Iterative solutions with energy selected bases for highly excited vibrations of tetra-atomic molecules

The use of energy selected bases (ESB) with iterative diagonalization of the Hamiltonian matrix is described for vibrations of tetra-atomic systems. The performance of the method is tested by computing vibrational states of HOOH below 10,000 cm(-1) (1296 A+ symmetry states) and H(2)CO below 13,500 cm(-1) (729 A(1) symmetry states). For iterative solutions, we tested both the implicitly restarted Lanczos method (IRLM) and the standard (nonreorthogonalizing) Lanczos approach. Comparison with other contracted basis approach as well as direct product grid representation shows superior performance of the ESB/IRLM approach. Of the two systems, H(2)CO is found to be more challenging than HOOH since it has much stronger couplings among vibrational modes, which leads to a drastically larger primitive basis set. For H(2)CO we also discuss some interesting behavior of the molecule in the high internal energy regime.     

A new Lanczos-based algorithm for simulating high-frequency two-dimensional electron spin resonance spectra

The Lanczos algorithm (LA) is a useful iterative method for the reduction of a large matrix to tridiagonal form. It is a storage efficient procedure requiring only the preceding two Lanczos vectors to compute the next. The quasi-minimal residual (QMR) method is a powerful method for the solution of linear equation systems, Ax = b. In this report we provide another application of the QMR method: we incorporate QMR into the LA to monitor the convergence of the Lanczos projections in the reduction of large sparse matrices. We demonstrate that the combined approach of the LA and QMR can be utilized efficiently for the orthogonal transformation of large, but sparse, complex, symmetric matrices, such as are encountered in the simulation of slow-motional 1D- and 2D-electron spin resonance (ESR) spectra. Especially in the 2D-ESR simulations, it is essential that we store all of the Lanczos vectors obtained in the course of the LA recursions and maintain their orthogonality. In the LA-QMR application, the QMR weight matrix mitigates the problem that the Lanczos vectors lose orthogonality after many LA projections. This enables substantially more Lanczos projections, as required to achieve convergence for the more challenging ESR simulations. It, therefore, provides better accuracy for the eigenvectors and the eigenvalues of the large sparse matrices originating in 2D-ESR simulations than does the previously employed method, which is a combined approach of the LA and the conjugate-gradient (CG) methods, as evidenced by the quality and convergence of the 2D-ESR simulations. Our results show that very slow-motional 2D-ESR spectra at W-band (95 GHz) can be reliably simulated using the LA-QMR method, whereas the LA-CG consistently fails. The improvements due to the LA-QMR are of critical importance in enabling the simulation of high-frequency 2D-ESR spectra, which are characterized by their very high resolution to molecular orientation.     

HO2 ro-vibrational bound-state calculations for large angular momentum: J = 30, 40, and 50

The Lanczos homogeneous filter diagonalization method and the real Chebyshev filter diagonalization scheme incorporating doubling of the autocorrelation functions have been employed to compute the HO2 ro-vibrational states for high total angular momenta, J = 30, 40, and 50. For such computationally challenging calculations, we have adopted a parallel computing strategy to perform the matrix-vector multiplications. Low-lying bound states and high-lying bound states close to the dissociation threshold are reported. For low-lying bound states, a spectroscopic assignment has been attempted and the widely used approximate J-shifting method has been tested for this deep-well system. For high-lying bound states, the attempted spectroscopic assignments as well as the J-shifting approximation fail because of very strong Coriolis mixing, indicating that the Coriolis couplings are important for this system.     

