Efficient calculation of potential energy surfaces for the generation of vibrational wave functions

Anharmonic Vibrational Spectroscopy of Germanium-Containing Clusters, GexC4-x and GexSi4-x (x = 0-4), for Interstellar Detection

An extensive, high-level theoretical study on tetra-atomic germanium carbide/silicide clusters is presented. Accurate harmonic and anharmonic vibrational frequencies and rotational constants are calculated at the CCSD(T)-F12a(b)/cc-pVT(Q)Z-F12 levels of theory. With growing capabilities to discern more of the chemical composition of the interstellar medium (ISM), an accurate database of reference material is required. The presence of carbon is ubiquitous in the ISM, and silicon is known to be present in interstellar dust grains; however, germanium-containing molecules remain elusive. To begin understanding the presence and role of germanium in the ISM, we present this study of the vibrational and rotational spectroscopic properties of various germanium-containing molecules to aid in their potential identification in the ISM with modern observational tools such as the James Webb Space Telescope. Structures studied herein include rhomboidal (r-), diamond (d-), and trapezoidal (t-) tetra-atomic molecules of the form GexC4-x and GexSi4-x, where x = 0-4. The most promising structure for detection is r-Ge2C2 via the ν4 mode with a frequency of 802.7 cm-1 (12.5 μm) and an intensity of 307.2 km mol-1. Other molecules that are potentially detectable, i.e., through vibrational modes or rotational transitions, include r-Ge3C, r-GeSi3, d-GeC3, r-GeC3, and t-Ge2C2.

Performance of Effective Harmonic Oscillator Approach for the Calculations of Vibrational Transition Energies of Large Molecules

The accuracy and performance of the effective harmonic oscillator approximation for the description of anharmonic vibrational structure calculations are tested for large molecular systems and compared with experimental values along with vibrational self-consistent field and second-order perturbation theories. The effective harmonic oscillator approach is an effective single-particle approximation where the variational parameters are the centroids and widths of the multidimensional Gaussian product functions posited as the vibrational wave functions. A comprehensive calculation for 849 transitions that include the fundamentals, two and three quanta overtone transitions, and several combination bands of three polyaromatic hydrocarbons and one DNA nucleobase with a total of 231 normal modes are assessed. A comparison of EHO results with the experimental values is done for the polyaromatic hydrocarbons, and a close agreement is found between the two results. It also offers anharmonic eigenstates and eigenfunctions that are nearly identical with vibrational self-consistent field theory. An extensive analysis on the resultant wave functions of the excited states is performed. The overall root-mean-square deviation (RMSD) between these two methods for 849 transitions understudy is only about 8.3 cm-1, suggesting the effective harmonic oscillator as a viable alternative for the reliable calculations of transition energies of large molecular systems.

VSCF/VCI theory based on the Podolsky Hamiltonian

While the vibrational spectra of semi-rigid molecules can be computed on approaches relying on the Watson Hamiltonian, floppy molecules or molecular clusters are better described by Hamiltonians, which are capable of dealing with any curvilinear coordinates. It is the kinetic energy operator (KEO) of these Hamiltonians, which render the correlated calculations relying on them rather costly. Novel implementation of vibrational self-consistent field theory and vibrational configuration interaction theory on the basis of the Podolsky Hamiltonian are reported, in which the inverse of the metric tensor, i.e., the G matrix, is represented by an n-mode expansion expressed in terms of polynomials. An analysis of the importance of the individual terms of the KEO with respect to the truncation orders of the n-mode expansion is provided. Benchmark calculations have been performed for the cis-HOPO and methanimine, H2CNH, molecules and are compared to experimental data and to calculations based on the Watson Hamiltonian and the internal coordinate path Hamiltonian.

The Near-Sightedness of Many-Body Interactions in Anharmonic Vibrational Couplings

Couplings between vibrational motions are driven by electronic interactions, and these couplings carry special significance in vibrational energy transfer, multidimensional spectroscopy experiments, and simulations of vibrational spectra. In this investigation, the many-body contributions to these couplings are analyzed computationally in the context of clathrate-like alkali metal cation hydrates, including Cs+(H2O)20, Rb+(H2O)20, and K+(H2O)20, using both analytic and quantum-chemistry potential energy surfaces. Although the harmonic spectra and one-dimensional anharmonic spectra depend strongly on these many-body interactions, the mode-pair couplings were, perhaps surprisingly, found to be dominated by one-body effects, even in cases of couplings to low-frequency modes that involved the motion of multiple water molecules. The origin of this effect was traced mainly to geometric distortion within water monomers and cancellation of many-body effects in differential couplings, and the effect was also shown to be agnostic to the identity of the ion. These outcomes provide new understanding of vibrational couplings and suggest the possibility of improved computational methods for the simulation of infrared and Raman spectra.

