Vibrational coupled cluster theory

The role of microenvironments on computed vibrationally-resolved emission spectra: The case of oxazines

Oxazine dyes act as reporters of their near environment by the response of their fluorescence spectra. At the same time, their fluorescence spectra exhibit a pronounced vibrational progression. In this work, we computationally investigate the impact of near-environment models consisting of aggregated water as well as betaine molecules on the vibrational profile of fluorescence spectra of different oxazine derivatives. For aggregated betaine and a water molecule located above the plane of the dyes, we observe a distinct modification of the vibrational profile, which is more pronounced than the effect of a continuum description of a solvent environment. Our analysis shows that this effect cannot be explained by a pure change in the electronic structure, but that also vibrational degrees of freedom of the environment can be decisive for the vibrational profile and should, hence, not generally be neglected.

Harmonic and anharmonic vibrational computations for biomolecular building blocks: Benchmarking DFT and basis sets by theoretical and experimental IR spectrum of glycine conformers

Advanced vibrational spectroscopic experiments have reached a level of sophistication that can only be matched by numerical simulations in order to provide an unequivocal analysis, a crucial step to understand the structure-function relationship of biomolecules. While density functional theory (DFT) has become the standard method when targeting medium-size or larger systems, the problem of its reliability and accuracy are well-known and have been abundantly documented. To establish a reliable computational protocol, especially when accuracy is critical, a tailored benchmark is usually required. This is generally done over a short list of known candidates, with the basis set often fixed a priori. In this work, we present a systematic study of the performance of DFT-based hybrid and double-hybrid functionals in the prediction of vibrational energies and infrared intensities at the harmonic level and beyond, considering anharmonic effects through vibrational perturbation theory at the second order. The study is performed for the six-lowest energy glycine conformers, utilizing available "state-of-the-art" accurate theoretical and experimental data as reference. Focusing on the most intense fundamental vibrations in the mid-infrared range of glycine conformers, the role of the basis sets is also investigated considering the balance between computational cost and accuracy. Targeting larger systems, a broad range of hybrid schemes with different computational costs is also tested.

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.

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.

Vibrational ADAPT-VQE: Critical points lead to problematic convergence

Quantum chemistry is one of the most promising applications for which quantum computing is expected to have a significant impact. Despite considerable research in the field of electronic structure, calculating the vibrational properties of molecules on quantum computers remains a relatively unexplored field. In this work, we develop a vibrational Adaptive Derivative-Assembled Pseudo-Trotter Variational Quantum Eigensolver (vADAPT-VQE) formalism based on an infinite product representation (IPR) of anti-Hermitian excitation operators of the Full Vibrational Configuration Interaction (FVCI) wavefunction, which allows for preparing eigenstates of vibrational Hamiltonians on quantum computers. In order to establish the vADAPT-VQE algorithm using the IPR, we study the exactness of disentangled Unitary Vibrational Coupled Cluster (dUVCC) theory and show that dUVCC can formally represent the FVCI wavefunction in an infinite expansion. To investigate the performance of the vADAPT-VQE algorithm, we numerically study whether the vADAPT-VQE algorithm generates a sequence of operators that may represent the FVCI wavefunction. Our numerical results indicate frequent appearance of critical points in the wavefunction preparation using vADAPT-VQE. These results imply that one may encounter diminishing usefulness when preparing vibrational wavefunctions on quantum computers using vADAPT-VQE and that additional studies are required to find methods that can circumvent this behavior.

Time dependent vibrational electronic coupled cluster (VECC) theory for non-adiabatic nuclear dynamics

A time-dependent vibrational electronic coupled-cluster (VECC) approach is proposed to simulate photo-electron/UV-VIS absorption spectra as well as time-dependent properties for non-adiabatic vibronic models, going beyond the Born-Oppenheimer approximation. A detailed derivation of the equations of motion and a motivation for the ansatz are presented. The VECC method employs second-quantized bosonic construction operators and a mixed linear and exponential ansatz to form a compact representation of the time-dependent wave-function. Importantly, the method does not require a basis set, has only a few user-defined inputs, and has a classical (polynomial) scaling with respect to the number of degrees of freedom (of the vibronic model), resulting in a favorable computational cost. In benchmark applications to small models and molecules, the VECC method provides accurate results compared to multi-configurational time-dependent Hartree calculations when predicting short-time dynamical properties (i.e., photo-electron/UV-VIS absorption spectra) for non-adiabatic vibronic models. To illustrate the capabilities, the VECC method is also successfully applied to a large vibronic model for hexahelicene with 14 electronic states and 63 normal modes, developed in the group by Aranda and Santoro [J. Chem. Theory Comput. 17, 1691, (2021)].

