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

Hardware efficient quantum algorithms for vibrational structure calculations

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

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.

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

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

The Molpro quantum chemistry package

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

Using computed infrared intensities for the reduction of vibrational configuration interaction bases

The Adaptive Vibrational Configuration Interaction (A-VCI) algorithm is an iterative process that computes the anharmonic spectrum of a molecule using nested bases to discretize the Hamiltonian operator. For large molecular systems, the size of the discretization space and the computation time quickly become prohibitive. It is therefore necessary to develop new methods to further limit the number of basis functions. Most of the time, the interpretation of an experimental infrared spectrum does not require the calculation of all eigenvalues but only those corresponding to vibrational states with significant intensity. In this paper, a technique that uses infrared intensities is introduced to select a subset of eigenvalues to be precisely calculated. Thus, we build smaller nested bases and reduce both the memory footprint and the computational time. We validate the advantages of this new approach on a well-studied 7-atom molecular system (C2H4O), and we apply it on a larger 10-atom molecule (C4H4N2).

Characterizing structures, energetics, and spectra of species on the 1,3[H, C, As] potential energy surfaces: A high-level theoretical contribution

The ground and the low lying electronic states of structures on the ^1,3[H, C, As] potential energy surfaces were investigated with the highly correlated theoretical approaches CCSD(T), CCSD(T)-F12b, and CASSCF/MRCI along with the series of correlation consistent (aug-cc-pVnZ, n = D, T, Q, 5) basis sets. Energetic and spectroscopic parameters were obtained at the complete basis set limit, and the effect of core-valence correlation on these properties evaluated. Fundamental frequencies were also computed with the variational configuration interaction (VCI) approach. Heats of formation at 0 and 298.15 K were estimated for HCAs and CH, AsH, CAs, and HCAs, as well as the calculation of ionization potentials for HCAs. Comparisons of the present results with literature ones for the systems HCN/HNC, HCP/HPC highlight similarities and differences among these systems. Altogether, this investigation provides a very reliable characterization of the species on the surfaces and should guide future experimental studies on these systems.

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

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

Towards theoretical spectroscopy with error bars: systematic quantification of the structural sensitivity of calculated spectra

Molecular spectra calculated with quantum-chemical methods are subject to a number of uncertainties (e.g., errors introduced by the computational methodology) that hamper the direct comparison of experiment and computation. Judging these uncertainties is crucial for drawing reliable conclusions from the interplay of experimental and theoretical spectroscopy, but largely relies on subjective judgment. Here, we explore the application of methods from uncertainty quantification to theoretical spectroscopy, with the ultimate goal of providing systematic error bars for calculated spectra. As a first target, we consider distortions of the underlying molecular structure as one important source of uncertainty. We show that by performing a principal component analysis, the most influential collective distortions can be identified, which allows for the construction of surrogate models that are amenable to a statistical analysis of the propagation of uncertainties in the molecular structure to uncertainties in the calculated spectrum. This is applied to the calculation of X-ray emission spectra of iron carbonyl complexes, of the electronic excitation spectrum of a coumarin dye, and of the infrared spectrum of alanine. We show that with our approach it becomes possible to obtain error bars for calculated spectra that account for uncertainties in the molecular structure. This is an important first step towards systematically quantifying other relevant sources of uncertainty in theoretical spectroscopy.

Uncertainty quantification is applied in theoretical spectroscopy to obtain error bars accounting for the structural sensitivity of calculated spectra.

Toward Elimination of Discrepancies between Theory and Experiment: Anharmonic Rotational-Vibrational Spectrum of Water in Solid Noble Gas Matrices

Rotational–vibrational spectroscopy of water in solid noble gas matrices has been studied for many decades. Despite that, discrepancies persist in the literature about the assignment of specific bands. We tackle the involved rotational–vibrational spectrum of the water isotopologues H₂¹⁶O, HD¹⁶O, and D₂¹⁶O with an unprecedented combination of experimental high-resolution matrix isolation infrared (MI-IR) spectroscopy and computational anharmonic vibrational spectroscopy by vibrational configuration interaction (VCI) on high-level ab initio potential energy surfaces. With VCI, the average deviation to gas-phase experiments is reduced from >100 to ≈1 cm^–1 when compared to harmonic vibrational spectra. Discrepancies between MI-IR and VCI spectra are identified as matrix effects rather than missing anharmonicity in the theoretical approach. Matrix effects are small in Ne (≈1.5 cm^–1) and a bit larger in Ar (≈10 cm^–1). Controversial assignments in Ne MI-IR spectra are resolved, for example, concerning the ν₃ triad in HDO. We identify new transitions, for example, the ν₂ 1₀₁ ← 1₁₀ transition in D₂O and H₂O or the ν₃ 0₀₀ ← 1₀₁ transition in D₂O, and reassign bands, for example, the band at 3718.9 cm^–1 that is newly assigned as the 1₁₀ ← 1₁₁ transition. The identification and solution of discrepancies for a well-studied benchmark system such as water prove the importance of an iterative and one-hand combination of theory and experiment in the field of high-resolution infrared spectroscopy of single molecules. As the computational costs involved in the VCI approach are reasonably low, such combined experimental/theoretical studies can be extended to molecules larger than triatomics.

