Vibrational Configuration Interaction Calculations Research Articles

Comparison of curvilinear coordinates within vibrational structure calculations based on automatically generated potential energy surfaces.

For floppy molecules showing internal rotations and/or large amplitude motions, curvilinear internal coordinates are known to be superior to rectilinear normal coordinates within vibrational structure calculations. Due to the myriad definitions of internal coordinates, automated and efficient potential energy surface generators necessitate a high degree of flexibility, supporting the properties arising from these coordinates. Within this work, an approach to deal with these challenges is presented, including key elements, such as the selection of appropriate fit functions, the exploitation of symmetry, the positioning of grid points, or elongation limits for different coordinates. These elements are tested for five definitions of curvilinear coordinates, with three of them being generated in an automated manner. Calculations for semi-rigid molecules, namely H2O, H2CO, CH2F2, and H2CNH, demonstrate the general functionality of the implemented algorithms. Additional calculations for the HOPO molecule highlight the benefits of these curvilinear coordinates for systems with large amplitude motions. This new implementation allowed us to compare the performance of these different coordinate systems with respect to the convergence of the underlying expansion of the potential energy surface and subsequent vibrational configuration interaction calculations.

Solving the puzzle of the carbonic acid vibrational spectrum - An anharmonic story.

Against the general belief that carbonic acid is too unstable for synthesis, it was possible to synthesize the solidas well as gas-phase carbonic acid.It was suggested that solid carbonic acid might exist in Earth's upper troposphere and in the harsh environments of other solar bodies,where it undergoes a cycle of synthesis, decomposition, and dimerization.To provide spectroscopic data for probing the existence of extraterrestrial carbonic acid,matrix-isolation infrared (MI-IR) spectroscopy has shown to be essential.However, early assignments within the harmonic approximation using scaling factors impeded a full interpretation of the rather complex MI-IR spectrum of H2CO3. Recently, carbonic acid was detected in the Galactic center molecular cloud and triggered new interest in the anharmonic spectrum.In this regard, we substantially reassign our Argon MI-IR spectra relying on accurate anharmonic calculations. We calculate a four-mode potential energy surface (PES) at the explicitly correlated coupled-cluster theory using up to triple-zeta basis sets, i.e., CCSD(T)-F12/cc-pVTZ-F12. On this PES, we perform vibrational self-consistent field and configuration interaction (VSCF/VCI) calculations to obtain accurate vibrational transition frequencies and resonance analysis of the fundamentals, first overtones, and combination bands.

Determination of spectroscopic constants from rovibrational configuration interaction calculations

Rotational constants and centrifugal distortion constants of a molecule are the essence of its rotational or rovibrational spectrum (e.g., from microwave, millimeter wave, and infrared experiments). These parameters condense the spectroscopic characteristics of a molecule and, thus, are a valuable resource in terms of presenting and communicating spectroscopic observations. While spectroscopic parameters are obtained from experimental spectra by fitting an effective rovibrational Hamiltonian to transition frequencies, the ab initio calculation of these parameters is usually done within vibrational perturbation theory. In the present work, we investigate an approach related to the experimental fitting procedure, but relying solely on ab initio data obtained from variational calculations, i.e., we perform a nonlinear least squares fit of Watson's A- and S-reduced rotation-vibration Hamiltonian to rovibrational state energies (resp. transition frequencies) from rotational-vibrational configuration interaction calculations. We include up to sextic centrifugal distortion constants. By relying on an educated guess of spectroscopic parameters from vibrational configuration interaction and vibrational perturbation theory, the fitting procedure is very efficient. We observe excellent agreement with experimentally derived parameters.