Exploring Alternate Methods for the Calculation of High-Level Vibrational Corrections of NMR Spin-Spin Coupling Constants

Traditional nuclear magnetic resonance (NMR) calculations typically treat systems with a Born-Oppenheimer-derived electronic wave function that is solved for a fixed nuclear geometry. One can numerically account for this neglected nuclear motion by averaging over property values for all nuclear geometries with a vibrational wave function and adding this expectation value as a correction to an equilibrium geometry property value. Presented are benchmark coupled-cluster singles and doubles (CCSD) vibrational corrections to spin-spin coupling constants (SSCCs) computed at the level of vibrational second-order perturbation theory (VPT2) using the vibrational averaging driver of the CFOUR program. As CCSD calculations of vibrational corrections are very costly, cheaper electronic structure methods are explored via a newly developed Python vibrational averaging program within the Dalton Project. Namely, results obtained with the second-order polarization propagator approximation (SOPPA) and density functional theory (DFT) with the B3LYP and PBE0 exchange-correlation functionals are compared to the benchmark CCSD//CCSD(T) and experimental values. CCSD//CCSD(T) corrections are also combined with literature CC3 equilibrium geometry values to form the highest-order vibrationally corrected values available (i.e., CC3//CCSD(T) + CCSD//CCSD(T)). CCSD//CCSD(T) statistics showed favorable statistics in comparison to experimental values, albeit at an unfavorably high computational cost. A cheaper CCSD//CCSD(T) + B3LYP method showed quite similar mean absolute deviation (MAD) values as CCSD//CCSD(T), concluding that CCSD//CCSD(T) + B3LYP is optimal in terms of cost and accuracy. With reference to experimental values, a vibrational correction was not worth the cost for all of the other methods tested. Finally, deviation statistics showed that CC3//CCSD(T) + CCSD//CCSD(T) vibrational-corrected equilibrium values deteriorated in comparison to CCSD//CCSD(T) attributed to the use of a smaller basis set or lack of solvation effects for the CC3 equilibrium calculations.

A Critical Assessment on Calculating Vibrational Spectra in Nanostructured Materials

