions from all internal coordinates through second order in displacements from the origin and is comprised of over 500 parameters. By using the average energy gradient, the energy difference gradients, and the derivative couplings, all of which are obtained at little additional cost once the requisite eigenstates are known, the second order Hamiltonian is determined from MRCI calculations at only 35 nuclear configurations. This is essentially the same number of points required to obtain the frequencies for the ground state equilibrium structure using centered differences of gradients. The diabatic Hamiltonian provides a good description of the seam space, the (Nint-2)-dimensional space of conical intersection points, continuously connected to the minimum energy crossing point, enabling, for the first time, an analysis of the changes in the branching plane induced by seam curvature in the full seam space. Comparing the diabatic representation and MRCI results we find a good agreement for the ground state equilibrium structure, Req(1 2A), as well as the ground state energy and vertical excitation energy. In good agreement with the available experimental data are the ground state equilibrium structure and the excitation energy to the A 2A state, predicted here to involve a cone state level. Agreement between the harmonic frequencies at Req(1 2A) computed from the MRCI wave function and from the diabatic Hamiltonian is excellent for all but the three lowest energy normal modes where significant deviations are observed indicating the need for selected cubic and/or quartic terms. For the low-lying vibrational levels, the diabatic representation can be used to partition the normal modes into two groups, those that involve inter(diabatic) state coupling and those that are spectators as far as nonadiabatic effects are concerned. The spin-orbit coupling interaction is determined using the Breit-Pauli approximation and its incorporation into the diabatic Hamiltonian is discussed. [ABSTRACT FROM AUTHOR]

It is shown that spin-component-scaled second order Mo\ller-Plesset theory proposed by Grimme [J. Chem. Phys. 118, 9095 (2003)] can be interpreted as a two-parameter scaling of the zero order Hamiltonian, a generalization of the approach reported by Feenberg [Phys. Rev. 103, 1116 (1956)]. [ABSTRACT FROM AUTHOR]

Variationally optimized exponentially correlated Gaussian functions are employed to obtain nonrelativistic wave functions of the lithium atom and its negative ion. The energy levels are computed by means of the expansion in powers of the fine-structure constant α. The first term of this expansion corresponds to the nonrelativistic energy. The higher order terms represent the relativistic and radiative corrections and are determined by some effective Hamiltonians. Highly accurate expectation values of singular operators entering these Hamiltonians are computed using a set of expectation value identities. The resulting electron affinity of lithium atom 4984.96(18) cm-1 agrees very well with 4984.90(17) cm-1 of the latest measurements. [ABSTRACT FROM AUTHOR]

The time dependent real wave packet method using the helicity decoupling approximation was used to calculate the cross section evolution with collision energy (excitation function) of the O++H2(v=0,j=0)→OH++H reaction and its isotopic variants with D2 and HD, using the best available ab initio analytical potential energy surface. The comparison of the calculated excitation functions with exact quantum results and experimental data showed that the present quantum dynamics approach is a very useful tool for the study of the selected and related systems, in a quite wide collision energy interval (approximately 0.0–1.1 eV), involving a much lower computational cost than the quantum exact methods and without a significant loss of accuracy in the cross sections. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Frantsuzov and Mandelshtam [J. Chem. Phys. 121, 9247 (2004)] have recently demonstrated that a time evolving Gaussian approximation (TEGA) to the imaginary time propagator exp(-βH) is useful for numerical computations of anharmonically coupled systems with many degrees of freedom. In this paper we derive a new exact series representation for the imaginary time propagator whose leading order term is the TEGA. One can thus use the TEGA not only as an approximation but also to obtain the exact imaginary time propagator. We also show how the TEGA may be generalized to provide a family of TEGA’s. Finally, we find that the equations of motion governing the evolution of the center and width of the Gaussian may be thought of as introducing a quantum friction term to the classical evolution equations. [ABSTRACT FROM AUTHOR]

A formalism is presented for the calculation of relativistic corrections to molecular electronic energies and properties. After a discussion of the Dirac and Breit equations and their first-order Foldy-Wouthuysen [Phys. Rev. 78, 29 (1950)] transformation, we construct a second-quantization electronic Hamiltonian, valid for all values of the fine-structure constant α. The resulting α-dependent Hamiltonian is then used to set up a perturbation theory in orders of α2, using the general framework of time-independent response theory, in the same manner as for geometrical and magnetic perturbations. Explicit expressions are given to second order in α2 for the Hartree-Fock model. However, since all relativistic considerations are contained in the α-dependent Hamiltonian operator rather than in the wave function, the same approach may be used for other wave-function models, following the general procedure of response theory. In particular, by constructing a variational Lagrangian using the α-dependent electronic Hamiltonian, relativistic corrections can be calculated for nonvariational methods as well. [ABSTRACT FROM AUTHOR]