Density of states of alternant cyclic polyenes (CH)N by a direct Lanczos method

A direct full configuration interaction approach, previously used for studying individual low-lying eigenvalues, is combined with iterative Lanczos calculations, in order to obtain global properties of large Hermitean Hamiltonian matrices. To this effect systematic generation of random start vectors is used to compute statistical approximations to the density of states (DOS). Applications for cyclic polyenes in order to illustrate the viability of the scheme modeled by correlated, high-binding Pariser-Parr-Pople (PPP) Hamiltonians of increasing complexity are presented. The degree of correlation in the solutions is controlled by the parameter β. Convergence properties of the DOS for N = 10 and N = 14 are studied varying the extent of correlation. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 719–728, 1997     

Ab initio interatomic decay widths of excited states by applying Stieltjes imaging to Lanczos pseudospectra

Electronically excited states of atoms and molecules in an environment may decay in interatomic processes by transferring excess energy to neighboring species and ionizing them. The corresponding interatomic decay width is the most important characteristic of the decay allowing to calculate its efficiency and the final states' distribution. In this paper we present calculations of interatomic widths by the Fano-Stieltjes method applied to Lanczos pseudospectra, which has been previously shown to provide accurate autoionization widths in atoms and molecules. The use of Lanczos pseudospectra allows one to avoid the full diagonalization bottleneck and makes the method applicable to larger systems. We apply the present method to the calculation of interatomic decay widths in NeMg, NeAr and HCN[middle dot]Mg(n), n = 1, 2 clusters. The results are compared with widths obtained analytically and by other ab initio methods where available.     

An Efficient Algorithm for Calculating the Heat Capacity of a Large‐Scale Molecular System

We present an efficient algorithm for computing the heat capacity of a large‐scale molecular system. The new algorithm is based on a special Gaussian quadrature whose abscissas and weights are obtained by a simple Lanczos iteration. Our numerical results have indicated that this new computational scheme is quite accurate. We have also shown that this method is at least a hundred times faster than the earlier approach that is based on estimating the density of states and integrating with a simple quadrature formula.     

Theoretical study of the rovibrational spectrum of H2O-H2

In this paper we report transition frequencies and line strengths computed for H(2)O-H(2) and compare with the experimental observations of [M. J. Weida and D. J. Nesbitt, J. Chem. Phys. 110, 156 (1999)]. To compute the spectra we use a symmetry adapted Lanczos algorithm and an uncoupled product basis set. Our results corroborate the assignments of Weida and Nesbitt and there is good agreement between calculated and observed transitions. Possible candidates for lines that Weida and Nesbitt were not able to assign are presented. Several other bands that may be observable are also discovered. Although all the observed bands are associated with states localized near the global potential minimum, at which H(2)O acts as proton acceptor, a state with significant amplitude near the T-shape secondary potential minimum at which H(2)O acts as proton donor is identified by examining many different probability density plots.     

Quantum calculation of ro-vibrational states: methodology and DOCl application results

An improved Lanczos eigenvalue analysis method has been developed to compute the bound ro-vibrational states for the DOCl system at a total angular momentum of J = 0 and J = 30. In this method, the error norm is used to identify all the true eigenvalues, using the Lanczos algorithm without re-orthogonalization. For ro-vibrational spectroscopy calculations, the comparisons among experimental results, the exact quantum mechanical calculations, and the widely used approximate adiabatic rotation method have been made for J = 30. For J = 0, the density of states (DOS) in both the bound and unimolecular dissociation regime have been computed, whereas for the J = 30 case, only the DOS in the lower portion of the bound spectrum has been reported, because of substantial computational tasks.     

Avoiding the van der Waals endpoint problem using serial atomic insertion

In the past analyses of the so-called van der Waals end point problem focused on thermodynamic integration. Here we investigate which of the recommendations, such as the need for soft-core potentials, are still valid when Bennett's acceptance ratio method is used. We show that in combination with Bennett's acceptance ratio method intermediate states characterized by the coupling parameter λ can be replaced by intermediate states in which Lennard-Jones interactions are turned on or off on an "atom by atom" basis. By doing so, there is no necessity to use soft-core potentials. In fact, one can compute free energy differences without dedicated code, making it possible to use any molecular dynamics program to compute alchemical free energy differences. Such an approach, which we illustrate by several examples, makes it possible to exploit the tremendous computational power of the graphics processing unit.     

