Ab initio calculation of anharmonic vibrational states of polyatomic systems: Electronic structure combined with vibrational self-consistent field

Multicomponent Density Functional Theory: Impact of Nuclear Quantum Effects on Proton Affinities and Geometries

Nuclear quantum effects such as zero point energy play a critical role in computational chemistry and often are included as energetic corrections following geometry optimizations. The nuclear-electronic orbital (NEO) multicomponent density functional theory (DFT) method treats select nuclei, typically protons, quantum mechanically on the same level as the electrons. Electron-proton correlation is highly significant, and inadequate treatments lead to highly overlocalized nuclear densities. A recently developed electron-proton correlation functional, epc17, has been shown to provide accurate nuclear densities for molecular systems. Herein, the NEO-DFT/epc17 method is used to compute the proton affinities for a set of molecules and to examine the role of nuclear quantum effects on the equilibrium geometry of FHF^-. The agreement of the computed results with experimental and benchmark values demonstrates the promise of this approach for including nuclear quantum effects in calculations of proton affinities, pK_a's, optimized geometries, and reaction paths.

Spectroscopic snapshots of the proton-transfer mechanism in water

The Grotthuss mechanism explains the anomalously high proton mobility in water as a sequence of proton transfers along a hydrogen-bonded (H-bonded) network. However, the vibrational spectroscopic signatures of this process are masked by the diffuse nature of the key bands in bulk water. Here we report how the much simpler vibrational spectra of cold, composition-selected heavy water clusters, D⁺(D₂O)_n, can be exploited to capture clear markers that encode the collective reaction coordinate along the proton-transfer event. By complexing the solvated hydronium "Eigen" cluster [D₃O⁺(D₂O)₃] with increasingly strong H-bond acceptor molecules (D₂, N₂, CO, and D₂O), we are able to track the frequency of every O-D stretch vibration in the complex as the transferring hydron is incrementally pulled from the central hydronium to a neighboring water molecule.

Intermediate vibrational coordinate localization with harmonic coupling constraints

Optimized normal coordinates can significantly improve the speed and accuracy of vibrational frequency calculations. However, over-localization can occur when using unconstrained spatial localization techniques. The unintuitive mixtures of stretching and bending coordinates that result can make interpreting spectra more difficult and also cause artificial increases in mode-coupling during anharmonic calculations. Combining spatial localization with a constraint on the coupling between modes can be used to generate coordinates with properties in-between the normal and fully localized schemes. These modes preserve the diagonal nature of the mass-weighted Hessian matrix to within a specified tolerance and are found to prevent contamination between the stretching and bending vibrations of the molecules studied without a priori classification of the different types of vibration present. Relaxing the constraint can also be used to identify which normal modes form specific groups of localized modes. The new coordinates are found to center on more spatially delocalized functional groups than their fully localized counterparts and can be used to tune the degree of vibrational correlation energy during anharmonic calculations.

Insight into structural phase transitions from the decoupled anharmonic mode approximation

We develop a formalism (decoupled anharmonic mode approximation, DAMA) that allows calculation of the vibrational free energy using density functional theory even for materials which exhibit negative curvature of the potential energy surface with respect to atomic displacements. We investigate vibrational modes beyond the harmonic approximation and approximate the potential energy surface with the superposition of the accurate potential along each normal mode. We show that the free energy can stabilize crystal structures at finite temperatures which appear dynamically unstable at T  =  0. The DAMA formalism is computationally fast because it avoids statistical sampling through molecular dynamics calculations, and is in principle completely ab initio. It is free of statistical uncertainties and independent of model parameters, but can give insight into the mechanism of a structural phase transition. We apply the formalism to the perovskite cryolite, and investigate the temperature-driven phase transition from the P21/n to the Immm space group. We calculate a phase transition temperature between 710 and 950 K, in fair agreement with the experimental value of 885 K. This can be related to the underestimation of the interaction of the vibrational states. We also calculate the main axes of the thermal ellipsoid and can explain the experimentally observed increase of its volume for the fluorine by 200-300% throughout the phase transition. Our calculations suggest the appearance of tunneling states in the high temperature phase. The convergence of the vibrational DOS and of the critical temperature with respect of reciprocal space sampling is investigated using the polarizable-ion model.