Vibrational spectroscopy is an omnipresent spectroscopic technique to characterize functional nanostructured materials such as zeolites, metal-organic frameworks (MOFs), and metal-halide perovskites (MHPs). The resulting experimental spectra are usually complex, with both low-frequency framework modes and high-frequency functional group vibrations. Therefore, theoretically calculated spectra are often an essential element to elucidate the vibrational fingerprint. In principle, there are two possible approaches to calculate vibrational spectra: (i) a static approach that approximates the potential energy surface (PES) as a set of independent harmonic oscillators and (ii) a dynamic approach that explicitly samples the PES around equilibrium by integrating Newton's equations of motions. The dynamic approach considers anharmonic and temperature effects and provides a more genuine representation of materials at true operating conditions; however, such simulations come at a substantially increased computational cost. This is certainly true when forces and energy evaluations are performed at the quantum mechanical level. Molecular dynamics (MD) techniques have become more established within the field of computational chemistry. Yet, for the prediction of infrared (IR) and Raman spectra of nanostructured materials, their usage has been less explored and remain restricted to some isolated successes. Therefore, it is currently not a priori clear which methodology should be used to accurately predict vibrational spectra for a given system. A comprehensive comparative study between various theoretical methods and experimental spectra for a broad set of nanostructured materials is so far lacking. To fill this gap, we herein present a concise overview on which methodology is suited to accurately predict vibrational spectra for a broad range of nanostructured materials and formulate a series of theoretical guidelines to this purpose. To this end, four different case studies are considered, each treating a particular material aspect, namely breathing in flexible MOFs, characterization of defects in the rigid MOF UiO-66, anharmonic vibrations in the metal-halide perovskite CsPbBr3, and guest adsorption on the pores of the zeolite H-SSZ-13. For all four materials, in their guest- and defect-free state and at sufficiently low temperatures, both the static and dynamic approach yield qualitatively similar spectra in agreement with experimental results. When the temperature is increased, the harmonic approximation starts to fail for CsPbBr3 due to the presence of anharmonic phonon modes. Also, the spectroscopic fingerprints of defects and guest species are insufficiently well predicted by a simple harmonic model. Both phenomena flatten the potential energy surface (PES), which facilitates the transitions between metastable states, necessitating dynamic sampling. On the basis of the four case studies treated in this Review, we can propose the following theoretical guidelines to simulate accurate vibrational spectra of functional solid-state materials: (i) For nanostructured crystalline framework materials at low temperature, insights into the lattice dynamics can be obtained using a static approach relying on a few points on the PES and an independent set of harmonic oscillators. (ii) When the material is evaluated at higher temperatures or when additional complexity enters the system, e.g., strong anharmonicity, defects, or guest species, the harmonic regime breaks down and dynamic sampling is required for a correct prediction of the phonon spectrum. These guidelines and their illustrations for prototype material classes can help experimental and theoretical researchers to enhance the knowledge obtained from a lattice dynamics study.

First-Principles Calculations of Excited-State Decay Rate Constants in Organic Fluorophores

In this Perspective, we discuss recent advances made to evaluate from first-principles the excited-state decay rate constants of organic fluorophores, focusing on the so-called static strategy. In this strategy, one essentially takes advantage of Fermi's golden rule (FGR) to evaluate rate constants at key points of the potential energy surfaces, a procedure that can be refined in a variety of ways. In this way, the radiative rate constant can be straightforwardly obtained by integrating the fluorescence line shape, itself determined from vibronic calculations. Likewise, FGR allows for a consistent calculation of the internal conversion (related to the non-adiabatic couplings) in the weak-coupling regime and intersystem crossing rates, therefore giving access to estimates of the emission yields when no complex photophysical phenomenon is at play. Beyond outlining the underlying theories, we summarize here the results of benchmarks performed for various types of rates, highlighting that both the quality of the vibronic calculations and the accuracy of the relative energies are crucial to reaching semiquantitative estimates. Finally, we illustrate the successes and challenges in determining the fluorescence quantum yields using a series of organic fluorophores.

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.

Efficient time-dependent vibrational coupled cluster computations with time-dependent basis sets at the two-mode coupling level: Full and hybrid TDMVCC[2]

The computation of the nuclear quantum dynamics of molecules is challenging, requiring both accuracy and efficiency to be applicable to systems of interest. Recently, theories have been developed for employing time-dependent basis functions (denoted modals) with vibrational coupled cluster theory (TDMVCC). The TDMVCC method was introduced along with a pilot implementation, which illustrated good accuracy in benchmark computations. In this paper, we report an efficient implementation of TDMVCC, covering the case where the wave function and Hamiltonian contain up to two-mode couplings. After a careful regrouping of terms, the wave function can be propagated with a cubic computational scaling with respect to the number of degrees of freedom. We discuss the use of a restricted set of active one-mode basis functions for each mode, as well as two interesting limits: (i) the use of a full active basis where the variational modal determination amounts essentially to the variational determination of a time-dependent reference state for the cluster expansion; and (ii) the use of a single function as an active basis for some degrees of freedom. The latter case defines a hybrid TDMVCC/TDH (time-dependent Hartree) approach that can obtain even lower computational scaling. The resulting computational scaling for hybrid and full TDMVCC[2] is illustrated for polyaromatic hydrocarbons with up to 264 modes. Finally, computations on the internal vibrational redistribution of benzoic acid (39 modes) are used to show the faster convergence of TDMVCC/TDH hybrid computations towards TDMVCC compared to simple neglect of some degrees of freedom.