Spectroscopic Identification of Trifluorosilylphosphinidene and Isomeric Phosphasilene and Silicon Trifluorophosphine Complex

The perfluorinated silylphosphinidene, F3SiP, in the triplet ground state is generated by the reaction of laser-ablated silicon atoms with PF3 in solid neon and argon matrices. The reactions proceed with the initial formation of a silicon trifluorophosphine complex, F3PSi, in the triplet ground state, and a more stable inserted phosphasilene, FPSiF2, in the singlet ground state upon deposition. The trifluorosilylphosphinidene was formed through F-migration reactions of FPSiF2 and F3PSi following a two-state mechanism under irradiation with visible light (λ = 470 nm) and full arc light (λ > 220 nm), respectively. High-level quantum-chemical methods support the identification of F3PSi, FPSiF2, and F3SiP by matrix-isolation IR spectroscopy.

Efficient vibrationally correlated calculations using n-mode expansion-based kinetic energy operators

Due to its efficiency and flexibility, the n-mode expansion is a frequently used tool for representing molecular potential energy surfaces in quantum chemical simulations. In this work, we investigate the performance of n-mode expansion-based models of kinetic energy operators in general polyspherical coordinate systems. In particular, we assess the operators with respect to accuracy in vibrationally correlated calculations and their effect on potential energy surface construction with the adaptive density guided approach. Our results show that the n-mode expansion-based operator variants are reliable and systematically improvable approximations of the full kinetic energy operator. Moreover, we introduce a workflow to generate the n-mode expanded kinetic energy operators on-the-fly within the adaptive density guided approach. This scheme can be applied in studies of species and coordinate systems, for which an analytical form of the kinetic energy operator is not available.

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.

Quasi-direct Quantum Molecular Dynamics: The Time-Dependent Adaptive Density-Guided Approach for Potential Energy Surface Construction

We present a new quasi-direct quantum molecular dynamics computational method which offers a compromise between quantum dynamics using a precomputed potential energy surface (PES) and fully direct quantum dynamics. This method is termed the time-dependent adaptive density-guided approach (TD-ADGA) and is a method for constructing a PES on the fly during a dynamics simulation. This is achieved by acquisition of new single-point (SP) calculations and refitting of the PES, depending on the need of the dynamics. The TD-ADGA is a further development of the adaptive density-guided approach (ADGA) for PES construction where the placement of SPs is guided by the density of the nuclear wave function. In TD-ADGA, the ADGA framework has been integrated into the time propagation of the time-dependent nuclear wave function and we use the reduced one-mode density of this wave function to guide when and where new SPs are placed. The PES is thus extended or updated if the wave function moves into new areas or if a certain area becomes more important. Here, we derive equations for the reduced one-mode density for the time-dependent Hartree (TDH) method and for multiconfiguration time-dependent Hartree (MCTDH) methods, but the TD-ADGA can be used with any time-dependent wave function method as long as a density is available. The TD-ADGA method has been investigated on molecular systems containing single- and double-minimum potentials and on single-mode and multi-mode systems. We explore different approaches to handle the fact that the TD-ADGA involves a PES that changes during the computation and show how results can be obtained that are in very good agreement with results obtained by using an accurate reference PES. Dynamics with TD-ADGA is essentially a black box procedure, where only the initialization of the system and how to compute SPs must be provided. The TD-ADGA thus makes it easier to carry out quantum molecular dynamics and the quasi-direct framework opens up the possibility to compute quantum dynamics accurately for larger molecular systems.

Determining internal coordinate sets for optimal representation of molecular vibration

Arising from the harmonic approximation in solving the vibrational Schrödinger equation, normal modes dissect molecular vibrations into distinct degrees of freedom. Normal modes are widely used as they give rise to descriptive vibrational notations and are convenient for expanding anharmonic potential energy surfaces as an alternative to higher-order Taylor series representations. Usually, normal modes are expressed in Cartesian coordinates, which bears drawbacks that can be overcome by switching to internal coordinates. Considering vibrational notations, normal modes with delocalized characters are difficult to denote, but internal coordinates offer a route to clearer notations. Based on the Hessian, normal mode decomposition schemes for a given set of internal coordinates can describe a normal mode by its contributions from internal coordinates. However, choosing a set of internal coordinates is not straightforward. While the Hessian provides unique sets of normal modes, various internal coordinate sets are possible for a given system. In the present work, we employ a normal mode decomposition scheme to choose an optimal set. Therefore, we screen reasonable sets based on topology and symmetry considerations and rely on a metric that minimizes coupling between internal coordinates. Ultimately, the Nomodeco toolkit presented here generates internal coordinate sets to find an optimal set for representing molecular vibrations. The resulting contribution tables can be used to clarify vibrational notations. We test our scheme on small to mid-sized molecules, showing how the space of definable internal coordinate sets can significantly be reduced.

Vibrationally correlated calculations in polyspherical coordinates: Taylor expansion-based kinetic energy operators

The efficiency of quantum chemical simulations of nuclear motion can in many cases greatly benefit from the application of curvilinear coordinate systems. This is rooted in the fact that a set of smartly selected curvilinear coordinates may represent the motion naturally well, thus decreasing the couplings between motions in these coordinates. In this study, we assess the validity of different Taylor expansion-based approximations of kinetic energy operators in a (curvilinear) polyspherical parametrization. To this end, we investigate the accuracy as well as the numerical performance of the approximations in time-independent vibrational coupled cluster and full vibrational interaction calculations for several test cases ranging from tri- to penta-atomic molecules. We find that several of the proposed schemes reproduce the vibrational ground state and excitation energies to a decent accuracy, justifying their application in future investigations. Furthermore, due to the restricted mode coupling and their inherent sum-of-products form, the new approximations open up the possibility of treating large molecular systems with efficient vibrational coupled cluster schemes in general coordinates.