We use the effective Hamiltonian that we recently fitted against the first 306 experimentally observed vibronic transitions of NO2 [Joyeux et al., J. Chem. Phys. 119, 5923 (2003)] to investigate the time domain nonadiabatic dynamics of this molecule on the coupled X 2A1 and A 2B2 electronic states, using both quantum mechanical and quasiclassical techniques. From the quantum mechanical point of view, we show that the transfer of population to the electronic ground state originating from a wave packet launched on the excited state occurs in a stepwise fashion. The evolution of wave packets launched on the electronic ground state is instead more complex because the crossing seam is located close to the bottom of the electronic excited state. We next use the mapping formalism, which replaces the discrete electronic degrees of freedom by continuous ones, to obtain a classical description of the coupled electronic states. We propagate Gaussian swarms of trajectories to show that this approach can be used to calculate the populations in each electronic state. We finally propose a very simple trajectory surface hopping model, which assumes that trajectories have a constant probability to jump onto the other state in a particular region of the phase space and a null hopping probability outside from this region. Quasiclassical calculations show that this model enables a precise estimation of complex quantities, as for example the projection of the instantaneous probability density on given planes. [ABSTRACT FROM AUTHOR]

The excited-state intramolecular proton-transfer dynamics associated with the ketoenolic tautomerization reaction in 2-(2′-hydroxyphenyl)-oxazole is simulated according to a numerically exact quantum-dynamics propagation method and a full-dimensional excited-state potential energy surface, based on an ab initio reaction surface Hamiltonian. The reported simulations involve the propagation of 35-dimensional wave packets according to the recently developed matching-pursuit/split-operator-Fourier-transform (MP/SOFT) method by Wu and Batista, [J. Chem. Phys. 121, 1676 (2004)]. The underlying propagation scheme recursively applies the time-evolution operator as defined by the Trotter expansion to second order accuracy in dynamically adaptive coherent-state expansions. Computations of time-dependent survival amplitudes, photoabsorption cross sections, and time-dependent reactant(product) populations are compared to the corresponding calculations based on semiclassical approaches, including the Herman-Kluk semiclassical initial value representation method. The reported results demonstrate the capabilities of the MP/SOFT method as a valuble computational tool to study ultrafast reaction dynamics in polyatomic systems as well as to validate semiclassical simulations of complex (nonintegrable) quantum dynamics in multidimensional model systems. [ABSTRACT FROM AUTHOR]

In Part III [J. Chem. Phys. 124, 064102 (2005)] of this series of papers on exact decoupling of the Dirac Hamiltonian within transformation theory, we developed the most general account on how to treat magnetic and electric properties in a unitary transformation theory on the same footing. In this paper we present an implementation of a general algorithm for the calculation of magnetic as well as electric properties within the framework of Douglas-Kroll-Hess theory. The formal and practical principles of this algorithm are described. We present the first high-order Douglas-Kroll-Hess results for property operators. As for model properties we propose to use the well-defined radial moments, i.e., expectation values of rk, which can be understood as terms of the Taylor-series expansion of any property operator. Such moments facilitate a rigorous comparison of methods free of uncertainties which may arise in a direct comparison with experiment. This is important in view of the fact that various approaches to two-component molecular properties may yield numerically very small terms whose approximate or inaccurate treatment would not be visible in a direct comparison to experimental data or to another approximate computational reference. Results are presented for various degrees of decoupling of the model properties within the Douglas-Kroll-Hess scheme. [ABSTRACT FROM AUTHOR]

The formulation of path-integral centroid dynamics is extended to the quantum dynamics of density operators evolving from general initial states by means of the nonequilibrium projection operator technique. It is shown that the new formulation provides a basis for applying the method of centroid dynamics to nonequilibrium situations and that it allows the derivation of new formal relations, which can be useful in improving current equilibrium centroid dynamics methods. A simple approximation of uniform relaxation for the unprojected portion of the Liouville space propagator leads to a class of practically solvable equations of motion for the centroid variables, but with an undetermined parameter of relaxation. This new class of equations encompasses the centroid molecular-dynamics (CMD) method as a limiting case, and can be applied to both equilibrium and nonequilibrium situations. Tests for the equilibrium dynamics of one-dimensional model systems demonstrate that the new equations with appropriate choice of the relaxation parameter are comparable to the CMD method. [ABSTRACT FROM AUTHOR]

Given a general, N-particle Hamiltonian operator, analogs of the Hohenberg-Kohn theorem are derived for functions that are more general than the particle density, including density matrices and the diagonal elements thereof. The generalization of Lieb’s Legendre transform ansatz to the generalized Hohenberg-Kohn functional not only solves the υ-representability problem for these entities, but, more importantly, also solves the N-representability problem. Restricting the range of operators explored by the Legendre transform leads to a lower bound on the true functional. If all the operators of interest are incorporated in the restricted maximization, however, the variational principle dictates that exact results are obtained for the systems of interest. This might have important implications for practical work not only for density matrices but also for density functionals. A follow-up paper will present a useful alternative approach to the v- and N-representability problems based on the constrained search formalism. [ABSTRACT FROM AUTHOR]