Vibrational heat-bath configuration interaction with semistochastic perturbation theory using harmonic oscillator or VSCF modals

Vibrational heat-bath configuration interaction (VHCI)-a selected configuration interaction technique for vibrational structure theory-has recently been developed in two independent works [J. H. Fetherolf and T. C. Berkelbach, J. Chem. Phys. 154, 074104 (2021); A. U. Bhatty and K. R. Brorsen, Mol. Phys. 119, e1936250 (2021)], where it was shown to provide accuracy on par with the most accurate vibrational structure methods with a low computational cost. Here, we eliminate the memory bottleneck of the second-order perturbation theory correction using the same (semi)stochastic approach developed previously for electronic structure theory. This allows us to treat, in an unbiased manner, much larger perturbative spaces, which are necessary for high accuracy in large systems. Stochastic errors are easily controlled to be less than 1 cm-1. We also report two other developments: (i) we propose a new heat-bath criterion and an associated exact implicit sorting algorithm for potential energy surfaces expressible as a sum of products of one-dimensional potentials; (ii) we formulate VHCI to use a vibrational self-consistent field (VSCF) reference, as opposed to the harmonic oscillator reference configuration used in previous reports. Our tests are done with quartic and sextic force fields, for which we find that with VSCF, the minor improvements to accuracy are outweighed by the higher computational cost associated the matrix element evaluations. We expect VSCF-based VHCI to be important for more general potential representations, for which the harmonic oscillator basis function integrals are no longer analytic.

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.

Finite-temperature many-body perturbation theory for anharmonic vibrations: Recursions, algebraic reduction, second-quantized reduction, diagrammatic rules, linked-diagram theorem, finite-temperature self-consistent field, and general-order algorithm

A unified theory is presented for finite-temperature many-body perturbation expansions of the anharmonic vibrational contributions to thermodynamic functions, i.e., the free energy, internal energy, and entropy. The theory is diagrammatically size-consistent at any order, as ensured by the linked-diagram theorem proved in this study, and, thus, applicable to molecular gases and solids on an equal footing. It is also a basis-set-free formalism, just like its underlying Bose-Einstein theory, capable of summing anharmonic effects over an infinite number of states analytically. It is formulated by the Rayleigh-Schrödinger-style recursions, generating sum-over-states formulas for the perturbation series, which unambiguously converges at the finite-temperature vibrational full-configuration-interaction limits. Two strategies are introduced to reduce these sum-over-states formulas into compact sum-over-modes analytical formulas. One is a purely algebraic method that factorizes each many-mode thermal average into a product of one-mode thermal averages, which are then evaluated by the thermal Born-Huang rules. Canonical forms of these rules are proposed, dramatically expediting the reduction process. The other is finite-temperature normal-ordered second quantization, which is fully developed in this study, including a proof of thermal Wick's theorem and the derivation of a normal-ordered vibrational Hamiltonian at finite temperature. The latter naturally defines a finite-temperature extension of size-extensive vibrational self-consistent field theory. These reduced formulas can be represented graphically as Feynman diagrams with resolvent lines, which include anomalous and renormalization diagrams. Two order-by-order and one general-order algorithms of computing these perturbation corrections are implemented and applied up to the eighth order. The results show no signs of Kohn-Luttinger-type nonconvergence.

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.

An approximation to the vibrational coupled-cluster method for CH-stretching of large molecules: application to naphthalene and anthracene

We propose an approximation to the vibrational coupled-cluster method (VCCM) to describe the CH-stretching region of the vibrational spectrum of large molecules. The vibrational modes of a molecule are divided into two sets: the target set and the bath set. The target set includes the CH stretches and the modes that are strongly coupled with the CH stretches and/or involve strong Fermi resonances with a CH stretch fundamental. The rest of the modes are in the bath set. First, the effective harmonic oscillator (EHO) approximation is invoked for the whole system to obtain the zeroth-order frequencies and modified potentials. The effects of interaction between the bath set and the target sets are included in the modified potential from the EHO calculation. The VCCM equations are constructed with the modified potential from the EHO calculations and for the target set only. The transition energies and intensities are calculated using such a truncated VCCM approximation. The proposed method is applied to calculate the IR spectra of naphthalene and anthracene. The results with three different criteria for selecting the modes in the target set are compared with the experimental IR spectra.