Universal anharmonic potential energy surfaces for XY2-type molecules

An approach to generate anharmonic potential energy surfaces for both linear and bent XY2-type molecules from their equilibrium geometries, Hessians, and total atomization energies alone is presented. Two key features of the potential energy surfaces are that (a) they reproduce the harmonic behavior around the equilibrium geometries exactly and (b) they have the correct limiting behavior with respect to total bond dissociation. The potentials are constructed from two diatomic potentials, for which both the Morse or Varshni potentials are tested, and a triatomic potential, for which modified forms of the Anderson-n potential are tested. Potential energy surfaces for several linear and bent molecules are constructed from ab initio data, and the third-order derivatives of these surfaces at their equilibrium geometries are compared to the results of finite difference computations. For bent molecules, the vibrational spectra predicted by vibrational configuration interaction calculations on these surfaces are compared to experiment. A modified version of the Anderson-n potential, in combination with the Varshni potential, is demonstrated to predict vibrational frequencies associated with bond angle bending an average of 20 cm−1 below the harmonic oscillator approximation and with a fourfold reduction in the root-mean-square deviation from experiment compared to the harmonic oscillator approximation.

Vibrational Tunneling Spectra of Molecules with Asymmetric Wells: A Combined Vibrational Configuration Interaction and Instanton Approach.

A combined approach that uses the vibrational configuration interaction (VCI) and semiclassical instanton theory was developed to study vibrational tunneling spectra of molecules with multiple wells in full dimensionality. The method can be applied to calculate low-lying vibrational states in the systems with an arbitrary number of minima, which are not necessarily equal in energy or shape. It was tested on a two-dimensional double-well model system and on malonaldehyde, and the calculations reproduced the exact quantum mechanical (QM) results with high accuracy. The method was subsequently applied to calculate the vibrational spectrum of the asymmetrically deuterated malonaldehyde with nondegenerate vibrational frequencies in the two wells. The spectrum is obtained at a cost of single-well VCI calculations used to calculate the local energies. The interactions between states of different wells are computed semiclassically using the instanton theory at a comparatively negligible computational cost. The method is particularly suited to systems in which the wells are separated by large potential barriers and tunneling splittings are small, for example, in some water clusters, when the exact QM methods come at a prohibitive computational cost.

Incremental vibrational configuration interaction theory, iVCI: Implementation and benchmark calculations.

The implementation of an algorithm for the determination of vibrational state energies based on a many-body expansion within the framework of configuration interaction theory is presented. An efficient evaluation of the increments within this approach is realized by an iterative configuration selection scheme. The new algorithm is characterized by low memory demands and an embarassingly parallel workload. The convergence of the expansion has been studied for a series of small molecules of increasing size, namely, formaldehyde, ketene, ethylene, and diborane. A threshold function has been employed to reduce the number of increments for high orders of the expansion. Benchmark calculations with respect to customary configuration-selective vibrational configuration interaction calculations are provided.

VCI Calculations Based on Canonical and Localized Normal Coordinates for Non-Abelian Molecules: Accurate Assignment of the Vibrational Overtones of Allene.

Vibrational configuration interaction calculations (VCI) have been performed to study the impact of the nature of the underlying coordinate systems, i.e., canonical vs localized normal coordinates, on accurate vibrational structure calculations for non-Abelian molecules. Once the correlation space is represented by real-valued primitive Hartree products, the assignment of vibrational states beyond the fundamentals is usually a tedious task and is further complicated by the use of non-symmetry-adapted coordinates. Our recently presented approach based on sparse grid integration of overlap integrals of the VCI wave function with the corresponding harmonic oscillator wave function has been used to determine and assign all fundamentals and vibrational overtones of allene and its deuterated isotopologue. Excellent agreement with available experimental results is observed in all cases.

Vibrationally resolved coupled-cluster x-ray absorption spectra from vibrational configuration interaction anharmonic calculations.

Vibrationally resolved near-edge x-ray absorption spectra at the K-edge for a number of small molecules have been computed from anharmonic vibrational configuration interaction calculations of the Franck-Condon factors. The potential energy surfaces for ground and core-excited states were obtained at the core-valence separated CC2, CCSD, CCSDR(3), and CC3 levels of theory, employing the adaptive density-guided approach scheme to select the single points at which to perform the energy calculations. We put forward an initial attempt to include pair-mode coupling terms to describe the potential of polyatomic molecules.

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.

Highly Accurate Quartic Force Field and Rovibrational Spectroscopic Constants for the Azirinyl Cation (c-C2NH2+) and Its Isomers.