Comprehensive quantum chemical analysis of the (ro)vibrational spectrum of thiirane and its deuterated isotopologue

The (ro)vibrational spectra of thiirane, c-C2H4S, and its fully deuterated isotopologue, c-C2D4S, have been studied by means of vibrational configuration interaction theory, VCI, its incremental variant, iVCI, and subsequent variational rovibrational calculations, RVCI, which rely on multidimensional potential energy surfaces of coupled-cluster quality including up to four-mode coupling terms. Accurate geometrical parameters, fundamental vibrational transitions and first overtones, rovibrational spectra and rotational spectroscopic constants have been determined from these calculations and were compared with experimental results whenever available. A number of tentative misassignments in the vibrational spectra could be resolved and most results for the deuterated thiirane are high-level predictions, which may guide experiments to come. Besides this, a new implementation of infrared intensities within the iVCI framework has been tested for the transitions of the title compounds and are compared with results obtained from standard VCI calculations.

Pitfalls in the n-mode representation of vibrational potentials

Simulations of anharmonic vibrational motion rely on computationally expedient representations of the governing potential energy surface. The n-mode representation (n-MR)-effectively a many-body expansion in the space of molecular vibrations-is a general and efficient approach that is often used for this purpose in vibrational self-consistent field (VSCF) calculations and correlated analogues thereof. In the present analysis, a lack of convergence in many VSCF calculations is shown to originate from negative and unbound potentials at truncated orders of the n-MR expansion. For cases of strong anharmonic coupling between modes, the n-MR can both dip below the true global minimum of the potential surface and lead to effective single-mode potentials in VSCF that do not correspond to bound vibrational problems, even for bound total potentials. The present analysis serves mainly as a pathology report of this issue. Furthermore, this insight into the origin of VSCF non-convergence provides a simple, albeit ad hoc, route to correct the problem by "painting in" the full representation of groups of modes that exhibit these negative potentials at little additional computational cost. Somewhat surprisingly, this approach also reasonably approximates the results of the next-higher n-MR order and identifies groups of modes with particularly strong coupling. The method is shown to identify and correct problematic triples of modes-and restore SCF convergence-in two-mode representations of challenging test systems, including the water dimer and trimer, as well as protonated tropine.

Scalable generalized screening for high-order terms in the many-body expansion: Algorithm, open-source implementation, and demonstration

The many-body expansion lies at the heart of numerous fragment-based methods that are intended to sidestep the nonlinear scaling of ab initio quantum chemistry, making electronic structure calculations feasible in large systems. In principle, inclusion of higher-order n-body terms ought to improve the accuracy in a controllable way, but unfavorable combinatorics often defeats this in practice and applications with n ≥ 4 are rare. Here, we outline an algorithm to overcome this combinatorial bottleneck, based on a bottom-up approach to energy-based screening. This is implemented within a new open-source software application ("Fragme∩t"), which is integrated with a lightweight semi-empirical method that is used to cull subsystems, attenuating the combinatorial growth of higher-order terms in the graph that is used to manage the calculations. This facilitates applications of unprecedented size, and we report four-body calculations in (H2O)64 clusters that afford relative energies within 0.1 kcal/mol/monomer of the supersystem result using less than 10% of the unique subsystems. We also report n-body calculations in (H2O)20 clusters up to n = 8, at which point the expansion terminates naturally due to screening. These are the largest n-body calculations reported to date using ab initio electronic structure theory, and they confirm that high-order n-body terms are mostly artifacts of basis-set superposition error.

CRYSTAL23: A Program for Computational Solid State Physics and Chemistry

The Crystal program for quantum-mechanical simulations of materials has been bridging the realm of molecular quantum chemistry to the realm of solid state physics for many years, since its first public version released back in 1988. This peculiarity stems from the use of atom-centered basis functions within a linear combination of atomic orbitals (LCAO) approach and from the corresponding efficiency in the evaluation of the exact Fock exchange series. In particular, this has led to the implementation of a rich variety of hybrid density functional approximations since 1998. Nowadays, it is acknowledged by a broad community of solid state chemists and physicists that the inclusion of a fraction of Fock exchange in the exchange-correlation potential of the density functional theory is key to a better description of many properties of materials (electronic, magnetic, mechanical, spintronic, lattice-dynamical, etc.). Here, the main developments made to the program in the last five years (i.e., since the previous release, Crystal17) are presented and some of their most noteworthy applications reviewed.

