An adaptive density-guided approach for the generation of potential energy surfaces of polyatomic molecules

Tailored anharmonic potential energy surfaces for infrared signatures

Accurately calculated infrared spectra are essential for supporting experimental interpretation, yet full-space anharmonic vibrational structure calculations are only feasible for a limited number of degrees of freedom. Fortunately, characteristic spectroscopic signatures are often dominated by a few key vibrations. We propose a computational protocol specifically tailoring high dimensional anharmonic potential energy surfaces for the accurate and efficient calculation of such spectral signatures with vibrational coupled cluster response theory. Our protocol focuses on the selection of appropriate coordinates for the relevant degrees of freedom and the identification of specific mode-coupling terms for the potential energy surface that require more thorough treatment. This includes applying different levels of electronic structure theory and selecting a restricted set of higher mode-coupling terms (> mode pairs). We validate this protocol on two spectral regions: the fundamental CO stretching vibrations in uracil and the fundamental OH stretchings in catechol. Our findings indicate that the convergence behaviour towards harmonic frequencies in the so-called FALCON algorithm is an effective indicator for the locality character of the relevant degrees of freedom. We find that the CO stretchings in uracil are better described using normal coordinates, while the description with local FALCON coordinates of the OH-stretching vibrations in catechol showed superior performances in VCC spectra calculations. Overall, our protocol offers valuable guidelines for accurate and efficient anharmonic calculation of vibrational spectral signatures.

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.

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

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

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

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

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.

Optimizing the number of measurements for vibrational structure on quantum computers: coordinates and measurement schemes

One of the primary challenges prohibiting demonstrations of practical quantum advantages for near-term devices amounts to excessive measurement overheads for estimating relevant physical quantities such as ground state energies. However, with major differences between the electronic and vibrational structures of molecules, the question of how the resource requirements of computing anharmonic, vibrational states can be reduced remains relatively unexplored compared to its electronic counterpart. Importantly, bosonic commutation relations, distinguishable Hilbert spaces and vibrational coordinates allow manipulations of the vibrational system that can be exploited to minimize resource requirements. In this work, we investigate the impact of different coordinate systems and measurement schemes on the number of measurements needed to estimate anharmonic, vibrational states for a variety of three-mode (six-mode) molecules. We demonstrate an average of 3-fold (1.5-fold), with up to 7-fold (2.5-fold), reduction in the number of measurements required by employing appropriate coordinate transformations, based on an automized construction of qubit Hamiltonians from a conventional vibrational structure program.

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.

Hybrid Quantum-Classical Boson Sampling Algorithm for Molecular Vibrationally Resolved Electronic Spectroscopy with Duschinsky Rotation and Anharmonicity

Using a photonic quantum computer for boson sampling has demonstrated a tremendous advantage over classical supercomputers. It is highly desirable to develop boson sampling algorithms for realistic scientific problems. In this work, we propose a hybrid quantum-classical sampling (HQCS) algorithm to calculate the optical spectrum for complex molecules considering Duschinsky rotation effects and anharmonicity. The classical sum-over-states method for this problem has a computational complexity that exponentially increases with system size. The HQCS algorithm creates an intermediate harmonic potential energy surface (PES) to bridge the initial and final PESs. The magnitude and sign of the overlap between the initial and the intermediate state are estimated by boson sampling and classical algorithms, respectively. The overlap between the intermediate and the final state is efficiently evaluated by classical algorithms. The feasibility of HQCS is demonstrated in calculations of the emission spectrum of a Morse model as well as the pyridine molecule.