BNg3F3: the first three noble gas atoms inserted into mono-centric neutral compounds - a theoretical study

Following the study of HXeOXeH and HXeCCXeH, in which two Xe atoms were inserted into H2O and C2H2 theoretically and experimentally, the structures and stability of BNg3F3 (Ng = Ar, Kr and Xe), in which three Ng atoms are inserted into BF3, have been explored theoretically using DFT and ab initio calculations. It is shown that BNg3F3 (Ng = Ar, Kr and Xe) with D3h symmetry are local minima with short B-Ng bond lengths of 1.966, 2.027 and 2.214 Å at the CCSD(T)/aug-cc-pVTZ/LJ18 level, which are close to their covalent limits. Note that although BNg3F3 (Ng = Kr and Xe) are energetically higher than the dissociation products 3Ng + BF3, they are still kinetically stable as metastable species with protecting barriers of 13.38 and 17.99 kcal mol(-1) for BKr3F3 and BXe3F3. Moreover, BKr3F3, the tri-Kr-inserted compound, even has comparable kinetic stability to HXeOXeH and HXeOXeF. In addition, upon the formation of BNg3F3, there is a large amount of charge transferred from B to Ng of at least 0.619 e. The calculated Wiberg Bond Indices (WBI) suggest that B-Ng bonds are naturally singly bonded; the large vibrational frequencies of B-Ng and Ng-F stretching modes and the negative Laplacian electron density of B-Ng bonds confirm further that BNg3F3 are stiff molecules with covalent B-Ng bonds. It should be noted that three Ng atoms inserted into mono-centric neutral molecules have not been reported previously. We hope that the present theoretical study may provide important evidence for the experimental synthesis of BNg3F3.

A Noble-Gas Hydride in a Nitrogen Medium: Structure, Spectroscopy, and Intermolecular Vibrations of HXeBr@(N2)22

Noble-gas hydrides have been extensively studied in noble gas matrices. However, little is known on their stability and properties in molecular hosts. Here, HXeBr in the N2 environment is modeled at the B3LYP-D level of theory in a complete single shell of 22 N2 molecules. The system is compared to similar models of HXeBr in CO2 and Xe clusters. The optimized structure of (HXeBr)@(N2)22 is of low symmetry and is highly anisotropic. None of the N2 molecules are freely rotating, and the host molecules are not symmetrically positioned with respect to the HXeBr axis. The axes of the N2 molecules are nonuniformly distributed. The computed anharmonic H-Xe stretching frequency of HXeBr in the N2 cluster is in good accord with the experimental value. The soft-mode frequencies of the cluster including both intermolecular vibrations and librations, have a broad distribution that ranges from 8.7 to 107 cm(-1). It is expected that these findings and specifically, the single-shell model, may shed light also on the local structure and vibrations of other impurities in a molecular media.

Examining the impact of harmonic correlation on vibrational frequencies calculated in localized coordinates

Carefully choosing a set of optimized coordinates for performing vibrational frequency calculations can significantly reduce the anharmonic correlation energy from the self-consistent field treatment of molecular vibrations. However, moving away from normal coordinates also introduces an additional source of correlation energy arising from mode-coupling at the harmonic level. The impact of this new component of the vibrational energy is examined for a range of molecules, and a method is proposed for correcting the resulting self-consistent field frequencies by adding the full coupling energy from connected pairs of harmonic and pseudoharmonic modes, termed vibrational self-consistent field (harmonic correlation). This approach is found to lift the vibrational degeneracies arising from coordinate optimization and provides better agreement with experimental and benchmark frequencies than uncorrected vibrational self-consistent field theory without relying on traditional correlated methods.

Vibrational anharmonicity of small gold and silver clusters using the VSCF method

We study the vibrational spectra of small neutral gold (Au₂–Au₁₀) and silver (Ag₂–Au₅) clusters using the vibrational self-consistent field method (VSCF) in order to account for anharmonicity.