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.

Quantum chemical rovibrational analysis of aminoborane and its isotopologues

Aminoborane, H₂ NBH₂ and its isotopologues, H₂ N¹⁰ BH₂ , D₂ NBD₂ , and D₂ N¹⁰ BD₂ , have been studied by high-level ab initio methods. All calculations rely on multidimensional potential energy surfaces and dipole moment surfaces including high-order mode coupling terms, which have been obtained from electronic structure calculations at the level of explicitly correlated coupled-cluster theory, CCSD(T)-F12, or the distinguishable cluster approximation, DCSD. Subsequent vibrational structure calculations based on second-order vibrational perturbation theory, VPT2, and vibrational configuration interaction theory, VCI, were used to determine rotational constants, centrifugal distortion constants, vibrationally averaged geometrical parameters and (an)harmonic vibrational frequencies. The impact of core-correlation effects is discussed in detail. Rovibrational VCI calculations were used to simulate the gas phase spectra of these species and an in-depth analysis of the ν₇ band of aminoborane is provided. Color-coding is used to reveal the identity of the individual progressions of the rovibrational transitions for this particular mode.

Perturb-Then-Diagonalize Vibrational Engine Exploiting Curvilinear Internal Coordinates

The present paper is devoted to the implementation and validation of a second-order perturbative approach to anharmonic vibrations, followed by variational treatment of strong couplings (GVPT2) based on curvilinear internal coordinates. The main difference with respect to the customary Cartesian-based formulation is that the kinetic energy operator is no longer diagonal, and has to be expanded as well, leading to additional terms which have to be taken into proper account. It is, however, possible to recast all the equations as well-defined generalizations of the corresponding Cartesian-based counterparts, thus achieving a remarkable simplification of the new implementation. Particular attention is paid to the treatment of Fermi resonances with significant number of test cases analyzed fully, validating the new implementation. The results obtained in this work confirm that curvilinear coordinates strongly reduce the strength of inter-mode couplings compared to their Cartesian counterparts. This increases the reliability of low-order perturbative treatments for semi-rigid molecules and paves the way toward the reliable representation of more flexible molecules where small- and large-amplitude motions can be safely decoupled and treated at different levels of theory.

Comparative Analysis of Uncoupled Mode Approximations for Molecular Thermochemistry and Kinetics

The accurate prediction of thermochemistry and kinetic parameters is an important task for reaction modeling. Unfortunately, the commonly used harmonic oscillator model is often not accurate enough due to the absence of anharmonic effects. In this work, we improve the representation of an anharmonic potential energy surface (PES) using uncoupled mode (UM) approximations, which model the full-dimensional PES as a sum of one-dimensional potentials of each mode. We systematically analyze different PES sampling schemes and coordinate systems for constructing the one-dimensional potentials, and benchmark the performance of UM methods on data sets of molecular thermochemistry and kinetic properties. The results show that the accuracy of the UM approach strongly depends on how the one-dimensional potentials are defined. If one-dimensional potentials are constructed by sampling along normal mode directions (UM-N) or along the directions that minimize intermode coupling (E- and E'-optimized), the accuracies of the predicted properties are not significantly improved compared to the harmonic oscillator model. However, significant improvements can be achieved by sampling the torsional modes separately from the vibrational modes (UM-T and UM-VT). In this work, three types of coordinate systems are examined, including redundant internal coordinates (RIC), hybrid internal coordinates (HIC), and translation-rotation-internal coordinates (TRIC). The HIC and TRIC coordinate systems can outperform RIC since transition state species may contain large-amplitude interfragmentary motions that regular internal coordinates can not describe adequately. Among all the methods we examined, the activation energies and pre-exponential factors calculated using UM-VT with either TRIC or HIC best agree with the reference values. Since UM-VT requires only a number of additional single point energy calculations for each independent mode, the scaling of computational costs of UM-VT is the same as that of the standard harmonic oscillator model, making UM-VT an appealing way of calculating the thermochemistry and kinetic properties for large-size systems.