Fast Near Ab Initio Potential Energy Surfaces Using Machine Learning

A machine-learning based approach for evaluating potential energies for quantum mechanical studies of properties of the ground and excited vibrational states of small molecules is developed. This approach uses the molecular-orbital-based machine learning (MOB-ML) method to generate electronic energies with the accuracy of CCSD(T) calculations at the same cost as a Hartree-Fock calculation. To further reduce the computational cost of the potential energy evaluations without sacrificing the CCSD(T) level accuracy, GPU-accelerated Neural Network Potential Energy Surfaces (NN-PES) are trained to geometries and energies that are collected from small-scale Diffusion Monte Carlo (DMC) simulations, which are run using energies evaluated using the MOB-ML model. The combined NN+(MOB-ML) approach is used in variational calculations of the ground and low-lying vibrational excited states of water and in DMC calculations of the ground states of water, CH₅⁺, and its deuterated analogues. For both of these molecules, comparisons are made to the results obtained using potentials that were fit to much larger sets of electronic energies than were required to train the MOB-ML models. The NN+(MOB-ML) approach is also used to obtain a potential surface for C₂H₅⁺, which is a carbocation with a nonclassical equilibrium structure for which there is currently no available potential surface. This potential is used to explore the CH stretching vibrations, focusing on those of the bridging hydrogen atom. For both CH₅⁺ and C₂H₅⁺ the MOB-ML model is trained using geometries that were sampled from an AIMD trajectory, which was run at 350 K. By comparison, the structures sampled in the ground state calculations can have energies that are as much as ten times larger than those used to train the MOB-ML model. For water a higher temperature AIMD trajectory is needed to obtain accurate results due to the smaller thermal energy. A second MOB-ML model for C₂H₅⁺ was developed with additional higher energy structures in the training set. The two models are found to provide nearly identical descriptions of the ground state of C₂H₅⁺.

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.

Adaptive Fitting of Potential Energy Surfaces of Small to Medium-Sized Molecules in Sum-of-Product Form: Application to Vibrational Spectroscopy

A semi-automatic sampling and fitting procedure for generating sum-of-product (Born-Oppenheimer) potential energy surfaces based on a high-dimensional model representation is presented. The adaptive sampling procedure and subsequent fitting relies on energies only and can be used for re-fitting existing analytic potential energy surfaces in sum-of-product form or for direct fits from ab initio computa- tions. The method is tested by fitting ground electronic state potential energy surfaces for small to medium sized semi-rigid molecules, i.e., HFCO, HONO, and HCOOH, based upon ab initio computations at the CCSD(T)-F12/cc-pVTZ-F12 or MP2/aug-cc-pVTZ levels of theory. Vibrational eigenstates are computed using block improved relaxation in the Heidelberg MCTDH package and compared to available experimental and theoretical data. The new potential energy surfaces are compared to the best ones currently available for these molecules, in terms of accuracy, including of resulting vibrational states, required numbers of sampling points, and number of fitting parameters. The present procedure leads to compact expansions and scales well with the number of dimensions for simple potentials such as single or double wells.

Interpolation Methods for Molecular Potential Energy Surface Construction

The concept of a potential energy surface (PES) is one of the most important concepts in modern chemistry. A PES represents the relationship between the chemical system's energy and its geometry (i.e., atom positions) and can provide useful information about the system's chemical properties and reactivity. Construction of accurate PESs with high-level theoretical methodologies, such as density functional theory, is still challenging due to a steep increase in the computational cost with the increase of the system size. Thus, over the past few decades, many different mathematical approaches have been applied to the problem of the cost-efficient PES construction. This article serves as a short overview of interpolative methods for the PES construction, including global polynomial interpolation, trigonometric interpolation, modified Shepard interpolation, interpolative moving least-squares, and the automated PES construction derived from these.

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.

Evaluating the anharmonicity contributions to the molecular excited state internal conversion rates with finite temperature TD-DMRG