Accuracy of Different Electronic Basis Set Families for Anharmonic Molecular Vibrations: A Comprehensive Benchmark Study

In this work, the accuracy and convergence of different electronic basis set families for the computation of anharmonic molecular vibrational spectroscopic calculations are benchmarked. A series of 39 different basis sets from different families following their hierarchy are assessed on VSCF and VSCF-PT2 algorithms with commonly used MP2 and DFT based B3LYP-D potentials for a set of molecular systems. Such an effort has been validated in a previous work ( J. Phys. Chem. A 2020, 124, 9203-9221) with split-valence basis sets for fundamentals and intensities. Here, fundamental transitions, vibrationally excited states, and intensities are compared with the experimental data to estimate the accuracy for a series of Jensen, Dunning, Calendar, Karlsruhe, and Sapporo basis set families. The convergence of basis sets are also compared with the large ANO basis set. Comprehensive statistical error analysis in terms of accuracy and precision was carried out to assess the performance of each basis set. It is observed that the improvement for the calculated harmonic and anharmonic values from the smaller basis sets to the medium (i.e., triple-ξ) is considerable. Beyond this, from medium to large basis sets, the convergence is slow and mostly posits nearly converged values. Basis sets with and without diffuse functions offer characteristically different accuracies and convergence patterns. Finally, recommendations are given on the choice of basis set chosen as black-box which can balance between accuracy and computational time, estimation of the errors, and their selections especially for large molecules.

Accelerating Anharmonic Spectroscopy Simulations via Local-Mode, Multilevel Methods

Ab initio computer simulations of anharmonic vibrational spectra provide nuanced insight into the vibrational behavior of molecules and complexes. The computational bottleneck in such simulations, particularly for ab initio potentials, is often the generation of mode-coupling potentials. Focusing specifically on two-mode couplings in this analysis, the combination of a local-mode representation and multilevel methods is demonstrated to be particularly symbiotic. In this approach, a low-level quantum chemistry method is employed to predict the pairwise couplings that should be included at the target level of theory in vibrational self-consistent field (and similar) calculations. Pairs that are excluded by this approach are "recycled" at the low level of theory. Furthermore, because this low-level pre-screening will eventually become the computational bottleneck for sufficiently large chemical systems, distance-based truncation is applied to these low-level predictions without substantive loss of accuracy. This combination is demonstrated to yield sub-wavenumber fidelity with reference vibrational transitions when including only a small fraction of target-level couplings; the overhead of predicting these couplings, particularly when employing distance-based, local-mode cutoffs, is a trivial added cost. This combined approach is assessed on a series of test cases, including ethylene, hexatriene, and the alanine dipeptide. Vibrational self-consistent field (VSCF) spectra were obtained with an RI-MP2/cc-pVTZ potential for the dipeptide, at approximately a 5-fold reduction in computational cost. Considerable optimism for increased accelerations for larger systems and higher-order couplings is also justified, based on this investigation.

Vibrational Predissociation Spectra of C2 N- and C3 N- : Bending and Stretching Vibrations

We present infrared predissociation spectra of C2 N- (H2 ) and C 3 N- (H2 ) in the 300-1850 cm-1 range. Measurements were performed using the FELion cryogenic ion trap end user station at the Free Electron Lasers for Infrared eXperiments (FELIX) laboratory. For C2 N- (H2 ), we detected the CCN bending and CC-N stretching vibrations. For the C3 N- (H2 ) system, we detected the CCN bending, the CC-CN stretching, and multiple overtones and/or combination bands. The assignment and interpretation of the presented experimental spectra is validated by calculations of anharmonic spectra within the vibrational configuration interaction (VCI) approach, based on potential energy surfaces calculated at explicitly correlated coupled cluster theory (CCSD(T)-F12/cc-pVTZ-F12). The H2 tag acts as an innocent spectator, not significantly affecting the C2,3 N- bending and stretching mode positions. The recorded infrared predissociation spectra can thus be used as a proxy for the vibrational spectra of the bare anions.

Gaussian process regression adaptive density-guided approach: Toward calculations of potential energy surfaces for larger molecules

We present a new program implementation of the Gaussian process regression adaptive density-guided approach [Schmitz et al., J. Chem. Phys. 153, 064105 (2020)] for automatic and cost-efficient potential energy surface construction in the MidasCpp program. A number of technical and methodological improvements made allowed us to extend this approach toward calculations of larger molecular systems than those previously accessible and maintain the very high accuracy of constructed potential energy surfaces. On the methodological side, improvements were made by using a Δ-learning approach, predicting the difference against a fully harmonic potential, and employing a computationally more efficient hyperparameter optimization procedure. We demonstrate the performance of this method on a test set of molecules of growing size and show that up to 80% of single point calculations could be avoided, introducing a root mean square deviation in fundamental excitations of about 3 cm-1. A much higher accuracy with errors below 1 cm-1 could be achieved with tighter convergence thresholds still reducing the number of single point computations by up to 68%. We further support our findings with a detailed analysis of wall times measured while employing different electronic structure methods. Our results demonstrate that GPR-ADGA is an effective tool, which could be applied for cost-efficient calculations of potential energy surfaces suitable for highly accurate vibrational spectra simulations.