Calculation of absolute Raman scattering cross-sections using vibrational self-consistent field/vibrational configuration interaction wave functions

In the present study, the differential scattering cross-sections, depolarization ratios and Raman shifts of small molecular systems are obtained from configuration iteration wave functions of vibrational self-consistent field (VSCF) states. The transition polarizabilities were modeled using the Placzek approximation, neglecting those contributions not arising from the electric dipole mechanism. This theoretical approach is considered a good approximation for samples that absorb in the UV range if the excitation radiation falls in the visible region, as is the case of the molecules selected for the present study, namely: water, methane, and acetylene. Potential energy and electronic polarizability surfaces are calculated by the CCSD(T) and CC3 methods with aug-cc-p(C)V(T,Q,5)Z basis sets. The vibrational Hamiltonian includes the vibrational angular momentum contribution of the Watson kinetic energy operator. As expected, due to the variational nature of the VSCF and vibrational configuration interaction (VCI) methods, the Raman transition wavenumbers are substantially improved over the harmonic predictions. Surprisingly, the scattering cross-sections obtained using the harmonic approximation or the VSCF method better agrees with the experimental values than those cross-sections predicted using VCI wave functions. The more significant deviations of the VCI results from the experimental reference may be related to the significant uncertainties of the measured cross-sections. Still, it may also indicate that the VCI Raman transition moments may require a more accurate description of the electronic polarizability surface. Finally, the depolarization ratios calculated for H₂ O and C₂ D₂ using harmonic and VCI wave functions have similar accuracy, whereas, for C₂ H₂ and C₂ HD, the VCI results are more accurate.

Tailored anharmonic-harmonic vibrational profiles for fluorescent biomarkers

We propose a hybrid anharmonic-harmonic scheme for vibrational broadenings, which embeds a reduced-space vibrational configuration interaction (VCI) anharmonic wave function treatment in the independent-mode displaced harmonic oscillator (IMDHO) model. The resulting systematically-improvable VCI-in-IMDHO model allows including the vibronic effects of all vibrational degrees of freedom, while focusing the effort on the important degrees of freedom with minimal extra computational effort compared to a reduced-space VCI treatment. We show for oligothiophene examples that the VCI-in-IMDHO approach can yield accurate vibrational profiles employing smaller vibrational spaces in the VCI part than the reduced-space VCI approach. By this, the VCI-in-IMDHO model enables accurate calculation of vibrational profiles of common fluorescent dyes with more than 100 vibrational degrees of freedom. We illustrate this for three examples of fluorescent biomarkers of current interest. These are the oligothiophene-based fluorescent dye called HS84, 1,4-diphenylbutadiene, and an anthracene diimide. For all examples, we assess the impact of the anharmonic treatment on the vibrational broadening, which we find to be more pronounced for the intensities than for the peak positions.

Polaritonic effects in the vibronic spectrum of molecules in an optical cavity

We present a new computational framework to describe polaritons, which treats photons and electrons on the same footing using coupled-cluster theory. As a proof of concept, we study the coupling between the first electronically excited state of carbon monoxide and an optical cavity. We focus, in particular, on how the interaction with the photonic mode changes the vibrational spectroscopic signature of the electronic state, and how this is affected when tuning the cavity frequency and the light-matter coupling strength. For this purpose, we consider different methodologies and investigate the validity of the Born-Oppenheimer approximation in such situations.

A quantum computing view on unitary coupled cluster theory

We present a review of the Unitary Coupled Cluster (UCC) ansatz and related ansätze which are used to variationally solve the electronic structure problem on quantum computers. A brief history of coupled cluster (CC) methods is provided, followed by a broad discussion of the formulation of CC theory. This includes touching on the merits and difficulties of the method and several variants, UCC among them, in the classical context, to motivate their applications on quantum computers. In the core of the text, the UCC ansatz and its implementation on a quantum computer are discussed at length, in addition to a discussion on several derived and related ansätze specific to quantum computing. The review concludes with a unified perspective on the discussed ansätze, attempting to bring them under a common framework, as well as with a reflection upon open problems within the field.

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 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.