Using nonproduct quadrature grids to solve the vibrational Schrödinger equation in 12D

In this paper we propose a new quadrature scheme for computing vibrational spectra and apply it, using a Lanczos algorithm, to CH(3)CN. All 12 coordinates are treated explicitly. We need only 157'419'523 quadrature points. It would not be possible to use a product Gauss grid because 33 853 318 889 472 product Gauss points would be required. The nonproduct quadrature we use is based on ideas of Smolyak, but they are extended so that they can be applied when one retains basis functions θ(n(1))(r(1))···θ(n(D))(r(D)) that satisfy the condition α(1)n(1) + ··· + α(D)n(D) ≤ b, where the α(k) are integers. We demonstrate that it is possible to exploit the structure of the grid to efficiently evaluate the matrix-vector products required to use the Lanczos algorithm.     

Autoionization widths by Stieltjes imaging applied to Lanczos pseudospectra

Excited states of atoms and molecules lying above the ionization threshold can decay by electron emission in a process commonly known as autoionization. The autoionization widths can be calculated conveniently using Fano formalism and discretized atomic and molecular spectra by a standard procedure referred to as Stieltjes imaging. The Stieltjes imaging procedure requires the use of the full discretized spectrum of the final states of the autoionization, making its use for poly-atomic systems described by high-quality basis sets impractical. Following our previous work on photoionization cross-sections, here we show that also in the case of autoionization widths, the full diagonalization bottleneck can be overcome by the use of Lanczos pseudospectra. We test the proposed method by calculating the well-documented autoionization widths of inner-valence-excited neon and apply the new technique to autoionizing states of hydrofluoric acid and benzene.     

HOCl Ro-vibrational bound-state calculations for nonzero total angular momentum

The Lanczos homogeneous filter diagonalization method has been employed to compute the HOCl ro-vibrational states for a range of total angular momenta (J = 0, 1, 5, 10, 11, 20, 30) on a newly developed ab initio potential energy surface by Nanbu et al. (J. Theor. Comput. Chem. 2002, 1, 263). For such computationally challenging calculations, a parallel computing strategy has been incorporated into our method to perform the matrix-vector multiplications. For the computed low bound states, a spectroscopic assignment has been made and the widely used approximate adiabatic rotation method has been tested for the broad range of total angular momenta for this deep-well system. Comparison of experimental results with exact quantum mechanical calculations for the selected far-infrared transitions involving the range of total angular momenta has been made possible for the first time.     

An Anderson impurity model for efficient sampling of adiabatic potential energy surfaces of transition metal complexes

We present a model intended for rapid sampling of ground and excited state potential energy surfaces for first-row transition metal active sites. The method is computationally inexpensive and is suited for dynamics simulations where (1) adiabatic states are required "on-the-fly" and (2) the primary source of the electronic coupling between the diabatic states is the perturbative spin-orbit interaction among the 3d electrons. The model Hamiltonian we develop is a variant of the Anderson impurity model and achieves efficiency through a physically motivated basis set reduction based on the large value of the d-d Coulomb interaction U(d) and a Lanczos matrix diagonalization routine to solve for eigenvalues. The model parameters are constrained by fits to the partial density of states obtained from ab initio density functional theory calculations. For a particular application of our model we focus on electron transfer occurring between cobalt ions solvated by ammonium, incorporating configuration interaction between multiplet states for both metal ions. We demonstrate the capability of the method to efficiently calculate adiabatic potential energy surfaces and the electronic coupling factor we have calculated compares well to previous calculations and experiment. (     

Truncation of small matrix elements based on the Euclidean norm for blocked data structures

Methods for the removal of small symmetric matrix elements based on the Euclidean norm of the error matrix are presented in this article. In large scale Hartree-Fock and Kohn-Sham calculations it is important to be able to enforce matrix sparsity while keeping errors under control. Truncation based on some unitary-invariant norm allows for control of errors in the occupied subspace as described in (Rubensson et al. J Math Phys 49, 032103). The Euclidean norm is unitary-invariant and does not grow intrinsically with system size and is thus suitable for error control in large scale calculations. The presented truncation schemes repetitively use the Lanczos method to compute the Euclidean norms of the error matrix candidates. Ritz value convergence patterns are utilized to reduce the total number of Lanczos iterations.     