Approaching the "Zundel" Limit: Tuning the Vibrational Coupling in N2H+Ng, Ng = {He, Ne, Ar, Kr, Xe, and Rn}

The diazenylium ion (N₂H⁺) is a ubiquitous ion in dense molecular clouds. This ion is often used as a dense gas tracer in outer space. Most of the previous works on diazenylium ion have focused on the shared-proton stretch band, ν_H⁺. In this work, we have performed reduced-dimensional calculations to investigate the vibrational structure of N₂H⁺Ng, Ng = {He, Ne, Ar, Kr, Xe, and Rn}. We demonstrate a few interesting things about this system. First, the vibrational coupling in N₂H⁺ can be tuned to switch on interesting anharmonic effects such as Fermi resonance or combination bands by tagging it with different noble gases. Second, a comparison of the vibrational spectrum from N₂H⁺He to N₂H⁺Rn shows that the ν_H⁺ can be swept from an "Eigen-like" to a "Zundel-like" limiting case. Anharmonic calculations were performed using a multilevel approach, which utilized the MP2 and CCSD(T) levels of theories. Binding energies for the elimination of Ng in N₂H⁺Ng are also reported.

Implementation of the self-consistent phonons method with ab initio potentials (AI-SCP)

The self-consistent phonon (SCP) method allows one to include anharmonic effects when treating a many-body quantum system at thermal equilibrium. The system is then described by an effective temperature-dependent harmonic Hamiltonian, which can be used to estimate its various dynamic and static properties. In this paper, we combine SCP with ab initio (AI) potential energy evaluation in which case the numerical bottleneck of AI-SCP is the evaluation of Gaussian averages of the AI potential energy and its derivatives. These averages are computed efficiently by the quasi-Monte Carlo method utilizing low-discrepancy sequences leading to a fast convergence with respect to the number, S, of the AI energy evaluations. Moreover, a further substantial (an-order-of-magnitude) improvement in efficiency is achieved once a numerically cheap approximation of the AI potential is available. This is based on using a perturbation theory-like (the two-grid) approach in which it is the average of the difference between the AI and the approximate potential that is computed. The corresponding codes and scripts are provided.

Spectroscopic characterization of [H, Cl, S, O] molecular system: Potential candidate for detection in Venus atmosphere

Accurate spectroscopic parameters have been obtained for the identification of the [H, Cl, S, O] molecular system in the Venus atmosphere using computational methods. These calculations employed both standard and explicitly correlated coupled cluster techniques. All isomers possess C1 symmetry, with HOSCl being the most stable isomer. Only HOSCl and trigonal-HSOCl isomers are thermodynamically stable relative to the first dissociation limit HCl + SO. Fundamental modes of the lowest three isomers exhibit many anharmonic resonances, resulting in complex spectra. All isomers are found to be stable in the visible region as the calculation of vertical energy transition indicates. No electronic states were found to strongly absorb in the near UV-vis region.

Positioning of grid points for spanning potential energy surfaces-How much effort is really needed?

The positions of grid points for representing a multidimensional potential energy surface (PES) have a non-negligible impact on its accuracy and the associated computational effort for its generation. Six different positioning schemes were studied for PESs represented by n-mode expansions as needed for the accurate calculation of anharmonic vibrational frequencies by means of vibrational configuration interaction theory. A static approach, which has successfully been used in many applications, and five adaptive schemes based on Gaussian process regression have been investigated with respect to the number of necessary grid points and the accuracy of the fundamental modes for a small set of test molecules. A comparison with a related, more sophisticated, and consistent approach by Christiansen et al. is provided. The impact of the positions of the ab initio grid points is discussed for multilevel PESs, for which the computational effort of the individual electronic structure calculations decreases for increasing orders of the n-mode expansion. As a result of that, the ultimate goal is not the maximal reduction of grid points but rather the computational cost, which is not directly related.

Convergence of series expansions in rovibrational configuration interaction (RVCI) calculations

Rotational and rovibrational spectra are a key in astrophysical studies, atmospheric science, pollution monitoring, and other fields of active research. The ab initio calculation of such spectra is fairly sensitive with respect to a multitude of parameters and all of them must be carefully monitored in order to yield reliable results. Besides the most obvious ones, i.e., the quality of the multidimensional potential energy surface and the vibrational wavefunctions, it is the representation of the μ-tensor within the Watson Hamiltonian, which has a significant impact on the desired line lists or simulated spectra. Within this work, we studied the dependence of high-resolution rovibrational spectra with respect to the truncation order of the μ-tensor within the rotational contribution and the Coriolis coupling operator of the Watson operator. Moreover, the dependence of the infrared intensities of the rovibrational transitions on an n-mode expansion of the dipole moment surface has been investigated as well. Benchmark calculations are provided for thioformaldehyde, which has already served as a test molecule in other studies and whose rovibrational spectrum was found to be fairly sensitive. All calculations rely on rovibrational configuration interaction theory and the discussed high-order terms of the μ-tensor are a newly implemented feature, whose theoretical basics are briefly discussed.