Coupled Anharmonic Thermochemistry from Stratified Monte Carlo Integration

This study presents configuration integral Monte Carlo integration (CIMCI), a new semiclassical method for handling fully coupled anharmonicity in gas-phase thermodynamics that promises to be black boxable, to be applicable to all kinds of anharmonicity, and to scale better at higher dimensionality than other methods for handling gas-phase molecular anharmonicity. The method does so using automatically and recursively stratified, simultaneous Monte Carlo (MC) integration of multiple functions, following a modified version of the standard MISER scheme that converges at a rate of about the square of naïve MC integration. For the small systems analyzed by this study where proper reference data is available (H₂O and H₂O₂), the method's anharmonic entropy corrections match reference data better than those of other black box anharmonic methods, e.g., vibrational perturbation theory (VPT2) and the McClurg hindered rotor model used with automatic detection of rotors; for H₂O₂ and NH₂OH, the method is also in general agreement with one-dimensional hindered rotor treatments at low temperatures. This holds even when sampling with CIMCI is done with primitive force fields, e.g., UFF, while the competing methods are used with proper, comprehensive potentials, e.g., the M06-2X metahybrid density-functional theory (DFT) functional.

Multicomponent heat-bath configuration interaction with the perturbative correction for the calculation of protonic excited states

In this study, we extend the multicomponent heat-bath configuration interaction (HCI) method to excited states. Previous multicomponent HCI studies have been performed using only the variational stage of the HCI algorithm as they have largely focused on the calculation of protonic densities. Because this study focuses on energetic quantities, a second-order perturbative correction after the variational stage is essential. Therefore, this study implements the second-order Epstein-Nesbet correction to the variational stage of multicomponent HCI for the first time. Additionally, this study introduces a new procedure for calculating reference excitation energies for multicomponent methods using the Fourier-grid Hamiltonian (FGH) method, which should allow the one-particle electronic basis set errors to be better isolated from errors arising from an incomplete description of electron-proton correlation. The excited-state multicomponent HCI method is benchmarked by computing protonic excitations of the HCN and FHF^- molecules and is shown to be of similar accuracy to previous excited-state multicomponent methods such as the multicomponent time-dependent density-functional theory and equation-of-motion coupled-cluster theory relative to the new FGH reference values.

General Perturb-Then-Diagonalize Model for the Vibrational Frequencies and Intensities of Molecules Belonging to Abelian and Non-Abelian Symmetry Groups

In this paper, we show that the standard second-order vibrational perturbation theory (VPT2) for Abelian groups can be used also for non-Abelian groups without employing specific equations for two- or threefold degenerate vibrations but rather handling in the proper way all the degeneracy issues and deriving the peculiar spectroscopic signatures of non-Abelian groups (e.g., l -doubling) by a posteriori transformations of the eigenfunctions. Comparison with the results of previous conventional implementations shows a perfect agreement for the vibrational energies of linear and symmetric tops, thus paving the route to the transparent extension of the equations already available for asymmetric tops to the energies of spherical tops and the infrared and Raman intensities of molecules belonging to non-Abelian symmetry groups. The whole procedure has been implemented in our general engine for vibro-rotational computations beyond the rigid rotor/harmonic oscillator model and has been validated on a number of test cases.

Reduced Two-Electron Interactions in Anharmonic Molecular Vibrational Calculations Involving Localized Normal Coordinates

Spatially localized vibrational normal mode coordinates are shown to reduce the importance of calculating the full set of two-electron terms in the molecular electronic Schrödinger equation. Electron correlation and dispersion interactions become less significant in (E,E)-1,3,5,7-octatetraene vibrational self-consistent field calculations when displacing remote atoms along multiple coordinates. Electron correlation interactions between spatially remote modes are also found to be less important compared to their corresponding uncorrelated interaction terms. Attenuation of the Coulomb operator indicates that the two-electron terms between remote electrons become less important for accurately describing the strongly contributing mode-coupling terms between sets of localized vibrational modes.