First-principles anharmonic quantum calculations for peptide spectroscopy: VSCF calculations and comparison with experiments

First-principles quantum calculations for anharmonic vibrational spectroscopy of three protected dipeptides are carried out and compared with experimental data.

Ab Initio Studies of Structural and Vibrational Properties of Protonated Water Cluster H7O3(+) and Its Deuterium Isotopologues: An Application of Driven Molecular Dynamics

In this work, we present infrared (IR) spectra of H7O3(+) and its deuterium isotopomers calculated by direct molecular dynamics (MD) simulations at the B3LYP/6-31+G** computational level. The calculated spectra obtained at 100, 300, and 500 K were compared to available experimental observations, and spectral features were assigned using normal-mode analysis (NMA) and driven molecular dynamics (DMD). Spectral peaks at 2410 and 2540 cm(-1) were assigned to asymmetric and symmetric stretches of the bridging hydrogen (BH) using NMA. The weak spectral features at 2166 and 2275 cm(-1) were assigned to a combination band of BH asymmetric stretch, H2O in phase wagging, OO stretch, and H3O(+) rocking vibrations by DMD simulations. Our observation of BH stretch vibrations as low as 2166 cm(-1) is in good agreement with the assignment of the low-resolution spectrum obtained by Schwarz at 2200-2300 cm(-1) [Schwarz, H. A. J. Chem. Phys. 1977, 67, 5525-5534] and vibrational predissociation spectrum by Lee et al. ∼2300 cm(-1) [Okumura, M.; Yeh, L. I.; Myers, J. D.; Lee, Y. T. J. Chem. Phys. 1990, 94, 3416-3427].

Vibrational Signature of a Single Water Molecule Adsorbed on Pt(111): Toward a Reliable Anharmonic Description

In this study, we present a thorough benchmarking of our direct anharmonic vibrational variation-perturbation approach for adsorbed molecules on surfaces. We then use our method to describe the vibrational structure of a water molecule adsorbed on a Pt(111) surface and compare our results with the available experimental data. By using an explicitly correlated hybrid method to describe the molecule-surface interaction, we improve on the initial periodic PBE/DZP potential energy landscape and obtain vibrational frequencies that are of near-experimental accuracy. We introduce an implementation of anharmonic z-polarized IR intensity calculation and explain the absence of antisymmetric O-H stretch in the experimental data for the adsorbed water molecule, while the symmetric O-H stretch is predicted to be visible.

CC/DFT Route toward Accurate Structures and Spectroscopic Features for Observed and Elusive Conformers of Flexible Molecules: Pyruvic Acid as a Case Study

The structures and relative stabilities as well as the rotational and vibrational spectra of the three low-energy conformers of pyruvic acid (PA) have been characterized using a state-of-the-art quantum-mechanical approach designed for flexible molecules. By making use of the available experimental rotational constants for several isotopologues of the most stable PA conformer, Tc-PA, the semiexperimental equilibrium structure has been derived. The latter provides a reference for the pure theoretical determination of the equilibrium geometries for all conformers, thus confirming for these structures an accuracy of 0.001 Å and 0.1 deg for bond lengths and angles, respectively. Highly accurate relative energies of all conformers (Tc-, Tt-, and Ct-PA) and of the transition states connecting them are provided along with the thermodynamic properties at low and high temperatures, thus leading to conformational enthalpies accurate to 1 kJ mol(-1). Concerning microwave spectroscopy, rotational constants accurate to about 20 MHz are provided for the Tt- and Ct-PA conformers, together with the computed centrifugal-distortion constants and dipole moments required to simulate their rotational spectra. For Ct-PA, vibrational frequencies in the mid-infrared region accurate to 10 cm(-1) are reported along with theoretical estimates for the transitions in the near-infrared range, and the corresponding infrared spectrum including fundamental transitions, overtones, and combination bands has been simulated. In addition to the new data described above, theoretical results for the Tc- and Tt-PA conformers are compared with all available experimental data to further confirm the accuracy of the hybrid coupled-cluster/density functional theory (CC/DFT) protocol applied in the present study. Finally, we discuss in detail the accuracy of computational models fully based on double-hybrid DFT functionals (mainly at the B2PLYP/aug-cc-pVTZ level) that avoid the use of very expensive CC calculations.