Spectral Signatures of Protonated Noble Gas Clusters of Ne, Ar, Kr, and Xe: From Monomers to Trimers

The structures and spectral features of protonated noble gas clusters are examined using a first principles approach. Protonated noble gas monomers (NgH⁺) and dimers (NgH⁺Ng) have a linear structure, while the protonated noble gas trimers (Ng₃H⁺) can have a T-shaped or linear structure. Successive binding energies for these complexes are calculated at the CCSD(T)/CBS level of theory. Anharmonic simulations for the dimers and trimers unveil interesting spectral features. The symmetric NgH⁺Ng are charactized by a set of progression bands, which involves one quantum of the asymmetric Ng-H⁺ stretch with multiple quanta of the symmetric Ng-H⁺ stretch. Such a spectral signature is very robust and is predicted to be observed in both T-shaped and linear isomers of Ng₃H⁺. Meanwhile, for selected asymmetric NgH⁺Ng’, a Fermi resonance interaction involving the first overtone of the proton bend with the proton stretch is predicted to occur in ArH⁺Kr and XeH⁺Kr.

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.

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.

Performance of Vibrational Self-Consistent Field Theory for Accurate Potential Energy Surfaces: Fundamentals, Excited States, and Intensities

The performance of vibrational structure calculations beyond harmonic approximation in the framework of the vibrational self-consistent field method with second-order perturbation corrections (VSCF-PT2) is investigated in conjunction with very accurate potential energy surfaces (PESs) given by various coupled-cluster electronic structure theories. The quality of anharmonic calculations depends on the accuracy of the underlying multidimensional PES obtained from its functional form, which is given by the level of electronic structure theory. Two such highest levels of typical coupled-cluster electronic structure methods, CCSD and the ″gold standard″ CCSD(T), along with their variants such as CCD, CR-CCL (completely renormalized CR-CC(2,3) approach), and CCSD(TQ) are tested for the construction of accurate anharmonic potentials without any fitting or ad hoc scaling and using cc-pVTZ basis sets. The accuracy of VSCF-PT2 theory in comparison to experimental values is tested for a series of 16 molecules with 135 fundamental bands, 64 overtones, and combination bands and also for 39 intensities. It is found that CCD and CCSD bind the potential tighter than CCSD(T) and the computed VSCF-PT2 transitions are more blue-shifted showing higher deviation from the experiment. In general, VSCF-PT2 results computed at the CCSD(T) potential offer a good cost/accuracy ratio, with the mean absolute deviation and the mean absolute percentage error with the experiment being ∼16 cm^-1 and 1.38, respectively, for fundamentals. Additionally, while the CR-CCL and CCSD(TQ) methods offer similar levels of accuracies as compared to CCSD(T), the former offers a better accuracy/cost ratio than the latter and is a suitable alternative to CCSD(T).

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.

Two-dimensional Infrared Spectroscopy Reveals Better Insights of Structure and Dynamics of Protein

Proteins play an important role in biological and biochemical processes taking place in the living system. To uncover these fundamental processes of the living system, it is an absolutely necessary task to understand the structure and dynamics of the protein. Vibrational spectroscopy is an established tool to explore protein structure and dynamics. In particular, two-dimensional infrared (2DIR) spectroscopy has already proven its versatility to explore the protein structure and its ultrafast dynamics, and it has essentially unprecedented time resolutions to observe the vibrational dynamics of the protein. Providing several examples from our theoretical and experimental efforts, it is established here that two-dimensional vibrational spectroscopy provides exceptionally more information than one-dimensional vibrational spectroscopy. The structural information of the protein is encoded in the position, shape, and strength of the peak in 2DIR spectra. The time evolution of the 2DIR spectra allows for the visualisation of molecular motions.

Structural and vibrational characterization of HCO+ and Rg-HCO+, Rg = {He, Ne, Ar, Kr, and Xe}

The structures of the formyl ion (HCO⁺) and its rare gas tagged counterparts (Rg-HCO⁺, Rg = He, Ne, Ar, Kr, and Xe) were studied at the coupled-cluster singles, doubles, and perturbative triples [CCSD(T)]/aug-cc-pVTZ level of theory and basis set. A linear structure for these tagged complexes was predicted. The Rg binding energies for Rg-HCO⁺ are also examined at the CCSD(T) level. It was found that the binding interaction increases from He-HCO⁺ to Xe-HCO⁺. A multilevel potential energy surface built at the CCSD(T) and second-order Møller-Plesset perturbation levels of theory were used to study these species' vibrational spectra. By changing the Rg in the first-solvation shell for HCO⁺, the Fermi resonance interaction between the first H⁺ bend overtone and the asymmetric and symmetric H-C-O stretches can be modulated. This Fermi resonance modulation is demonstrated by examining a series of rare gas solvated HCO⁺.

Vibrational spectrum and photochemistry of phosphaketene HPCO

The vibrational spectra of the simplest phosphaketene HPCO and its isotopologue DPCO in solid Ar-matrices at 12.0 K have been analyzed with the aid of the computations at the CCSD(T)-F12a/cc-pVTZ-F12 level using configuration-selective vibrational configuration interaction (VCI). In addition to the four IR fundamentals, four overtone and ten combination bands have been unambiguously identified. Furthermore, the photochemistry of HPCO in the matrix has been investigated for the first time. Upon UV-light irradiation (365 or 266 nm), CO-elimination occurs by forming the parent phosphinidene HP that can be trapped by ˙NO to yield the elusive phosphinimine-N-oxyl radical HPNO˙. In contrast, an excimer laser (193 nm) irradiation of HPCO causes additional decomposition to H˙ and ˙PCO with concomitant formation of the long-sought phosphaethyne HOCP.

