A new efficient method for the calculation of interior eigenpairs and its application to vibrational structure problems

Zero-Point-Energy Driven Isotopic Exchange of the [H3O]- anion Probed by Mid-Infrared Action Spectroscopy

We present the first observation of vibrational transitions in the [H3O]- anion, an intermediate in the anion-molecule reaction of water, H2O, and hydride, H-, using a laser-induced isotopic H/D exchange reaction action spectroscopy scheme applied to anions. The observed bands are assigned as the fundamental and first overtone of the H2O-H- vibrational stretching mode, based on anharmonic calculations within the vibrational perturbation theory and vibrational configuration interaction. Although the D2O·D- species has the lowest energy, our experiments confirm the D2O·H- isotope to be a sink of the H/D exchange reaction. Ab initio calculations corroborate that the formation of D2O·H- is favored, as the zero-point-energy difference is larger between D2 and H2 than between D2O·H- and D2O·D-.

Using nested tensor train contracted basis functions with group theoretical techniques to compute (ro)-vibrational spectra of molecules with non-Abelian groups

In this paper, we use nested tensor-train contractions to compute vibrational and ro-vibrational energy levels of molecules with five and six atoms. At each step, we fully exploit symmetry by using symmetry adapted basis functions obtained from an irreducible tensor method. Contracted basis functions are determined by diagonalizing reduced dimensional Hamiltonian matrices. The size of matrices of eigenvectors, used to account for coupling between groups of coordinates, is reduced by discarding rows and columns. The size of the matrices that must be diagonalized is thus substantially reduced, making it possible to use direct eigensolvers, even for molecules with five and six atoms. The symmetry-adapted contracted vibrational basis functions have been used to compute J = 0 energy levels of the CH3CN (C3v) and J > 0 levels of CH4.

From the Automated Calculation of Potential Energy Surfaces to Accurate Infrared Spectra

Advances in the development of quantum chemical methods and progress in multicore architectures in computer science made the simulation of infrared spectra of isolated molecules competitive with respect to established experimental methods. Although it is mainly the multidimensional potential energy surface that controls the accuracy of these calculations, the subsequent vibrational structure calculations need to be carefully converged in order to yield accurate results. As both aspects need to be considered in a balanced way, we focus on approaches for molecules of up to 12-15 atoms with respect to both parts, which have been automated to some extent so that they can be employed in routine applications. Alternatives to machine learning will be discussed, which appear to be attractive, as long as local regions of the potential energy surface are sufficient. The automatization of these methods is still in its infancy, and the generalization to molecules with large amplitude motions or molecular clusters is far from trivial, but many systems relevant for astrophysical studies are already in reach.

A numerical-tensorial "hybrid" nuclear motion Hamiltonian and dipole moment operator for spectra calculation of polyatomic nonrigid molecules

The analysis and modeling of high-resolution spectra of nonrigid molecules require a specific Hamiltonian and group-theoretical formulation that differs significantly from that of more familiar rigid systems. Within the framework of Hougen-Bunker-Johns (HBJ) theory, this paper is devoted to the construction of a nonrigid Hamiltonian based on a suitable combination of numerical calculations for the nonrigid part in conjunction with the irreducible tensor operator method for the rigid part. For the first time, a variational calculation from ab initio potential energy surfaces is performed using the HBJ kinetic energy operator built from vibrational, large-amplitude motion, and rotational tensor operators expressed in terms of curvilinear and normal coordinates. Group theory for nonrigid molecules plays a central role in the characterization of the overall tunneling splittings and is discussed in the present approach. The construction of the dipole moment operator is also examined. Validation tests consisting of a careful convergence study of the energy levels as well as a comparison of results obtained from independent computer codes are given for the nonrigid molecules CH2, CH3, NH3, and H2O2. This work paves the way for the modeling of high-resolution spectra of larger nonrigid systems.

