Multiresolution potential energy surfaces for vibrational state calculations

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.

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.

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.

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.

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.

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.

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.

Matrix Product State Formulation of the MCTDH Theory in Local Mode Representations for Anharmonic Potentials

The matrix product state formulation of the multiconfiguration time-dependent Hartree theory, MPS-MCTDH, reported previously [Kurashige, J. Chem. Phys. 2018, 19, 194114] is extended to realistic anharmonic potentials with n-mode representations beyond the linear vibronic coupling model. For realistic vibrational potentials, the local mode representation should give a more compact representation of the potentials, i.e., lowering the dimensionality of the entanglements, than the normal coordinates, and the MPS-MCTDH formulation should work more efficiently and maintain the accuracy with a small bond dimension of the MPS ansatz. In fact, it was confirmed that the use of the local coordinates made the interaction matrices diagonal dominant and the number of terms in the n-body expansion of the potentials was significantly reduced. The method was applied to the IR spectrum of the CH₂O molecule, the zero-point energies, and the vibrational energy redistribution dynamics of polyenes C_2nH_2n+2. The results showed that the efficiency of the MPS-MCTDH method is significantly accelerated by the use of local coordinates even if the long-range interactions are included in the potential.

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.

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

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

Efficient and Automated Quantum Chemical Calculation of Rovibrational Nonresonant Raman Spectra

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

Advances in vibrational configuration interaction theory - part 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.

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⁺.

Towards complete assignment of the infrared spectrum of the protonated water cluster H+(H2O)21

The spectroscopic features of protonated water species in dilute acid solutions have been long sought after for understanding the microscopic behavior of the proton in water with gas-phase water clusters H⁺(H₂O)_n extensively studied as bottom-up model systems. We present a new protocol for the calculation of the infrared (IR) spectra of complex systems, which combines the fragment-based Coupled Cluster method and anharmonic vibrational quasi-degenerate perturbation theory, and demonstrate its accuracy towards the complete and accurate assignment of the IR spectrum of the H⁺(H₂O)₂₁ cluster. The site-specific IR spectral signatures reveal two distinct structures for the internal and surface four-coordinated water molecules, which are ice-like and liquid-like, respectively. The effect of inter-molecular interaction between water molecules is addressed, and the vibrational resonance is found between the O-H stretching fundamental and the bending overtone of the nearest neighboring water molecule. The revelation of the spectral signature of the excess proton offers deeper insight into the nature of charge accommodation in the extended hydrogen-bonding network underpinning this aqueous cluster.

Protonated water species have been the subject of numerous experimental and computational studies. Here the authors provide a nearly complete assignment of the experimental IR spectrum of the H⁺(H₂O)₂₁ water cluster based on high-level wavefunction theory and anharmonic vibrational quasi-degenerate perturbation theory.

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.

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.

High-Level Rovibrational Calculations on Ketenimine

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

On the separability of large-amplitude motions in anharmonic frequency calculations

Nuclear vibrational theories based upon the Watson Hamiltonian are ubiquitous in quantum chemistry, but are generally unable to model systems in which the wavefunction can delocalise over multiple energy minima, i.e. molecules that have low-energy torsion and inversion barriers. In a 2019 Chemical Reviews article, Puzzarini et al. note that a common workaround is to simply decouple these problematic modes from all other vibrations in the system during anharmonic frequency calculations. They also point out that this approximation can be "ill-suited", but do not quantify the errors introduced. In this work, we present the first systematic investigation into how separating out or constraining torsion and inversion vibrations within potential energy surface (PES) expansions affects the accuracy of computed fundamental wavenumbers for the remaining vibrational modes, using a test set of 19 tetratomic molecules for which high quality analytic potential energy surfaces and fully-coupled anharmonic reference fundamental frequencies are available. We find that the most effective and efficient strategy is to remove the mode in question from the PES expansion entirely. This introduces errors of up to +10 cm-1 in stretching fundamentals that would otherwise couple to the dropped mode, and ±5 cm-1 in all other fundamentals. These errors are approximately commensurate with, but not necessarily additional to, errors due to the choice of electronic structure model used in constructing spectroscopically accurate PES.