Anharmonic Vibrational Calculations Based on Group-Localized Coordinates: Applications to Internal Water Molecules in Bacteriorhodopsin

An efficient anharmonic vibrational method is developed exploiting the locality of molecular vibration. Vibrational coordinates localized to a group of atoms are employed to divide the potential energy surface (PES) of a system into intra- and inter-group contributions. Then, the vibrational Schrödinger equation is solved based on a PES, in which the inter-group coupling is truncated at the harmonic level while accounting for the intra-group anharmonicity. The method is applied to a pentagonal hydrogen bond network (HBN) composed of internal water molecules and charged residues in a membrane protein, bacteriorhodopsin. The PES is calculated by the quantum mechanics/molecular mechanics (QM/MM) calculation at the level of B3LYP-D3/aug-cc-pVDZ. The infrared (IR) spectrum is computed using a set of coordinates localized to each water molecule and amino acid residue by second-order vibrational quasi-degenerate perturbation theory (VQDPT2). Benchmark calculations show that the proposed method yields the N-D/O-D stretching frequencies with an error of 7 cm-1 at the cost reduced by more than five times. In contrast, the harmonic approximation results in a severe error of 150 cm-1. Furthermore, the size of QM regions is carefully assessed to find that the QM regions should include not only the pentagonal HBN itself but also its HB partners. VQDPT2 calculations starting from transient structures obtained by molecular dynamics simulations have shown that the structural sampling has a significant impact on the calculated IR spectrum. The incorporation of anharmonicity, sufficiently large QM regions, and structural samplings are of essential importance to reproduce the experimental IR spectrum. The computational spectrum paves the way for decoding the IR signal of strong HBNs and helps elucidate their functional roles in biomolecules.

Infrared Spectra and Theoretical Calculations of BSe2 and BSe2-: The Pseudo-Jahn-Teller Effect

Matrix isolation infrared spectroscopy has been employed to study the reaction of laser-ablated boron atoms with hydrogen selenide in a 5 K solid argon matrix. On the basis of the isotopic shifts as well as the theoretical frequency calculations, triatomic molecule BSe₂ and its anion BSe₂^- were identified. Both BSe₂ and BSe₂^- were predicted to have D_∞h symmetric structures with nearly identical structure parameters and bond strengths by quantum chemical calculations. Whereas the observed antisymmetric B-Se stretching frequency of BSe₂ is much lower than that of BSe₂^-, the anomalously low antisymmetric B-Se stretching frequency of BSe₂ is attributed to a pseudo-Jahn-Teller effect due to the mixing of the X²Π_g ground state with the A²Π_u excited state. In addition, H₂BSe, HBSe, and HSeBSe molecules were produced in the reaction.

Fermi resonance switching in KrH+Rg and XeH+Rg (Rg = Ne, Ar, Kr, and Xe)

Matrix isolation experiments have been successfully employed to extensively study the infrared spectrum of several proton-bound rare gas complexes. Most of these studies have focused on the spectral signature for the H⁺ stretch (ν₃) and its combination bands with the intermolecular stretch coordinate (ν₁). However, little attention has been paid to the Fermi resonance interaction between the H⁺ stretch (ν₃) and H⁺ bend overtone (2ν₂) in the asymmetric proton-bound rare gas dimers, RgH⁺Rg'. In this work, we have investigated this interaction on KrH⁺Rg and XeH⁺Rg with Rg = (Ne, Ar, Kr, and Xe). A multilevel potential energy surface (PES) was used to simulate the vibrational structure of these complexes. This PES is a dual-level comprising of second-order Møller-Plesset perturbation theory and coupled-cluster singles doubles with perturbative triples [CCSD(T)] levels of ab initio theories. We found that when both the combination bands (nν₁ + ν₃) and bend overtone 2ν₂ compete to borrow intensity from the ν₃ band, the latter wins over the former, which then results in the suppression of the nν₁ + ν₃ bands. The current simulations offer new assignments for the ArH⁺Xe and KrH⁺Xe spectra. Complete basis set (CBS) binding energies for these complexes were also calculated at the CCSD(T)/CBS level.

A pair potential modeling study of F3− in neon matrices

First-principles investigations of the trifluoride anion in a neon environment reveal a small blue-shift of the fundamental vibrational excitations.