Novel methodology for systematically constructing global effective models from ab initio-based surfaces: A new insight into high-resolution molecular spectra analysis

In this paper, a novel methodology is presented for the construction of ab initio effective rotation-vibration spectroscopic models from potential energy and dipole moment surfaces. Non-empirical effective Hamiltonians are obtained via the block-diagonalization of selected variationally computed eigenvector matrices. For the first time, the derivation of an effective dipole moment is carried out in a systematic way. This general approach can be implemented quite easily in most of the variational computer codes and turns out to be a clear alternative to the rather involved Van Vleck perturbation method. Symmetry is exploited at all stages to translate first-principles calculations into a set of spectroscopic parameters to be further refined on experiment. We demonstrate on H₂CO, PH₃, CH₄, C₂H₄, and SF₆ that the proposed effective model can provide crucial information to spectroscopists within a very short time compared to empirical spectroscopic models. This approach brings a new insight into high-resolution spectrum analysis of polyatomic molecules and will be also of great help in the modeling of hot atmospheres where completeness is important.

Comparison of body definitions for incremental vibrational configuration interaction theory (iVCI)

Within incremental vibrational configuration interaction theory (iVCI), the vibrational state energy is determined by means of a many-body expansion, i.e., it is a sum of terms of increasing order, which allow for an embarrassingly parallel evaluation. The convergence of this expansion depends strongly on the definition of the underlying bodies, which essentially decompose the correlation space into fragments. The different definitions considered here comprise mode-based bodies, excitation level-based bodies, and energy-based bodies. An analysis of the convergence behavior revealed that accounting for resonances within these definitions is mandatory and leads to a substantial improvement of the convergence, that is, the expansions can be truncated at lower orders. Benchmark calculations and systematic comparisons of the different body definitions for a small set of molecules, i.e., ketene, ethene, and diborane, have been conducted to study the overall performance of these iVCI implementations with respect to accuracy and central processing unit time.

Efficient and Automated Quantum Chemical Calculation of Rovibrational Nonresonant Raman Spectra

An outline of a newly developed program for the simulation of rovibrational nonresonant Raman spectra is presented. This program is an extension of our recently developed code for rovibrational infrared spectra [J. Chem Phys. 152 (2020) 244104] and relies on vibrational wavefunctions from variational configuration interaction theory to allow for an almost fully automated calculation of such spectra in pure ab initio fashion. Due to efficient contraction schemes this program requires modest computational resources and it can be controlled by only a few lines of input. As the required polarizability surfaces are also computed in an automated fashion, this implementation enables the routine application to small molecules. For demonstrating its capabilities, benchmark calculations for water H216O are compared to reference data and spectra for the beryllium dihydride dimer, Be2H4 (D2h), are predicted. The inversion symmetry of the D2h systems lead to complementary infrared and Raman spectra, which are needed both for a comprehensive investigation of this system.

Advances in vibrational configuration interaction theory - part 2: Fast screening of the correlation space

For larger molecules, the computational demands of configuration selective vibrational configuration interaction theory (cs-VCI) are usually dominated by the configuration selection process, which commonly is based on second order vibrational Møller-Plesset perturbation (VMP2) theory. Here we present two techniques, which lead to substantial accelerations of such calculations while retaining the desired high accuracy of the final results. The first one introduces the concept of configuration classes, which allows for a highly efficient exploitation of the analogs of the Slater-Condon rules in vibrational structure calculations with large correlation spaces. The second approach uses a VMP2 like vector for augmenting the targeted vibrational wavefunction within the selection of configurations and thus avoids any intermediate diagonalization steps. The underlying theory is outlined and benchmark calculations are provided for highly correlated vibrational states of several molecules.

Advances in vibrational configuration interaction theory - part 1: Efficient calculation of vibrational angular momentum terms

Finite basis vibrational configuration interaction theory (VCI) is a highly accurate method for the variational calculation of state energies and related properties, but suffers from fast growing computational costs in dependence of the size of the correlation space. In this series of papers, concepts and techniques will be presented, which diminish the computational demands and thus broaden the applicability of this method to larger molecules or more complex situations. This first part focuses on a highly efficient implementation of the vibrational angular momentum (VAM) terms as occurring in the Watson Hamiltonian and the prediagonalization of initial subspaces within an iterative configuration selective VCI implementation. Working equations and benchmark calculations are provided, the latter demonstrating the increased performance of the new algorithm.