Understanding of the C-H stretch region of infra-red spectroscopy: an analysis of the final state wavefunctions

The nature of the wavefunctions associated with the final states in the CH stretching region of several medium sized molecules is analysed. The number of optically bright transitions is much larger than the number of CH oscillators present in the molecule, and they are spread over a range of about 300 cm^-1. Several of them are clustered together within about 5 cm^-1 with near equal intensities. The final states of all these transitions are superpositions of multiple zeroth order states. In almost all of such superpositions, no single zeroth order state has more than 50% weight. Several multiquantum states, with three to four quanta of excitation dominate the final states, with the CH chromophore contributing only a small weightage. Thus the band structure of the CH stretch region is due to several optically bright transitions whose final states are superpositions of low frequency multiquantum states with the CH chromophore contributing only a small weight to make them spectroscopically active.

My Trajectory in Molecular Reaction Dynamics and Spectroscopy

This is the story of a career in theoretical chemistry during a time of dramatic changes in the field due to phenomenal growth in the availability of computational power. It is likewise the story of the highly gifted graduate students and postdoctoral fellows that I was fortunate to mentor throughout my career. It includes reminiscences of the great mentors that I had and of the exciting collaborations with both experimentalists and theorists on which I built much of my research. This is an account of the developments of exciting scientific disciplines in which I was involved: vibrational spectroscopy, molecular reaction mechanisms and dynamics, e.g., in atmospheric chemistry, and the prediction of new, exotic molecules, in particular noble gas molecules. From my very first project to my current work, my career in science has brought me the excitement and fascination of research. What a wonderful pursuit!

Vibrational heat-bath configuration interaction

We introduce vibrational heat-bath configuration interaction (VHCI) as an accurate and efficient method for calculating vibrational eigenstates of anharmonic systems. Inspired by its origin in electronic structure theory, VHCI is a selected CI approach that uses a simple criterion to identify important basis states with a pre-sorted list of anharmonic force constants. Screened second-order perturbation theory and simple extrapolation techniques provide significant improvements to variational energy estimates. We benchmark VHCI on four molecules with 12-48 degrees of freedom and use anharmonic potential energy surfaces truncated at fourth and sixth orders. When compared to other methods using the same truncated potentials, VHCI produces vibrational spectra of tens or hundreds of states with sub-wavenumber accuracy at low computational cost.

A general implementation of time-dependent vibrational coupled-cluster theory

The first general excitation level implementation of the time-dependent vibrational coupled cluster (TDVCC) method introduced in a recent publication [J. Chem. Phys. 151, 154116 (2019)] is presented. The general framework developed for time-independent vibrational coupled cluster (VCC) calculations has been extended to the time-dependent context. This results in an efficient implementation of TDVCC with general coupling levels in the cluster operator and Hamiltonian. Thus, the convergence of the TDVCC[k] hierarchy toward the complete-space limit can be studied for any sum-of-product Hamiltonian. Furthermore, a scheme for including selected higher-order excitations for a subset of modes is introduced and studied numerically. Three different definitions of the TDVCC autocorrelation function (ACF) are introduced and analyzed in both theory and numerical experiments. Example calculations are presented for an array of systems including imidazole, formyl fluoride, formaldehyde, and a reduced-dimensionality bithiophene model. The results show that the TDVCC[k] hierarchy converges systematically toward the full-TDVCC limit and that the implementation allows accurate quantum-dynamics simulations of large systems to be performed. Specifically, the intramolecular vibrational-energy redistribution of the 21-dimensional imidazole molecule is studied in terms of the decay of the ACF. Furthermore, the importance of product separability in the definition of the ACF is highlighted when studying non-interacting subsystems.

Anharmonic Phonon Dispersion in Polyethylene

The second-order Green's function method for anharmonic crystals has been applied to an infinite, periodic chain of polyethylene taking into account up to quartic force constants. The frequency-independent approximation to the Dyson self-energy gives rise to numerous divergent resonances, which are fortuitous. Instead, solving the Dyson equation self-consistently with a frequency-dependent self-energy resists divergences from resonances or zero-frequency acoustic vibrations. The calculated anharmonic phonon dispersion, which nonetheless displays many true resonances, and anharmonic phonon density of states furnish hitherto unknown details that explain smaller features of observed vibrational spectra.

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.