Time-dependent fluctuations in the distance x(t) between two segments along a polymer are one measure of its overall conformational dynamics. The dynamics of x(t), modeled as the coordinate of a particle moving in a one-dimensional potential well in thermal contact with a reservoir, is treated with a generalized Langevin equation whose memory kernel K(t) can be calculated from the time-correlation function of distance fluctuations C(t)≡≤x(0)x(t)≤. We compute C(t) for a semiflexible continuum model of the polymer and use it to determine K(t) via the GLE. The calculations demonstrate that C(t) is well approximated by a Mittag-Leffler function and K(t) by a power-law decay on time scales of several decades. Both functions depend on a number of parameters characterizing the polymer, including chain length, degree of stiffness, and the number of intervening residues between the two segments. The calculations are compared with the recent observation of a nonexponential C(t) and a power law K(t) in the conformational dynamics within single molecule proteins [Min et al., Phys. Rev. Lett. 94, 198302 (2005)]. [ABSTRACT FROM AUTHOR]

A ring with spin-orbit effects coupled to a conducting wire is shown to exhibit a phase delay which is spin dependent. The key is that the coupling of the ring to the wire is over an extended spatial range and not just along a single point; this breaks the symmetry and makes the ring states couple differently to forward and backward moving wire states. This results, for properly injected spin states, in a spin-flipping probability which is dependent on the energy of the injected electron and can therefore be easily controlled. Several systems are presented and shown to exhibit this effect including the basic ring which couples to a wire as well as a ring which mediates between two wires, and a spiral between two wires. [ABSTRACT FROM AUTHOR]

Using a five-state, all-mode vibronic coupling model Hamiltonian derived in a previous publication [A. Markmann et al., J. Chem. Phys. 122, 144320 (2005)], we have calculated the photoelectron spectrum of the pentatetraene cation in the neighborhood of the B 2E state, which can be represented with charge-localized components. To this end, quantum nuclear dynamics calculations were performed using the multiconfiguration time-dependent Hartree method, taking all 21 vibrational normal modes into account. Compared to experiment, the main features are reproduced but higher accuracy experiments are necessary to gauge the accuracy of the predictions for the vibronic progressions at the rising flank of the spectrum. [ABSTRACT FROM AUTHOR]

We have employed the Douglas-Kroll-Hess approximation to derive the perturbative Hamiltonians involved in the calculation of NMR spin-spin couplings in molecules containing heavy elements. We have applied this two-component quasirelativistic approach using finite perturbation theory in combination with a generalized Kohn-Sham code that includes the spin-orbit interaction self-consistently and works with Hartree-Fock and both pure and hybrid density functionals. We present numerical results for one-bond spin-spin couplings in the series of tetrahydrides CH4, SiH4, GeH4, and SnH4. Our two-component Hartree-Fock results are in good agreement with four-component Dirac-Hartree-Fock calculations, although a density-functional treatment better reproduces the available experimental data. [ABSTRACT FROM AUTHOR]

The damped quantum rotation (DQR) theory, formulated originally for methyl-like atomic groupings, is now extended to hindered (N>3)-fold molecular rotors, such as the cyclopentadienyl, benzene, and cycloheptatrienyl rings in solid phase environments. It heightens the significance of the Pauli principle in shaping up the stochastic dynamics of such objects, reflected in NMR line shapes. The corresponding NMR line-shape equation is derived; its stochastic part is shown for the first time to have the double commutator form for any values of the quantum-mechanical (coherence-damping) rate constants entering it. Constraints on the relative magnitudes of such constants are determined under which the DQR line-shape equation is converted into the phenomenological Alexander-Binsch equation describing classical jumps of the rotor. When all the quantum rate constants happen to be equal, the phenomenological model of equal jump rates between any two of the N (equivalent) orientations of the rotor is reproduced. On the other hand, the seemingly most plausible (for N>3) nearest-neighbor hopping model does not have any peculiar grounds in the DQR approach. For the special instances of stochastic molecular motions addressed in this work, the extended DQR formalism affords a quantification of the “degree of classicality” represented by a complete set of the relevant quantum rate constants. In view of our earlier experimental findings for the methyl rotors, the very occurrence of the nonclassical DQR effects seems unquestionable even for the objects of the size of benzene. The question of under what circumstances such effects can be big enough to be detected experimentally will be addressed in Part II of this work. [ABSTRACT FROM AUTHOR]