Adaptive density-guided approach to double incremental potential energy surface construction

We present a combination of the recently developed double incremental expansion of potential energy surfaces with the well-established adaptive density-guided approach to grid construction. This unique methodology is based on the use of an incremental expansion for potential energy surfaces, known as n-mode expansion; an incremental many-body representation of the electronic energy; and an efficient vibrational density-guided approach to automated determination of grid dimensions and granularity. The reliability of the method is validated calculating potential energy surfaces and obtaining fundamental excitation energies for three moderate-size chain-like molecular systems. The use of our methodology leads to considerable computational savings for potential energy surface construction compared to standard approaches while maintaining a high level of accuracy in the resulting potential energy surfaces. Additional investigations indicate that our method can be applied to covalently bound and strongly interacting molecular systems, even though these cases are known to be very unfavorable for fragmentation schemes. We therefore conclude that the presented methodology is a robust and flexible approach to potential energy surface construction, which introduces considerable computational savings without compromising the accuracy of vibrational spectra calculations.

The Molpro quantum chemistry package

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

Anharmonic Vibrational Analysis of Biomolecules and Solvated Molecules Using Hybrid QM/MM Computations

Quantum mechanics/molecular mechanics (QM/MM) calculations are applied for anharmonic vibrational analyses of biomolecules and solvated molecules. The QM/MM method is implemented into a molecular dynamics (MD) program, GENESIS, by interfacing with external electronic structure programs. Following the geometry optimization and the harmonic normal-mode analysis based on a partial Hessian, the anharmonic potential energy surface (PES) is generated from QM/MM energies and gradients calculated at grid points. The PES is used for vibrational self-consistent field (VSCF) and post-VSCF calculations to compute the vibrational spectrum. The method is first applied to a phosphate ion in solution. With both the ion and neighboring water molecules taken as a QM region, IR spectra of representative hydration structures are calculated by the second-order vibrational quasi-degenerate perturbation theory (VQDPT2) at the level of B3LYP/cc-pVTZ and TIP3P force field. A weight-average of IR spectra over the structures reproduces the experimental spectrum with a mean absolute deviation of 16 cm^–1. Then, the method is applied to an enzyme, P450 nitric oxide reductase (P450nor), with the NO molecule bound to a ferric (Fe^III) heme. Starting from snapshot structures obtained from MD simulations of P450nor in solution, QM/MM calculations have been carried out at the level of B3LYP-D3/def2-SVP(D). The spin state of Fe^III(NO) is likely a closed-shell singlet state based on a ratio of N–O and Fe–NO stretching frequencies (ν_N–O and ν_Fe–NO) calculated for closed- and open-shell singlet states. The calculated ν_N–O and ν_Fe–NO overestimate the experimental ones by 120 and 75 cm^–1, respectively. The electronic structure and solvation of Fe^III(NO) affect the structure around the heme of P450nor leading to an increase in ν_N–O and ν_Fe–NO.

Effects of intermolecular interactions on absorption intensities of the fundamental and the first, second, and third overtones of OH stretching vibrations of methanol and t-butanol‑d9 in n-hexane studied by visible/near-infrared/infrared spectroscopy

Visible (Vis), near-infrared (NIR) and IR spectra in the 15,600-2500cm^-1 region were measured for methanol, methanol-d₃, and t-butanol-d₉ in n-hexane to investigate effects of intermolecular interaction on absorption intensities of the fundamental and the first, second, and third overtones of their OH stretching vibrations. The relative area intensities of OH stretching bands of free and hydrogen-bonded species were plotted versus the vibrational quantum number using logarithm plots (V=1-4) for 0.5M methanol, 0.5M methanol‑d₃, and 0.5M t-butanol-d₉ in n-hexane. In the logarithm plots the relative intensities of free species yield a linear dependence irrespective of the solutes while those of hydrogen-bonded species deviate significantly from the linearity. The observed results suggest that the modifications in dipole moment functions of the OH bond induced by the formation of the hydrogen bondings change transient dipole moment, leading to the deviations of the dependences of relative absorption intensities on the vibrational quantum number from the linearity.

Anharmonic vibrational spectra from double incremental potential energy and dipole surfaces

Using incremental approaches, size limitations for property surface generations are pushed significantly, enabling accurate large molecule anharmonic vibrational spectra calculations.

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

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

Pushing the limits in accurate vibrational structure calculations: anharmonic frequencies of lithium fluoride clusters (LiF)n, n = 2-10

The vibrational spectra of a series of small lithium fluoride clusters, i.e. (LiF)n, n = 2-10, were studied by vibrational configuration interaction (VCI) calculations relying on potential energy surfaces including three-mode coupling terms and being obtained from explicitly correlated local coupled cluster calculations. Due to the account for anharmonicity effects, the simulated spectra allow for a direct comparison with experimental data and may thus help to identify clusters in the experiments. Even structurally closely related clusters can clearly be distinguished by infrared spectroscopy. The largest system in this study required more than 1000 basis functions in the electronic structure calculations and more than 10(7) configurations in the vibrational structure calculations and became computationally feasible only due to a combination of different approximations and highly parallelized algorithms.