On the synergy of matrix-isolation infrared spectroscopy and vibrational configuration interaction computations

The key feature of matrix-isolation infrared (MI-IR) spectroscopy is the isolation of single guest molecules in a host system at cryogenic conditions. The matrix mostly hinders rotation of the guest molecule, providing access to pure vibrational features. Vibrational self-consistent field (VSCF) and configuration interaction computations (VCI) on ab initio multimode potential energy surfaces (PES) give rise to anharmonic vibrational spectra. In a single-sourced combination of these experimental and computational approaches, we have established an iterative spectroscopic characterization procedure. The present article reviews the scope of this procedure by highlighting the strengths and limitations based on the examples of water, carbon dioxide, methane, methanol, and fluoroethane. An assessment of setups for the construction of the multimode PES on the example of methanol demonstrates that CCSD(T)-F12 level of theory is preferable to compute (a) accurate vibrational frequencies and (b) equilibrium or vibrationally averaged structural parameters. Our procedure has allowed us to uniquely assign unknown or disputed bands and enabled us to clarify problematic spectral regions that are crowded with combination bands and overtones. Besides spectroscopic assignment, the excellent agreement between theory and experiment paves the way to tackle questions of rather fundamental nature as to whether or not matrix effects are systematic, and it shows the limits of conventional notations used by spectroscopists.

Dual Basis Approach for Ab Initio Anharmonic Calculations of Vibrational Spectroscopy: Application to Microsolvated Biomolecules

A dual electronic basis set approach is introduced for more efficient but accurate calculations of the anharmonic vibrational spectra in the framework of the vibrational self-consistent field (VSCF) theory. In this approach, an accurate basis set is used to compute the vibrational spectra at the harmonic level. The results are used to scale the potential surface from a more modest but much more efficient basis set. The scaling is such that at the harmonic level the new, scaled potential agrees with one of the accurate basis sets. The approach is tested in the application of the microsolvated, protected amino acid Ac-Phe-OMe, using the scaled anharmonic hybrid potential in the VSCF and VSCF-PT2 algorithms. The hybrid potential method yields results that are in good accord with the experiment and very close to those obtained in calculations with the high-level, very costly potential from the large basis set. At the same time, the hybrid potential calculations are considerably less expensive. The results of the hybrid calculations are much more accurate than those computed from the potential surface corresponding to the modest basis set. The results are very encouraging for using the hybrid potential method for inexpensive yet sufficiently accurate anharmonic calculations for the spectra of large biomolecules.

Neural Network Potential Energy Surfaces for Small Molecules and Reactions

We review progress in neural network (NN)-based methods for the construction of interatomic potentials from discrete samples (such as ab initio energies) for applications in classical and quantum dynamics including reaction dynamics and computational spectroscopy. The main focus is on methods for building molecular potential energy surfaces (PES) in internal coordinates that explicitly include all many-body contributions, even though some of the methods we review limit the degree of coupling, due either to a desire to limit computational cost or to limited data. Explicit and direct treatment of all many-body contributions is only practical for sufficiently small molecules, which are therefore our primary focus. This includes small molecules on surfaces. We consider direct, single NN PES fitting as well as more complex methods that impose structure (such as a multibody representation) on the PES function, either through the architecture of one NN or by using multiple NNs. We show how NNs are effective in building representations with low-dimensional functions including dimensionality reduction. We consider NN-based approaches to build PESs in the sums-of-product form important for quantum dynamics, ways to treat symmetry, and issues related to sampling data distributions and the relation between PES errors and errors in observables. We highlight combinations of NNs with other ideas such as permutationally invariant polynomials or sums of environment-dependent atomic contributions, which have recently emerged as powerful tools for building highly accurate PESs for relatively large molecular and reactive systems.

Charge-Inverted Hydrogen-Bridged Bond in HCa(μ-H)3E (E = Si, Ge, and Sn): Matrix Isolation Infrared Spectroscopic and Theoretical Studies

Matrix isolation infrared spectroscopy combined with quantum-chemical calculations were employed to study the reactions of calcium atoms with silane, germane, and stannane in a 4 K argon matrix. The ion pairs [HCa]⁺ and [EH₃]^- (E = Si, Ge, and Sn) in both the classical structure HCaEH₃ and the bridged structure HCa(μ-H)₃E were identified based on the H/D isotopic substitution experiments and quantum-chemical calculations. The results show that the reaction between ground-state Ca and EH₄ proceeds inefficiently, and only after the photolytic activation of Ca atoms to the Ca(¹P:4s4p) state does insertion occur to give HCaEH₃, which rearranges to HCa(μ-H)₃E upon photolysis. Topological analysis of the electronic structure suggests that the nonclassical structure HCa(μ-H)₃E is formed by the electrostatic interaction with charge-inverted hydrogen bridge bond, while HCaEH₃ is dominated by (HCa)⁺(EH₃)^- ion pair interactions.

Hardware efficient quantum algorithms for vibrational structure calculations

We introduce a framework for the calculation of ground and excited state energies of bosonic systems suitable for near-term quantum devices and apply it to molecular vibrational anharmonic Hamiltonians. Our method supports generic reference modal bases and Hamiltonian representations, including the ones that are routinely used in classical vibrational structure calculations. We test different parametrizations of the vibrational wavefunction, which can be encoded in quantum hardware, based either on heuristic circuits or on the bosonic Unitary Coupled Cluster Ansatz. In particular, we define a novel compact heuristic circuit and demonstrate that it provides a good compromise in terms of circuit depth, optimization costs, and accuracy. We evaluate the requirements, number of qubits and circuit depth, for the calculation of vibrational energies on quantum hardware and compare them with state-of-the-art classical vibrational structure algorithms for molecules with up to seven atoms.