Two-component quasirelativistic approaches are in principle capable of reproducing results from fully relativistic calculations based on the four-component Dirac equation (with fixed particle number). For one-electron systems, this also holds in practice, but in many-electron systems one has to transform the two-electron interaction, which is necessary because a picture change occurs when going from the Dirac equation to a two-component method. For one-electron properties, one can take full account of picture change in a manageable way, but for the electron interaction, this would spoil the computational advantages which are the main reason to perform quasirelativistic calculations. Exploiting those picture change effects are largest in the atomic cores, which in molecular applications do not differ too much from the cores of isolated neutral atoms, we propose an elegant, efficient, and accurate approximation to the two-electron picture change problem. The new approach, called the “model potential” approach because it makes use of atomic (four- and two-component) data to estimate picture change effects in molecules, shares with the nuclear-only approach that the Douglas-Kroll operator needs to be constructed only once (not in each self-consistent-field iteration) and that no time-consuming multicenter relativistic two-electron integrals need to be calculated. The new approach correctly describes the screening of both the nearest nucleus and distant nuclei, for the scalar-relativistic as well as the spin-orbit parts of the Hamiltonian. The approach is tested on atomic and molecular-orbital energies as well as spectroscopic constants of the lead dimer. [ABSTRACT FROM AUTHOR]

Using a five-state, all-mode vibronic coupling model Hamiltonian derived in a previous publication [A. Markmann et al., J. Chem. Phys. 122, 144320 (2005)], we have calculated the photoelectron spectrum of the pentatetraene cation in the neighborhood of the B 2E state, which can be represented with charge-localized components. To this end, quantum nuclear dynamics calculations were performed using the multiconfiguration time-dependent Hartree method, taking all 21 vibrational normal modes into account. Compared to experiment, the main features are reproduced but higher accuracy experiments are necessary to gauge the accuracy of the predictions for the vibronic progressions at the rising flank of the spectrum. [ABSTRACT FROM AUTHOR]

In 12C13CH2 129 vibrational term values up to 10 000 cm-1 are merged, about 60% of which are newly reported. They are fitted using an effective Hamiltonian with a standard deviation of 0.22 cm-1. The vibrational assignments and vibrational constants are listed and discussed. The energy pattern is found to be very similar to the one in 12C2H2 with additional anharmonic resonances arising from the lack of u/g character in the asymmetric isotopolog. [ABSTRACT FROM AUTHOR]

We simulated the photoisomerization dynamics of an azobenzenophane with a semiclassical surface hopping approach and a semiempirical reparametrized quantum mechanics/molecular mechanics Hamiltonian. Only one of the two azobenzene chromophores in the molecule is taken into account quantum mechanically: the other one is treated by molecular mechanics. Both n→π* and π→π* excitations are considered. Our results show that the photoisomerization reaction mainly involves the rotation around the N==N double bond. The excited state relaxation features are in qualitative agreement with experimental time-resolved fluorescence results. [ABSTRACT FROM AUTHOR]

In 12C13CH2 129 vibrational term values up to 10 000 cm-1 are merged, about 60% of which are newly reported. They are fitted using an effective Hamiltonian with a standard deviation of 0.22 cm-1. The vibrational assignments and vibrational constants are listed and discussed. The energy pattern is found to be very similar to the one in 12C2H2 with additional anharmonic resonances arising from the lack of u/g character in the asymmetric isotopolog. [ABSTRACT FROM AUTHOR]

We introduce new ideas for calculating resonance energies and widths. It is shown that a non-Hermitian–Lanczos approach can be used to compute eigenvalues of H+W, where H is the Hamiltonian and W is a complex absorbing potential (CAP), without evaluating complex matrix-vector products. This is done by exploiting the link between a CAP-modified Hamiltonian matrix and a real but nonsymmetric matrix U suggested by Mandelshtam and Neumaier [J. Theor. Comput. Chem. 1, 1 (2002)] and using a coupled-two-term Lanczos procedure. We use approximate resonance eigenvectors obtained from the non-Hermitian–Lanczos algorithm and a very good CAP to obtain very accurate energies and widths without solving eigenvalue problems for many values of the CAP strength parameter and searching for cusps. The method is applied to the resonances of HCO. We compare properties of the method with those of established approaches. [ABSTRACT FROM AUTHOR]

Deep electronic tunneling through molecular barriers in donor-bridge-acceptor complexes is studied using an analytically solvable model. The effective tunneling matrix element is formulated as a sum over vibronic tunneling pathways. For a symmetric system the frequency of tunneling oscillations is shown to increase with the strength of electronic-nuclear coupling at the bridge, the number of electronic-nuclear coupling sites, or the frequency of a bridge vibration. Acceleration by several orders of magnitude is demonstrated within the range of realistic molecular parameters. © 2005 American Institute of Physics. [ABSTRACT FROM AUTHOR]