The azirinyl cation is an aromatic cyclic molecule that is isoelectronic with cyclopropenylidene, c-C3H2, and c-C3H3+. Cyclopropenylidene has been shown to be ubiquitous, existing in many different astrophysical environments. Given the similar chemistry between C and N, and the relative abundances between C and N in astrophysical environments, it is expected that there should be aromatic ringed molecules that incorporate N in the ring, but as yet, no such molecule has been identified. To address this issue, the present study uses high levels of electronic structure theory to compute a highly accurate quartic force field (QFF) for the azirinyl cation and its two lowest lying isomers, the cyanomethyl and isocyanomethyl cations. The theoretical approach uses the singles and doubles coupled-cluster method that includes a perturbative correction for connected triple excitations, CCSD(T), together with extrapolation to the one-particle basis set limit and corrections for scalar relativity and core-correlation. The QFF is then used in a second-order vibrational perturbation theory analysis (VPT2) to compute the fundamental vibrational frequencies and rovibrational spectroscopic constants for all three C2NH2+ isomers. The reliability of the VPT2 vibrational frequencies is tested by comparison to vibrational configuration interaction (VCI) calculations, and excellent agreement is found between the two approaches. Fundamental vibrational frequencies and rovibrational spectroscopic constants for all singly substituted 13C, 15N, and D isotopologues are also reported. It is expected that the highly accurate spectroscopic data reported herein will be useful in the identification of these cations in high-resolution experimental or astronomical observations.

The interplay of VSCF/VCI calculations and matrix-isolation IR spectroscopy – Mid infrared spectrum of CH3CH2F and CD3CD2F

We present the first matrix-isolation infrared (MI-IR) spectra of CH3CH2F and its isotopologue CD3CD2F in Neon and Argon matrix, together with new gas-phase IR spectra. Extensive vibrational self-consistent field and configuration interaction (VSCF/VCI) calculations are performed, based on an ab initio potential energy surface at ae-CCSD(T)-F12a/cc-pCVTZ-F12 level of electronic structure theory. We encounter an excellent agreement between VCI calculated transitions and the experimental MI-IR and gas-phase IR spectra. Mean absolute deviations are scattering between 1 and 4 cm−1. The interplay of accurate vibrational structure calculations and high-resolution infrared experiments enables unprecedented insights in the CH respectively CD stretch region, providing the first rigorous assignment of the energetically very close ν1,ν12 and ν13 fundamental transitions.

PES-Learn: An Open-Source Software Package for the Automated Generation of Machine Learning Models of Molecular Potential Energy Surfaces.

We introduce a free and open-source software package (PES-Learn) which largely automates the process of producing high-quality machine learning models of molecular potential energy surfaces (PESs). PES-Learn incorporates a generalized framework for producing grid points across a PES that is compatible with most electronic structure theory software. The newly generated or externally supplied PES data can then be used to train and optimize neural network or Gaussian process models in a completely automated fashion. Robust hyperparameter optimization schemes designed specifically for molecular PES applications are implemented to ensure that the best possible model for the data set is fit with high quality. The performance of PES-Learn toward fitting a few semiglobal PESs from the literature is evaluated. We also demonstrate the use of PES-Learn machine learning models in carrying out high-level vibrational configuration interaction computations on water and formaldehyde.

Localized Normal Coordinates in Accurate Vibrational Structure Calculations: Benchmarks for Small Molecules.

The impact of localized CH-stretching normal coordinates in comparison to canonical normal coordinates on the performance of accurate vibrational structure calculations has been studied for simple molecules of up to eight atoms. Two aspects have been considered in detail, (a) the (pre)screening of coupling terms within an n-mode expansion of the multidimensional potential energy surface and (b) the demands in vibrational configuration interaction calculations (VCI). All calculations have been performed in a realistic setup, and the effect of any approximation has been measured in deviations of the final VCI frequencies, which allows for a direct comparison with experimental data.

Accurate Vibrational Configuration Interaction Calculations on Diborane and Its Isotopologues.