Generalized Vibrational Perturbation Theory for Rotovibrational Energies of Linear, Symmetric and Asymmetric Tops: Theory, Approximations, and Automated Approaches to Deal with Medium-to-Large Molecular Systems

Models going beyond the rigid-rotor and the harmonic oscillator levels are mandatory for providing accurate theoretical predictions for several spectroscopic properties. Different strategies have been devised for this purpose. Among them, the treatment by perturbation theory of the molecular Hamiltonian after its expansion in power series of products of vibrational and rotational operators, also referred to as vibrational perturbation theory (VPT), is particularly appealing for its computational efficiency to treat medium-to-large systems. Moreover, generalized (GVPT) strategies combining the use of perturbative and variational formalisms can be adopted to further improve the accuracy of the results, with the first approach used for weakly coupled terms, and the second one to handle tightly coupled ones. In this context, the GVPT formulation for asymmetric, symmetric, and linear tops is revisited and fully generalized to both minima and first-order saddle points of the molecular potential energy surface. The computational strategies and approximations that can be adopted in dealing with GVPT computations are pointed out, with a particular attention devoted to the treatment of symmetry and degeneracies. A number of tests and applications are discussed, to show the possibilities of the developments, as regards both the variety of treatable systems and eligible methods.

Efficient anharmonic vibrational spectroscopy for large molecules using local-mode coordinates

This article presents a general computational approach for efficient simulations of anharmonic vibrational spectra in chemical systems. An automated local-mode vibrational approach is presented, which borrows techniques from localized molecular orbitals in electronic structure theory. This approach generates spatially localized vibrational modes, in contrast to the delocalization exhibited by canonical normal modes. The method is rigorously tested across a series of chemical systems, ranging from small molecules to large water clusters and a protonated dipeptide. It is interfaced with exact, grid-based approaches, as well as vibrational self-consistent field methods. Most significantly, this new set of reference coordinates exhibits a well-behaved spatial decay of mode couplings, which allows for a systematic, a priori truncation of mode couplings and increased computational efficiency. Convergence can typically be reached by including modes within only about 4 Å. The local nature of this truncation suggests particular promise for the ab initio simulation of anharmonic vibrational motion in large systems, where connection to experimental spectra is currently most challenging.

FTIR, FT-Raman, UV-Visible spectra and quantum chemical calculations of allantoin molecule and its hydrogen bonded dimers

FTIR, FT-Raman and electronic spectra of allantoin molecule are recorded and investigated using DFT and MP2 methods with 6-311++G(d,p) basis set. The molecular structure, anharmonic vibrational spectra, natural atomic charges, non-linear optical properties, etc. have been computed for the ground state of allantoin. The anharmonic vibrational frequencies are calculated using PT2 algorithm (Barone method) as well as VSCF and CC-VSCF methods. These methods yield results that are in remarkable agreement with the experiment. The coupling strengths between pairs of modes are also calculated using coupling integral based on 2MR-QFF approximation. The simulations on allantoin dimers have been also performed at B3LYP/6-311++G(d,p) level of theory to investigate the effect of the intermolecular interactions on the molecular structure and vibrational frequencies of the monomer. Vibrational assignments are made with the great accuracy using PED calculations and animated modes. The combination and overtone bands have been also identified in the FTIR spectrum with the help of anharmonic computations. The electronic spectra are simulated in gas and solution at TD-B3LYP/6-311++G(d,p) level of theory. The important global quantities such as electro-negativity, electronic chemical potential, electrophilicity index, chemical hardness and softness based on HOMO, LUMO energy eigenvalues are also computed. NBO analysis has been performed for monomer and dimers of allantoin at B3LYP/6-311++G(d,p) level of theory.

