Configuration selection as a route towards efficient vibrational configuration interaction calculations

A configuration selective vibrational configuration interaction (CI) approach is presented that efficiently reduces the variational space and thus leads to significant speedups in comparison to standard vibrational CI implementations. Deviations with respect to reference calculations are well below the accuracy of the underlying electronic structure calculations for the potential and hence are essentially negligible. Parallel implementations of the presented configuration selective vibrational CI approaches lead to further significant time savings. Benchmark calculations based on potential energy surfaces of coupled-cluster quality are presented for the fundamental modes of cis- and trans-difluoroethylene. The size-consistency error within the vibrational configuration interaction calculations of the difluoroethylene dimer has been studied in dependence on the excitation level.     

Comparison of the numerical stability of methods for anharmonic calculations of vibrational molecular energies

On model examples, we compare the performance of the vibrational self-consistent field, variational, and four perturbational schemes used for computations of vibrational energies of semi-rigid molecules, with emphasis on the numerical stability. Although the accuracy of the energies is primarily dependent on the quality of the potential energy surface, approximate approaches to the anharmonic vibrational problem often do not converge to the same results due to the approximations involved. For furan, the sensitivity to variations of the anharmonic potential was systematically investigated by adding random noise to the cubic and quartic constants. The self-consistent field methods proved to be the most resistant to the potential variations. The second order perturbational techniques are sensitive to random degeneracies and provided the least stable results. However, their stability could be significantly improved by a simple generalization of the perturbational formula. The variational configuration interaction is practically limited by the size of the matrix that can be diagonalized for larger molecules; however, relatively fewer states need to be involved than for smaller ones, in favor of the computing.     

Vibrational analyses for CHFClBr and CDFClBr based on high level ab initio calculations

Anharmonicity corrections to the harmonic vibrational spectra of CHFClBr and its deuterated isotopomer were computed by means of variational and perturbational approaches. A comparison of both methods is provided. Based on CCSD(T)/aug-cc-pVTZ electronic structure calculations excellent agreement with experimental data was obtained. Absolute mean deviations are in the range of about 4 cm(-1) for the fundamental modes, while slightly larger values of about 7 cm(-1) were found for the first vibrational overtones. In addition, vibrationally averaged structural parameters are provided for both molecules. The calculations will serve as a future starting point for parity-violation effects in vibrational transitions in these chiral molecules.     

A comparison of two methods for selecting vibrational configuration interaction spaces on a heptatomic system: ethylene oxide

Two recently developed methods for solving the molecular vibrational Schrodinger equation, namely, the parallel vibrational multiple window configuration interaction and the vibrational mean field configuration interaction, are presented and compared on the same potential energy surface of ethylene oxide, c-C(2)H(4)O. It is demonstrated on this heptatomic system with strong resonances that both approaches converge towards the same fundamental frequencies. This confirms their ability to tackle the vibrational problem of large molecules for which full configuration interaction calculations are not tractable.     

On the equivalence of conformational and enantiomeric changes of atomic configuration for vibrational circular dichroism signs

We study systematically the vibrational circular dichroism (VCD) spectra of the conformers of a simple chiral molecule, with one chiral carbon and an "achiral" alkyl substituent of varying length. The vibrational modes can be divided into a group involving the chiral center and its direct neighbors and the modes of the achiral substituent. Conformational changes that consist of rotations around the bond from the next-nearest neighbor to the following carbon, and bond rotations further in the chain, do not affect the modes around the chiral center. However, conformational changes within the chiral fragment have dramatic effects, often reversing the sign of the rotational strength. The equivalence of the effect of enantiomeric change of the atomic configuration and conformational change on the VCD sign (rotational strength) is studied. It is explained as an effect of atomic characteristics, such as the nuclear amplitudes in some vibrational modes as well as the atomic polar and axial tensors, being to a high degree determined by the local topology of the atomic configuration. They reflect the local physics of the electron motions that generate the chemical bonds rather than the overall shape of the molecule.     

Harmonic analysis of large systems. I. Methodology

Methods have been developed for the determination of vibrational frequencies and normal modes of large systems in the full conformational space (including all degrees of freedom) and in a reduced conformational space (reducing the number of degrees of freedom). The computational method, which includes Hessian generation and storage, full and iterative diagonalization techniques, and the refinement of the results, is presented. A method is given for the quasiharmonic analysis and the reduced basis quasiharmonic analysis. The underlying principle is that from the atomic fluctuations, an effective harmonic force field can be determined relative to the dynamic average structure. Normal mode analysis tools can be used to characterize quasiharmonic modes of vibration. These correspond to conventional normal modes except that anharmonic effects are included. Numerous techniques for the analyses of vibrational frequencies and normal modes are described. Criteria for the analysis of the similarity of low-frequency normal modes is presented. The approach to determining the natural frequencies and normal modes of vibration described here is general and applicable to any large system. © 1995 John Wiley & Sons, Inc.