The fundamental vibrational modes of 11B2H6, 11B2D6, 10B2H6, and 10B2D6 have been obtained from vibrational configuration interaction calculations including up to 6-tuple excitations. An n-mode expansion of the underlying potential energy surface obtained from explicitly correlated coupled cluster theory was truncated after the 4-mode coupling terms, which were found to be very important for these particular systems. All molecules are strongly affected by Fermi resonances, which are discussed in detail. The final results are in very good agreement with the available experimental data.

On the choice of coordinates in anharmonic theoretical vibrational spectroscopy: Harmonic vs. anharmonic coupling in vibrational configuration interaction.

By a suitable choice of coordinates, the computational effort required for calculations of anharmonic vibrational spectra can be reduced significantly. By using suitable localized-mode coordinates obtained from an orthogonal transformation of the conventionally used normal-mode coordinates, anharmonic couplings between modes can be significantly reduced. However, such a transformation introduces harmonic couplings between the localized modes. To elucidate the role of these harmonic couplings, we consider the vibrational self-consistent field (VSCF)/vibrational configuration interaction (VCI) calculations for both few-mode model systems and for ethene as a molecular test case. We show that large harmonic couplings can result in significant errors in localized-mode L-VSCF/L-VCI calculations and study the convergence with respect to the size of the VCI excitation space. To further elucidate the errors introduced by harmonic couplings, we discuss the connection between L-VSCF/L-VCI and vibrational exciton models. With the help of our results, we propose an algorithm for the localization of normal modes in suitable subsets that are chosen to strictly limit the errors introduced by the harmonic couplings while still leading to maximally localized modes.

Stretching of cis-formic acid: warm-up and cool-down as molecular work-out.

A new technique to rotationally simplify and Raman-probe conformationally and vibrationally excited small molecules is applied to the cis-trans isomerism of formic acid. It quintuples the previously available gas phase vibrational data base on this excited form of a strongly anharmonic planar molecule despite its limited spectral resolution. The newly determined cis-formic acid fundamentals allow for a balanced vibrational benchmark on both rotamers of formic acid. Assuming the adequacy of vibrational perturbation theory, it reveals weaknesses of standard methods for these systems like B3LYP-D3(BJ)/aVQZ VPT2 or PBE0-D3(BJ)/aVQZ VPT2. The functionals ωB97-XD and M06-2X additionally suffer from severe integration grid size and symmetry dependencies. The vibrational benchmark suggests B2PLYP-D3(BJ)/aVQZ VPT2 and MP2/aVQZ VPT2 as partially competitive and in any case efficient alternatives to computationally demanding coupled cluster vibrational configuration interaction calculations. Whether this is due to fortuitous compensation between electronic structure and vibrational perturbation error remains to be explored.

Low frequency vibrational anharmonicity and nuclear spin effects of Cl-(H2) and Cl-(D2).

Low frequency combination bands of 35Cl-(H2) and 35Cl-(D2) have been measured in the region between 600 and 1100 cm-1 by infrared predissociation spectroscopy in a cryogenic 22-pole ion trap using a free electron laser at the FELIX Laboratory as a tunable light source. The 35Cl-(H2) (35Cl-(D2)) spectrum contains three bands at 773 cm-1 (620 cm-1), 889 cm-1 (692 cm-1), and 978 cm-1 (750 cm-1) with decreasing intensity toward higher photon energies. Comparison of the experimentally determined transition frequencies with anharmonic vibrational self-consistent field and vibrational configuration interaction calculations suggests the assignment of the combination bands v1 + v2, 2v1 + v2, and 3v1 + v2 for 35Cl-(H2) and 2v1 + v2, 3v1 + v2, and 4v1 + v2 for 35Cl-(D2), where v1 is the 35Cl-⋯H2 stretching fundamental and v2 is the Cl-(H2) bend. The observed asymmetric temperature dependent line shape of the v1 + v2 transition can be modeled by a series of ∑+-∏ ro-vibrational transitions, when substantially decreasing the rotational constant in the vibrationally excited state by 35%. The spectrum of 35Cl-(D2) shows a splitting of 7 cm-1 for the strongest band which can be attributed to the tunneling of the ortho/para states of D2.