In this work, we propose a new method to calculate molecular nonradiative electronic relaxation rates based on the numerically exact time-dependent density matrix renormalization group theory. This method could go beyond the existing frameworks under the harmonic approximation (HA) of the potential energy surface (PES) so that the anharmonic effect could be considered, which is of vital importance when the electronic energy gap is much larger than the vibrational frequency. We calculate the internal conversion (IC) rates in a two-mode model with Morse potential to investigate the validity of HA. We find that HA is unsatisfactory unless only the lowest several vibrational states of the lower electronic state are involved in the transition process when the adiabatic excitation energy is relatively low. As the excitation energy increases, HA first underestimates and then overestimates the IC rates when the excited state PES shifts toward the dissociative side of the ground state PES. On the contrary, HA slightly overestimates the IC rates when the excited state PES shifts toward the repulsive side. In both cases, a higher temperature enlarges the error of HA. As a real example to demonstrate the effectiveness and scalability of the method, we calculate the IC rates of azulene from S₁ to S₀ on the ab initio anharmonic PES approximated by the one-mode representation. The calculated IC rates of azulene under HA are consistent with the analytically exact results. The rates on the anharmonic PES are 30%-40% higher than the rates under HA.

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.

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

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

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.

Vibrationally resolved emission spectra of luminescent conjugated oligothiophenes from anharmonic calculations

We report on accurate and efficient calculations of vibrationally resolved emission spectra for oligothiophenes from anharmonic vibrational configuration interaction wave-function calculations in reduced vibrational spaces. These reduced spaces are chosen based on the independent mode displaced harmonic oscillator model. Good agreement with experiment is obtained for all-trans oligothiophenes with two to five rings also when employing only a few active modes. Vibrational modes incorporating inter-ring carbon-carbon stretches and a ring breathing mode are found to be the main players in the vibrational progression for the emission from the first excited electronic state for all investigated oligothiophene derivatives. The presented framework is here illustrated for oligothiophenes, but we have made no underlying system-dependent assumptions and believe it to become a valuable tool for the rational design of fluorescence biomarkers.

A theoretical study on the infrared signatures of proton-bound rare gas dimers (Rg-H+-Rg), Rg = {Ne, Ar, Kr, and Xe}

The infrared spectrum of proton-bound rare gas dimers has been extensively studied via matrix isolation spectroscopy. However, little attention has been paid on their spectrum in the gas phase. Most of the Rg₂H⁺ has not been detected outside the matrix environment. Recently, Ar_nH⁺ (n = 3-7) has been first detected in the gas-phase [D. C. McDonald et al., J. Chem. Phys. 145, 231101 (2016)]. In that work, anharmonic theory can reproduce the observed vibrational structure. In this paper, we extend the existing theory to examine the vibrational signatures of Rg₂H⁺, Rg = {Ne, Ar, Kr, and Xe}. The successive binding of Rg to H⁺ was investigated through the calculation of stepwise formation energies. It was found that this binding is anti-cooperative. High-level full-dimensional potential energy surfaces at the CCSD(T)/aug-cc-pVQZ//MP2/aug-cc-pVQZ were constructed and used in the anharmonic calculation via discrete variable representation. We found that the potential coupling between the symmetric and asymmetric Rg-H⁺ stretch (ν₁ and ν₃ respectively) causes a series of bright n₁ν₁ + ν₃ progressions. From Ne₂H⁺ to Xe₂H⁺, an enhancement of intensities for these bands was observed.

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.

Accuracy of Frequencies Obtained with the Aid of Explicitly Correlated Wave Function Based Methods

We asses the basis set convergence of harmonic frequencies using different explicitly correlated wave function based methods. All commonly available CCSD(T) variants as well as MP2-F12 and MP4(F12*) are considered, and a hierarchy of the different approaches is established. As for reaction and atomization energies, CCSD(F12*)(T*) is a close approximation to CCSD(F12)(T*) and clearly superior to the other tested approximations. The used scaling for the triples correction enhances the accuracy relative to CCSD(F12*)(T) especially for small basis sets and is very attractive since no additional computational costs are added. However, this scaling slightly breaks size consistency, and therefore we additionally study the accuracy of CCSD(F12*)(T*) and CCSD(F12*)(T) in the context of calculating anharmonic frequencies to check if this causes problems in the generation of the potential energy surface (PES). We find a fast basis set convergence for harmonic and anharmonic frequencies. Already in the cc-pVDZ-F12 basis, the RMSD to the CBS limit is only around 4-5 cm^-1.