Specific Reaction Parameter Multigrid POTFIT (SRP-MGPF): Automatic Generation of Sum-of-Products Form Potential Energy Surfaces for Quantum Dynamical Calculations

We present Specific Reaction Parameter Multigrid POTFIT (SRP-MGPF), an automated methodology for the generation of global potential energy surfaces (PES), molecular properties surfaces, e.g., dipole, polarizabilities, etc. using a single random geometry as input. The SRP-MGPF workflow integrates: (i) a fully automated procedure for the global topographical characterization of a (intermolecular) PES based on the Transition State Search Using Chemical Dynamical Simulations (TSSCDS) family of methods;i (ii) the global optimization of the parameters of a semiempirical Hamiltonian in order to reproduce a given level of electronic structure theory; and (iii) a tensor decomposition algorithm which turns the resulting SRP-PES into sum of products (Tucker) form with the Multigrid POTFIT algorithm. The latter is necessary for quantum dynamical studies within the Multiconfiguration Time-Dependent Hartree (MCTDH) quantum dynamics method. To demonstrate our approach, we have applied our methodology to the cis-trans isomerization reaction in HONO in full dimensionality (6D). The resulting SRP-PES has been validated through the computation of classical on-the-fly dynamical calculations as well as calculations of the lowest vibrational eigenstates of HONO as well as high-energy wavepacket propagations.

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

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

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.

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

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

M-S Multiple Bond in HMSH, H2MS, and HMS Molecules (M = B, Al, Ga): Matrix Infrared Spectra and Theoretical Calculations

Reaction products of B, Al, and Ga atoms with H₂S have been identified in solid argon using matrix isolation infrared absorption spectroscopy. The results show that the ground state B atom reaction with H₂S gives the H₂BS molecule while for the Al atom the HAlSH molecule forms first, which then further isomerizes to H₂AlS upon >500 nm irradiation. The reaction of the Ga atom with H₂S only takes place upon photolysis to produce HGaSH in the matrix. The assignments of the major modes for these products were confirmed by appropriate ¹⁰B, ¹¹B, D₂S, and H₂³⁴S isotopic shifts and theoretical frequency calculations. Topological analysis of the electron density suggests that both HBSH and H₂BS molecules possess covalent B-S bond with significant double bond character, while the M-S bond in the heavier group 13 homologues (Al, Ga) was characterized as a polar covalent strong interaction.

Intrinsic structure of pentapeptide Leu-enkephalin: geometry optimization and validation by comparison of VSCF-PT2 calculations with cold ion spectroscopy

The intrinsic structure of an opioid peptide [Ala2, Leu5]-leucine enkephalin (ALE) has been investigated using first-principles based vibrational self-consistent field (VSCF) theory and cold ion spectroscopy. IR-UV double resonance spectroscopy revealed the presence of only one highly abundant conformer of the singly protonated ALE, isolated and cryogenically cooled in the gas phase. High-level quantum mechanical calculations of electronic structures in conjunction with a systematic conformational search allowed for finding a few low-energy candidate structures. In order to identify the observed structure, we computed vibrational spectra of the candidate structures and employed the theory at the semi-empirically scaled harmonic level and at the first-principles based anharmonic VSCF levels. The best match between the calculated "anharmonic" and the measured spectra appeared, indeed, for the most stable candidate. An average of two spectra calculated with different quantum mechanical potentials is proposed for the best match with experiment. The match thus validates the calculated intrinsic structure of ALE and demonstrates the predictive power of first-principles theory for solving structures of such large molecules.