Disentangling the Complex Vibrational Spectrum of the Protonated Water Trimer, H+(H2O)3, with Two-Color IR-IR Photodissociation of the Bare Ion and Anharmonic VSCF/VCI Theory.

Vibrational spectroscopy of the protonated water trimer provides a stringent constraint on the details of the potential energy surface (PES) and vibrational dynamics governing excess proton motion far from equilibrium. Here we report the linear spectrum of the cold, bare H+(H2O)3 ion using a two-color, IR-IR photofragmentation technique and follow the evolution of the bands with increasing ion trap temperature. The key low-energy features are insensitive to both D2 tagging and internal energy. The D2-tagged D+(D2O)3 spectrum is reported for the first time, and the isotope dependence of the band pattern is surprisingly complex. These spectra are reproduced by large-scale vibrational configuration interaction calculations based on a new full-dimensional PES, which treat the anharmonic effects arising from large amplitude motion. The results indicate such extensive mode mixing in both isotopologues that one should be cautious about assigning even the strongest features to particular motions, especially for the absorptions that occur close to the intramolecular bending mode of the water molecule.

On the benefits of localized modes in anharmonic vibrational calculations for small molecules.

Anharmonic vibrational calculations can already be computationally demanding for relatively small molecules. The main bottlenecks lie in the construction of the potential energy surface and in the size of the excitation space in the vibrational configuration interaction (VCI) calculations. To address these challenges, we use localized-mode coordinates to construct potential energy surfaces and perform vibrational self-consistent field and L-VCI calculations [P. T. Panek and C. R. Jacob, ChemPhysChem 15, 3365 (2014)] for all vibrational modes of two prototypical test cases, the ethene and furan molecules. We find that the mutual coupling between modes is reduced when switching from normal-mode coordinates to localized-mode coordinates. When using such localized-mode coordinates, we observe a faster convergence of the n-mode expansion of the potential energy surface. This makes it possible to neglect higher-order contributions in the n-mode expansion of the potential energy surface or to approximate higher-order contributions in hybrid potential energy surfaces, which reduced the computational effort for the construction of the anharmonic potential energy surface significantly. Moreover, we find that when using localized-mode coordinates, the convergence with respect to the VCI excitation space proceeds more smoothly and that the error at low orders is reduced significantly. This makes it possible to devise low-cost models for obtaining a first approximation of anharmonic corrections. This demonstrates that the use of localized-mode coordinates can be beneficial already in anharmonic vibrational calculations of small molecules and provides a possible avenue for enabling such accurate calculations also for larger molecules.

Optimizing Vibrational Coordinates To Modulate Intermode Coupling.

The choice of coordinate system strongly affects the convergence properties of vibrational structure computations. Two methods for efficient generation of improved vibrational coordinates are presented and justified by analysis of a model anharmonic two-mode Hessian and numerical computations on polyatomic molecules. To produce optimal coordinates, metrics which quantify off-diagonal couplings over a grid of Hessian matrices are minimized through unitary rotations of the vibrational basis. The first proposed metric minimizes the total squared off-diagonal coupling, and the second minimizes the total squared change in off-diagonal coupling. In this procedure certain anharmonic modes tend to localize, for example X-H stretches. The proposed methods do not rely on prior fitting of the potential energy, vibrational structure computations, or localization metrics, so they are unique from previous vibrational coordinate generation algorithms and are generally applicable to polyatomic molecules. Fitting the potential to the approximate n-mode representation in the optimized bases for all-trans polyenes shows that off-diagonal anharmonic couplings are substantially reduced by the new choices of coordinate system. Convergence of vibrational energies is examined in detail for ethylene, and it is shown that coupling-optimized modes converge in vibrational configuration interaction computations to within 1 cm(-1) using only 3-mode couplings, where normal modes require 4-mode couplings for convergence. Comparison of the vibrational configuration interaction convergence with respect to excitation level for the two proposed metrics shows that minimization of the total off-diagonal coupling is most effective for low-cost vibrational structure computations.