1 This article is a U.S. Government work and, as such, is in the public domain in the United States of America.

     

Vibrational frequencies and spectroscopic constants from quartic force fields for cis-HOCO: the radical and the anion

The use of accurate quartic force fields together with vibrational configuration interaction recently predicted gas phase fundamental vibrational frequencies of the trans-HOCO radical to within 4 cm(-1) of experimental results for the two highest frequency modes. Utilizing the same approach, we are providing a full list of fundamental vibrational frequencies and spectroscopic constants for the cis-HOCO system in both radical and anionic forms. Our predicted geometrical parameters of the cis-HOCO radical match experiment and previous computation to better than 1% deviation, and previous theoretical work agrees equally well for the anion. Correspondence between vibrational perturbation theory and variational vibrational configuration interaction for prediction of the frequencies of each mode is strong, better than 5 cm(-1), except for the torsional motion, similar to what has been previously identified in the trans-HOCO radical. Among other considerations, our results are immediately applicable to dissociative photodetachment experiments which initially draw on the cis-HOCO anion since it is the most stable conformer of the anion and is used to gain insight into the portion of the OH + CO potential surface where the HOCO radical is believed to form, and we are also providing highly accurate electron binding energies relevant to these experiments.     

Explicitly correlated treatment of the Ar-NO+ cation

We present an application of the recently developed explicitly correlated coupled cluster method to the generation of the three-dimensional potential energy surface (PES) of the Ar-NO(+) cationic complex. A good overall agreement is found with the standard coupled clusters techniques employing correlation consistent atomic basis sets (aug-cc-pVnZ, n= D, T, Q) of Wright et al. This PES is then used in quantum close-coupling scattering and variational calculations to treat the nuclear motions. The bound states energies of the Ar-NO(+) complex obtained by both approaches are in good agreement with the available experimental results. The analysis of the vibrational wavefunctions shows strong anharmonic resonances between the low frequency modes (intermonomer bending and stretching modes) and the wavefunctions exhibit large amplitude motions.     

Anharmonic vibrational calculations modeling the raman spectra of intermediates in the photoactive yellow protein (PYP) photocycle

The role of anharmonic effects in the vibrational spectroscopy of the dark state and two major chromophore intermediates of the photoactive yellow protein (PYP) photocycle is examined via ab initio vibrational self-consistent field (VSCF) calculations and time-resolved resonance Raman spectroscopy. For the first time, anharmonicity is considered explicitly in calculating the vibrational spectra of an ensemble consisting of the PYP chromophore surrounded by model compounds used as mimics of the important active-site residues. Predictions of vibrational frequencies on an ab initio corrected semiempirical potential energy surface show remarkable agreement with experimental frequencies for all three states, thus shedding light on the potential along the reaction path. For example, calculated frequencies for vibrational modes of the red-shifted intermediate, PYPL, exhibit an overall average error of 0.82% from experiment. Upon analysis of anharmonicity patterns in the PYP modes we observe a decrease in anharmonicity in the C8-C9 stretching mode nu29 (trans-cis isomerization marker mode) with the onset of the cis configuration in PYPL. This can be attributed to the loss of the hydrogen-bonding character of the adjacent C9-O2 to the methylamine (Cys69 backbone). For several of the modes, the anharmonicity is mostly due to mode-mode coupling, while for others it is mostly intrinsic. This study shows the importance of the inclusion of anharmonicity in theoretical spectroscopic calculations, and the sensitivity of experiments to anharmonicity. The characterization of protein active-site residues by small molecular mimics provides an acceptable chemical structural representation for biomolecular spectroscopy calculations.     

Configuration selection within vibrational multiconfiguration self-consistent field theory: application to bridged lithium compounds

A configuration selection scheme has been used to speed up vibrational multiconfiguration self-consistent field calculations. Deviations with respect to reference calculations were found to be negligible while yielding an acceleration of about two orders of magnitude. Its application to bridged lithium compounds (Li(2)H(2), Li(2)F(2), Li(2)O(2), and Li(3)F(3)) based on high-level coupled-cluster potential energy surfaces provides accurate vibrational transitions for all fundamental modes. The explicit inclusion of 4-mode couplings was found to be important for Li(2)H(2).     