Largely reduced grid densities in a vibrational self-consistent field treatment do not significantly impact the resultingwavenumbers

Especially for larger molecules relevant to life sciences, vibrational self-consistent field (VSCF) calculations can become unmanageably demanding even when only first and second order potential coupling terms are considered. This paper investigates to what extent the grid density of the VSCF’s underlying potential energy surface can be reduced without sacrificing accuracy of the resulting wavenumbers. Including single-mode and pair contributions, a reduction to eight points per mode did not introduce a significant deviation but improved the computational efficiency by a factor of four. A mean unsigned deviation of 1.3% from the experiment could be maintained for the fifteen molecules under investigation and the approach was found to be applicable to rigid, semi-rigid and soft vibrational problems likewise. Deprotonated phosphoserine, stabilized by two intramolecular hydrogen bonds, was investigated as an exemplary application.

Infrared identification of proton-bound rare-gas dimers (XeHXe)⁺, (KrHKr)⁺, and (KrHXe)⁺ and their deuterated species in solid hydrogen

Proton-bound rare-gas dimer (RgHRg)(+), in which Rg represents a rare-gas atom, serves as a prototypical system for proton solvation by inert-gas atoms. Until now, only centrosymmetric species with Rg = Ar, Kr, or Xe have been identified with infrared spectra. We employed electron bombardment during deposition of a mixture of Xe (or Kr) in p-H2 at 3.2 K to prepare (RgHRg)(+). Lines at 847.0 and 972.1 cm(-1) are assigned as the Rg-H-Rg antisymmetric stretching (ν3) mode and its combination with the Rg-H-Rg symmetric stretching (ν1 + ν3) mode of (XeHXe)(+) in solid p-H2, respectively. Lines at 871.1 and 974.0 cm(-1) are assigned as the ν3 and ν1 + ν3 modes of (KrHKr)(+) in solid p-H2, respectively. Slightly shifted and broadened lines were observed for these species in solid n-H2. These results agree satisfactorily with reported experimental values of (XeHXe)(+) and (KrHKr)(+) in solid Xe, Kr, and Ar, and with the quantum-chemically predicted anharmonic vibrational wavenumbers of these species in the gaseous phase; the significant spectral shifts in various matrixes are rationalized with the proton affinities of the hosts. When a mixture of Xe and Kr in p-H2 was used, an additional broad feature at 1284 cm(-1) was observed and assigned as the ν3 mode of (KrHXe)(+) in solid p-H2. This line shifted to 1280 cm(-1) in solid n-H2 and the corresponding line of (KrDXe)(+) was observed at 954 cm(-1) in n-D2. The observations of these lines are new; the wavenumbers significantly blue shifted from those of the centrosymmetric (RgHRg)(+) agree with the quantum-chemically predicted anharmonic vibrational wavenumbers of 1279 cm(-1) for (KrHXe)(+) and 916 cm(-1) for (KrDXe)(+). Analysis of the computational results shows that electronic correlation effects play a much greater role for the asymmetric than for the symmetric species. An interpretation for this is provided.

The impact of highly correlated potential energy surfaces on the anharmonically corrected IR spectrum of acetonitrile

This paper discusses the quality and feasibility of highly correlated ab initio techniques in a vibrational self-consistent field (VSCF) approach using acetonitrile as a model system. The topical renormalized coupled-cluster technique exploiting the similarity-transformed Hamiltonian's left eigenstates (i.e. CR-CC(2,3)) is investigated alongside the well-known Hartree-Fock (HF), Møller-Plesset second-order perturbation theory (MP2) and coupled cluster (CCSD(T)) methods. The inclusion of mode triple interactions is discussed and it is found that the use of an effective core potential (ECP) serves as a viable compromise during the highly demanding task of computing such contributions, thus enabling a grid-based evaluation of three mode interaction terms with coupled cluster techniques also for larger molecules. In this context, a previously proposed reduced coupling scheme [1] is investigated, confirming the applicability of this technique to a system exhibiting a rather complex electronic structure. A combination of Ahlrichs' triple-ζ valence polarized (TZVP) basis set with Dunning's set of core-valence correlation functions is found to deliver results in good agreement with experiment while being computationally very feasible. Since CH3CN exhibits four degenerate vibrational degrees of freedom, it serves as an ideal model system for critically assessing the qualities of the degenerate second-order perturbation theory corrected (DPT2) VSCF technique. Besides fundamental vibrations, a thorough investigation of overtone transitions and combination bands is conducted by means of comparing the results to both available and newly recorded experimental data.