Probing vibrational coupling via a grid-based quantum approach-an efficient strategy for accurate calculations of localized normal modes in solid-state systems

In this work an approach to investigate the properties of strongly localized vibrational modes of functional groups in bulk material and on solid-state surfaces is presented. The associated normal mode vectors are approximated solely on the basis of structural information and obtained via diagonalization of a reduced Hessian. The grid-based Numerov procedure in one and two dimensions is then applied to an adequate scan of the respective potential surface yielding the associated vibrational wave functions and energy eigenvalues. This not only provides a detailed description of anharmonic effects but also an accurate inclusion of the coupling between the investigated vibrational states on a quantum mechanical level. All results obtained for the constructed normal modes are benchmarked against their analytical counterparts obtained from the diagonalization of the total Hessian of the entire system. Three increasingly complex systems treated at quantum chemical level of theory have been considered, namely the symmetric and asymmetric stretch vibrations of an isolated water molecule, hydroxyl groups bound to the surface of GeO2 (001), α-quartz(001) and Rutil (001) as well as crystalline Li2 NH serving as an example for a bulk material. While the data obtained for the individual systems verify the applicability of the proposed methodology, comparison to experimental data demonstrates the accuracy of this methodology despite the restriction to limit this methodology to a few selected vibrational modes. The possibility to investigate vibrational phenomena of localized normal modes without the requirement of executing costly harmonic frequency calculations of the entire system enables the application of this method to cases in which the determination of normal modes is prohibitively expensive or not available for a particular level of theory. © 2018 Wiley Periodicals, Inc.

Structural sensitivity of CH vibrational band in methyl benzoate

The CH vibrational bands of methyl benzoate are studied to understand its coupling pattern with other vibrational bands of the biological molecule. This will facilitate to understand the biological structure and dynamics in spectroscopic as well as in microscopic study. Due to the congested spectroscopic pattern, near degeneracy, and strong anharmonicity of the CH stretch vibrations, assignment of the CH vibrational frequencies are often misleading. Anharmonic vibrational frequency calculation with multidimensional potential energy surface interprets the CH vibrational spectra more accurately. In this article we have presented the importance of multidimensional potential energy surface in anharmonic vibrational frequency calculation and discuss the unexpected red shift of asymmetric CH stretch vibration of methyl group. The CD stretch vibrational band which is splitted to double peaks due to the Fermi resonance is also discussed here.

Oxygen radical character in group 11 oxygen fluorides

Transition metal complexes bearing terminal oxido ligands are quite common, yet group 11 terminal oxo complexes remain elusive. Here we show that excited coinage metal atoms M (M = Au, Ag, Cu) react with OF₂ to form hypofluorites FOMF and group 11 oxygen metal fluorides OMF₂, OAuF and OAgF. These compounds have been characterized by IR matrix-isolation spectroscopy in conjunction with state-of-the-art quantum-chemical calculations. The oxygen fluorides are formed by photolysis of the initially prepared hypofluorites. The linear molecules OAgF and OAuF have a ³Σ ⁻ ground state with a biradical character. Two unpaired electrons are located mainly at the oxygen ligand in antibonding O−M π* orbitals. For the ²B₂ ground state of the OM^IIIF₂ compounds only an O−M single bond arises and a significant spin-density contribution was found at the oxygen atom as well.

While transition metal complexes bearing terminal oxido ligands are common, those of group 11 elements have yet to be experimentally observed. Here, Riedel and colleagues synthesise molecular oxygen fluorides of copper, silver and gold, and show that the oxo ligands possess radical character.

Anomalous description of the anharmonicity of bending motions of carbon–carbon double bonded molecules with the MP2 method: ethylene as a case study

In this work, we report anomalous descriptions of bending modes of the smallest carbon–carbon double bonded molecule ethylene with the MP2 method.

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.

Effects of Global and Local Anharmonicities on the Thermodynamic Properties of Sulfuric Acid Monohydrate

We use state-of-the-art electronic structure calculation methods and large basis sets to obtain reliable values for the thermodynamic properties of sulfuric acid monohydrate and study the effects of vibrational anharmonicity on these properties. We distinguish between two forms of vibrational anharmonicity: local anharmonicity, which refers to the anharmonicity of the vibrational modes of a given cluster conformer, and global anharmonicity, which originates from accounting for the presence of different conformers in the first place. In our most accurate approach, we solve the nuclear Schrödinger equation variationally for the intermolecular large-amplitude motions, thus quantum-mechanically accounting for the presence of higher-energy conformers for both reactants and products, while using the standard vibrational perturbational approach for the other vibrational modes. This results in a value of -11.0 kJ/mol for the reaction Gibbs free energy at 298.15 K. When standard vibrational perturbational approaches are employed, the effects of local anharmonicity depend heavily on the choice of the electronic structure calculation basis set. In fact, better results can often be achieved by combining a simple harmonic treatment for the vibrational partition function with a statistical mechanical accounting of global anharmonicity. Thus, we recommend that future studies that intend to include anharmonicity start by accounting for the presence of higher-energy conformers and only then consider whether local anharmonicity calculations are feasible and necessary.