变分过渡态理论对H＋H2及其同位素选态反应的研究

将选态速度常数的计算推广到任意指定反应物、过渡态的振动激发态.用此法计算了H+H_2(v)及其同位素经不同振动激发过渡态时的速度常数,发现弯曲振动模激发所得结果与实验值更符合,并且在给定能量下,过渡态的弯曲振动模激发比其对称伸缩模激发更有利于反应进行.     

Geometry optimization using improved virtual orbitals: a complete active space numerical gradient approach

The improved virtual orbital-complete active space configuration interaction (IVO-CASCI) method is extended to enable geometry optimization and the calculation of vibrational frequencies for ground and excited states using numerical energy gradients. Applications consider the ground state geometries and vibrational frequencies of the Be2, LiF, H2S, and HCN molecules, as well as excited state properties for HCN, systems that are sufficiently complex to access the efficacy of the method. Comparisons with other standard approaches (self-consistent field, second order Moller-Plesset perturbation theory, complete active space self-consistent field, and coupled cluster singles and doubles methods) demonstrate that the numerical gradient version of the IVO-CASCI approach generally fares comparable to or better for all systems studied. The accurate estimates for the Be2 bond length and vibrational frequency are notable since many other computationally facile methods produce poor results.     

Quadratically convergent algorithm for orbital optimization in the orbital-optimized coupled-cluster doubles method and in orbital-optimized second-order Møller-Plesset perturbation theory

Using a Lagrangian-based approach, we present a more elegant derivation of the equations necessary for the variational optimization of the molecular orbitals (MOs) for the coupled-cluster doubles (CCD) method and second-order M?ller-Plesset perturbation theory (MP2). These orbital-optimized theories are referred to as OO-CCD and OO-MP2 (or simply "OD" and "OMP2" for short), respectively. We also present an improved algorithm for orbital optimization in these methods. Explicit equations for response density matrices, the MO gradient, and the MO Hessian are reported both in spin-orbital and closed-shell spin-adapted forms. The Newton-Raphson algorithm is used for the optimization procedure using the MO gradient and Hessian. Further, orbital stability analyses are also carried out at correlated levels. The OD and OMP2 approaches are compared with the standard MP2, CCD, CCSD, and CCSD(T) methods. All these methods are applied to H(2)O, three diatomics, and the O(4)(+) molecule. Results demonstrate that the CCSD and OD methods give nearly identical results for H(2)O and diatomics; however, in symmetry-breaking problems as exemplified by O(4)(+), the OD method provides better results for vibrational frequencies. The OD method has further advantages over CCSD: its analytic gradients are easier to compute since there is no need to solve the coupled-perturbed equations for the orbital response, the computation of one-electron properties are easier because there is no response contribution to the particle density matrices, the variational optimized orbitals can be readily extended to allow inactive orbitals, it avoids spurious second-order poles in its response function, and its transition dipole moments are gauge invariant. The OMP2 has these same advantages over canonical MP2, making it promising for excited state properties via linear response theory. The quadratically convergent orbital-optimization procedure converges quickly for OMP2, and provides molecular properties that are somewhat different than those of MP2 for most of the test cases considered (although they are similar for H(2)O). Bond lengths are somewhat longer, and vibrational frequencies somewhat smaller, for OMP2 compared to MP2. In the difficult case of O(4)(+), results for several vibrational frequencies are significantly improved in going from MP2 to OMP2.     

Valence : A Massively Parallel Implementation of the Variational Subspace Valence Bond Method

This work describes the software package, Valence , for the calculation of molecular energies using the variational subspace valence bond (VSVB) method. VSVB is an ab initio electronic structure method based on nonorthogonal orbitals. Important features of practical value include high parallel scalability, wave functions that can be constructed automatically by combining orbitals from previous calculations, and ground and excited states that can be modeled with a single configuration or determinant. The open-source software package includes tools to generate wave functions, a database of generic orbitals, example input files, and a library build intended for integration with other packages. We also describe the interface to an external software package, enabling the computation of optimized molecular geometries and vibrational frequencies. © 2019 Wiley Periodicals, Inc.     