New developments of a multifrequency virtual spectrometer: stereo-electronic, dynamical, and environmental effects on chiroptical spectra

Computational spectroscopy has recently evolved from a field reserved for specialists toward a general tool allowing interpretations and analyses of experimental results. However, the current practice of providing tables of transitions for rigid geometries, possibly tuned by phenomenological broadening, is by far too naive. In order to improve this situation in the last few years we have been developing a general, robust, and user-friendly virtual spectrometer (VS) able to complement experimental studies for complex systems in condensed phases. The VS is based on flexible graphical pre- and postprocessing tools interfaced with general number-crunching software. This last tool is rooted in several electronic structure methodologies (DFT, TD-DFT, post-Hartree-Fock), powerful discrete/continuum models for describing environmental effects, and general vibrational and vibronic models. These last topics are the main focus of this work, which sketches our latest developments related to effective inclusion of anharmonic contributions, together with time-independent and/or time-dependent descriptions of vibronic transitions including Franck-Condon, Herzberg-Teller, and Duschinsky effects. Some test cases are described in some detail with the aim of showing the role of different effects in ruling vibrational (VCD) and electronic (ECD, CPL) chiral spectroscopies.

Quantum chemical and spectroscopic investigations of 3-methyladenine

FTIR, FT-Raman and UV-Vis spectra of 3-methyladenine have been recorded and investigated using quantum chemical calculations. The molecular geometry and vibrational spectra of 3-methyladenine in the ground state are computed by using HF and DFT methods with 6-311G(d,p) basis set. VSCF, CC-VSCF methods based on 2MR-QFF and PT2 (Barone method) have been utilized for computing anharmonic vibrational frequencies. These methods yield results that are in remarkable agreement with the experimental data. The magnitudes of coupling between pair of modes have been also computed. Vibrational modes are assigned with the help of visual inspection of atomic displacements. The electronic spectra, simulated at TD-B3LYP/6-311++G(d,p) level of theory, are compared to the experiment. The global quantities: electronic chemical potential, electrophilicity index, chemical hardness and softness based on HOMO and LUMO energy eigenvalues are also computed at B3LYP/6-311++G(d,p) level of theory.

Dispersion corrected DFT approaches for anharmonic vibrational frequency calculations: nucleobases and their dimers

Computational spectroscopy techniques have become in the last few years an effective means to analyze and assign infrared (IR) spectra of molecular systems of increasing dimensions and in different environments. However, transition from compilation of harmonic data to fully anharmonic simulations of spectra is still underway. The most promising results for large systems have been obtained, in our opinion, by perturbative vibrational approaches based on potential energy surfaces computed by hybrid (especially B3LYP) density functionals and medium size (e.g. SNSD) basis sets. In this framework, we are actively developing a comprehensive and robust computational protocol aimed at quantitative reproduction of the spectra of nucleic acid base complexes and their adsorption on solid supports (organic/inorganic). In this contribution we report the essential results of the first step devoted to isolated monomers and dimers. It is well known that in order to model the vibrational spectra of weakly bound molecular complexes dispersion interactions should be taken into proper account. In this work we have chosen two popular and inexpensive approaches to model dispersion interactions, namely the semi-empirical dispersion correction (D3) and pseudopotential based (DCP) methodologies both in conjunction with the B3LYP functional. These have been used for simulating fully anharmonic IR spectra of nucleobases and their dimers through generalized second order vibrational perturbation theory (GVPT2). We have studied, in particular, isolated adenine, hypoxanthine, uracil, thymine and cytosine, the hydrogen-bonded and stacked adenine and uracil dimers, and the stacked adenine-naphthalene heterodimer. Anharmonic frequencies are compared with standard B3LYP results and experimental findings, while the computed interaction energies and structures of complexes are compared to the best available theoretical estimates.