High-Level Rovibrational Calculations on Ketenimine

From an astrochemical point of view ketenimine (CH₂CNH) is a complex organic molecule (COM) and therefore likely to be a building block for biologically relevant molecules. Since it has been detected in the star-forming region Sagittarius B2(N), it is of high relevance in this field. Although experimental data are available for certain bands, for some energy ranges such as above 1200 cm^-1 reliable data virtually do not exist. In addition, high-level ab initio calculations are neither reported for ketenimine nor for one of its deuterated isotopologues. In this paper, we provide for the first time data from accurate quantum chemical calculations and a thorough analysis of the full rovibrational spectrum. Based on high-level potential energy surfaces obtained from explicitly correlated coupled-cluster calculations including up to 4-mode coupling terms, the (ro)vibrational spectrum of ketenimine has been studied in detail by variational calculations relying on rovibrational configuration interaction (RVCI) theory. Strong Fermi resonances were found for all isotopologues. Rovibrational infrared intensities have been obtained from dipole moment surfaces determined from the distinguishable cluster approximation. A comparison of the spectra of the CH₂CNH molecule with experimental data validates our results, but also reveals new insight about the system, which shows very strong Coriolis coupling effects.

Ab initio calculation of rovibrational states for non-degenerate double-well potentials: cis-trans isomerization of HOPO

The rovibrational spectra of metaphosphorous acid, HOPO, and its deuterated isotopologue have been studied by vibrational configuration interaction calculations, relying on the internal coordinate path Hamiltonian and the Watson Hamiltonian. Tunneling effects for the overtones of the torsional mode, which gives rise to the cis-trans isomerization, and its rovibrational transitions have been investigated in detail. Due to strong matrix effects, comparison with experimental data is hindered, and thus, the calculations provide accurate estimates for the fundamental modes of these species.

The Molpro quantum chemistry package

Molpro is a general purpose quantum chemistry software package with a long development history. It was originally focused on accurate wavefunction calculations for small molecules but now has many additional distinctive capabilities that include, inter alia, local correlation approximations combined with explicit correlation, highly efficient implementations of single-reference correlation methods, robust and efficient multireference methods for large molecules, projection embedding, and anharmonic vibrational spectra. In addition to conventional input-file specification of calculations, Molpro calculations can now be specified and analyzed via a new graphical user interface and through a Python framework.

Decomposing anharmonicity and mode-coupling from matrix effects in the IR spectra of matrix-isolated carbon dioxide and methane

A combined experimental and computational approach revealed similarities and differences in the vibrational signature of matrix-isolated carbon dioxide and methane.

Refined analysis of the X̃ 2A2←X̃ 1A1 photoelectron spectrum of furan

The X̃ ²A₂←X̃ ¹A₁ photoelectron spectrum of furan has been studied by a time-independent eigenstate-free Raman wave function approach based on multi-dimensional potential energy surfaces obtained from explicitly correlated distinguishable clusters calculations. Individual vibronic transitions with the most significant Franck-Condon factors were determined by our recently developed residual-based algorithm for the calculation of eigenpairs in conjunction with the formalism of contracted invariant Krylov subspaces. The account of anharmonic and temperature effects allowed us to explain most bands in an experimental high-resolution zero kinetic energy photoelectron spectrum. This led to the reassignment of many spectral features, as well as a refined interpretation of the intensity mechanism for the corresponding transitions.

On-the-Fly Computation of Frontal Orbitals in Density Matrix Expansions

We propose a method for computation of frontal (homo and lumo) orbitals in recursive polynomial expansion algorithms for the density matrix. Such algorithms give a computational cost that increases only linearly with system size for sufficiently sparse systems, but a drawback compared to the traditional diagonalization approach is that molecular orbitals are not readily available. Our method is based on the idea to use the polynomial of the density matrix expansion as an eigenvalue filter giving large separation between eigenvalues around homo and lumo [ Rubensson et al. J. Chem. Phys. 2008 , 128 , 176101 ]. This filter is combined with a shift-and-square (folded spectrum) method to move the desired eigenvalue to the end of the spectrum. In this work we propose a transparent way to select recursive expansion iteration and shift for the eigenvector computation that results in a sharp eigenvalue filter. The filter is obtained as a byproduct of the density matrix expansion, and there is no significant additional cost associated either with its construction or with its application. This gives a clear-cut and efficient eigenvalue solver that can be used to compute homo and lumo orbitals with sufficient accuracy in a small fraction of the total recursive expansion time. Our algorithms make use of recent homo and lumo eigenvalue estimates that can be obtained at negligible cost [ Rubensson et al. SIAM J. Sci. Comput . 2014 , 36 , B147 ]. We illustrate our method by performing self-consistent field calculations for large scale systems.