New theoretical and experimental infrared results on formaldehyde in solution

An extension of our combined procedure to determine a complete quartic force field and to resolve a vibrational problem thanks to a variational treatment is proposed for quantitative calculations of vibrational spectra in solution. Energies and gradients are obtained through a polarizable continuum model (PCM), the so-called self-consistent isodensity (SCI)-PCM. We present in this paper new experimental results dealing with formaldehyde in solution in cyclohexane, chloroform, THF, acetonitrile, DMSO and water; the obtained vibrational spectra are then compared with CCSD(T)/cc-pVQZ calculations. In addition, density functional theory (DFT) calculations have been carried out with the aim of both anticipating and positioning these approaches for larger sized molecules.     

Vibronic absorption, fluorescence, and phosphorescence spectra of psoralen: a quantum chemical investigation

Excited state potential energy hypersurfaces of 7H-furo[3,2-g][1]benzopyran-7-one (psoralen) have been explored employing (time-dependent) Kohn-Sham density functional theory. At selected points, we have determined electronic excitation energies and electric dipole (transition) moments utilizing a combined density functional/multireference configuration interaction method. Spin-orbit coupling has been taken into account employing an efficient, non-empirical spin-orbit mean-field Hamiltonian. Franck-Condon factors have been computed for vibrational modes with large displacements in the respective Dushinsky transformations. The simulated band spectra closely resemble experimental band shapes and thus validate the theoretically determined nuclear structures at the S(0), S(1), and T(1) minima. In the S(1) (pi(HOMO)-->pi*(LUMO)) state, the lactone bond of the pyrone ring is significantly elongated. From excited vibrational levels of the S(1) state a conical intersection between a (pi-->sigma*) excited state and the electronic ground state may be energetically accessible. Fast non-radiative decay via this relaxation pathway could explain the low fluorescence quantum yield of psoralen. The T(1) (pi(HOMO-1)-->pi*(LUMO)) exhibits a diradicaloid electronic structure with a broken C(5)-C(6) double bond in the pyrone ring. A variational multireference spin-orbit configuration interaction procedure yields a phosphorescence lifetime of 3 s, in excellent agreement with experimental estimates.     

A multiconfigurational SCF computational method for the resolution of the vibrational Schrödinger equation in polyatomic molecules

Summary A new variational method for solving the molecular vibration problem is proposed. The so-called VMCSCF method (vibrational multiconfigurational self-consistent field) is based on the super-CI algorithm, previously developed in the framework of electronicab initio calculations. This approach makes direct use of the generalised Brillouin theorem to ensure self-consistency. The method is dedicated to the study of strongly interacting states (vibrational resonances), which are one of the main sources of perturbation in vibrational spectra. The interest of the method to tackle resonance interactions is illustrated by means of test calculations performed on the water and formaldehyde molecules.     

Towards fast computations of correlated vibrational wave functions: vibrational coupled cluster response excitation energies at the two-mode coupling level

An efficient implementation of vibrational coupled cluster theory with two-mode excitations and a two-mode Hamiltonian is described. The algorithm is shown to scale cubically with respect to the number of modes which is identical to the scaling of the corresponding vibrational configuration interaction algorithm. This is achieved through the use of special intermediates. The same algorithm can also be used in vibrational M?ller-Plesset calculations. To improve performance, screening techniques have been implemented as well. Test calculations on polyaromatic hydrocarbons with up to 264 coupled modes and model systems with up to 1140 modes are used to illustrate the various features of the algorithm.     

Vibrational and thermal effects on the dipole polarizability of methane and carbon tetrachloride from vibrational structure calculations

We present a theoretical study of vibrational and thermal effects on the dipole polarizability of methane and carbon tetrachloride. Using a fourth order Taylor expansion in rectilinear normal coordinates of the potential and property surfaces we solve the vibrational problem using vibrational structure theory, e.g., through vibrational self-consistent-field or vibrational configuration-interaction theory. For each vibrational state we calculate in addition the vibrational state average polarizability. Constructing the vibrational partition function by "brute force" allows for prediction of thermal effects on the dipole polarizability. The method is not restricted in any way to polarizabilities nor to the specific representation of the potential and property surfaces employed in this work. Any molecular property with a suitable normal coordinate representation may be considered. We discuss the performance of vibrational self-consistent field as compared to vibrational configuration interaction and study in detail the convergence of the former method with respect to the number of vibrational states included in the thermal averaging. Based on calculations including up to 170,000 vibrational self-consistent-field states we present thermal effects on the dipole polarizability of methane and carbon tetrachloride in the temperature ranges 0-1100 and 0-500 K, respectively. The predicted thermal effect on the dipole polarizability of methane is found to be approximately 0.8% which compare well with previous experimental measurements.