Computational study of the rovibrational spectrum of (OCS)2

In this paper, we report a new intermolecular potential energy surface and rovibrational transition frequencies and line strengths computed for the OCS dimer. The potential is made by fitting energies obtained from explicitly correlated coupled-cluster calculations and fit using an interpolating moving least squares method. The rovibrational Schroedinger equation is solved with a symmetry-adapted Lanczos algorithm and an uncoupled product basis set. All four intermolecular coordinates are included in the calculation. On the potential energy surface we find, previously unknown, cross-shaped isomers and also polar and non-polar isomers. The associated wavefunctions and energy levels are presented. To identify polar and cross states we use both calculations of line strengths and vibrational parent analysis. Calculated rotational constants differ from their experimental counterparts by less than 0.001 cm(-1).     

Computing the chemical reaction path with a ray-based fast marching technique for solving the Hamilton-Jacobi equation in a general coordinate system

This article presents a ray-based fast marching approach for solving the static Hamilton-Jacobi equation. The approach is very general and can be used for both orthogonal and non-orthogonal coordinate system. The method is unconditionally stable, algorithmatically simple and highly accurate. As an application, we use the method to compute different types of reaction path. Specifically, we consider the path for which the change in action or time is less than that of all other conceivable paths connecting two states. Such reaction paths are efficiently evaluated by back-tracing on the least-action or least-time surfaces. The method is illustrated by applying it to the collinear reactions, F + H₂ →HF + H and HF + H→H + FH.     

Ne-HCl势能面和振转光谱的理论研究

利用量子化学计算方法CCSD(T)和大基组aug-cc-pVTZ加键函数3_s3_p2_d对Ne-HCl体系的分子间势能面进行了理论研究.结果表明,势能面上有两个势阱,分别对应于线性Ne-ClH和Ne-HCl构型.通过精确求解核运动方程发现,该从头算势能面分别支持5个(对Ne-HCl)和7个(Ne-DCl)振动束缚态.计算得到的振转跃迁频率与实值值吻合.     

Vibrational levels of Ar4: new odd-parity bosonic states

Vibrational levels of Ar4 are computed using the Lanczos algorithm and a large basis set. We find both even- and odd-parity states with wave functions that are invariant with respect to permutations of the Ar atoms. The odd-parity bosonic levels have not been computed previously. The even-parity levels are close to those obtained using the correlation-function Monte Carlo method (CFMC).     

A six-dimensional H(2)-H(2) potential energy surface for bound state spectroscopy

We present a six-dimensional potential energy surface for the (H(2))(2) dimer based on coupled-cluster electronic structure calculations employing large atom-centered Gaussian basis sets and a small set of midbond functions at the dimer's center of mass. The surface is intended to describe accurately the bound and quasibound states of the dimers (H(2))(2), (D(2))(2), and H(2)-D(2) that correlate with H(2) or D(2) monomers in the rovibrational levels (v,j)=(0,0), (0,2), (1,0), and (1,2). We employ a close-coupled approach to compute the energies of these bound and quasibound dimer states using our potential energy surface, and compare the computed energies for infrared and Raman transitions involving these states with experimentally measured transition energies. We use four of the experimentally measured dimer transition energies to make two empirical adjustments to the ab initio potential energy surface; the adjusted surface gives computed transition energies for 56 experimentally observed transitions that agree with experiment to within 0.036 cm(-1). For 26 of the 56 transitions, the agreement between the computed and measured transition energies is within the quoted experimental uncertainty. Finally, we use our potential energy surface to predict the energies of another 34 not-yet-observed infrared and Raman transitions for the three dimers.     

Decoherence effects on superpositions of chiral states in a chiral molecule

The superposition of chiral states of chiral molecules, as delocalized quantum states of a many-particle system, can be used for the experimental investigations of decoherence theory. In this regard, a great challenge is the precise quantification of the robustness of these superpositions against environmental effects. The methods so far proposed need the detailed specification of the internal states of the molecule, usually requiring heavy numerical calculations. Here, by using the linearized quantum Boltzmann equation and by borrowing ideas employed for analyzing other quantum systems, we present a general and simple approach, of wide applicability, which can be used to compute the dominant contribution to the decoherence rate for the superpositions of chiral states of chiral molecules, due to environmental scattering.