Zero-point Vibrational Energy Research Articles

Halogens in Acetophenones Direct the Hydrogen Bond Docking Preference of Phenol via Stacking Interactions.

Phenol is added to acetophenone (methyl phenyl ketone) and to six of its halogenated derivatives in a supersonic jet expansion to determine the hydrogen bonding preference of the cold and isolated 1:1 complexes by linear infrared spectroscopy. Halogenation is found to have a pronounced effect on the docking site in this intermolecular ketone balance experiment. The spectra unambiguously decide between competing variants of phenyl group stacking due to their differences in hydrogen bond strength. Structures where the phenyl group interaction strongly distorts the hydrogen bond are more difficult to quantify in the experiment. For unsubstituted acetophenone, phenol clearly prefers the methyl side despite a predicted sub-kJ/mol advantage that is nearly independent of zero-point vibrational energy, turning this complex into a challenging benchmark system for electronic structure methods, which include long range dispersion interactions in some way.

Synthesis, spectral, crystallographic, and computational investigation of a novel molecular hybrid 3-(1-((benzoyloxy)imino)ethyl)-2H-chromen-2-ones

Synthesis of 3-(1-((benzoyloxy)imino)ethyl)-2H-chromen-2-ones (1-5) was accomplished and it was characterized experimentally using various analytical techniques. Computational studies have been carried out for all compounds 1-5 using B3LYP method with 6-311++G(d,p) basis set. The optimized structural features viz. bond lengths, bond angles, and dihedral angles are compared with their single-crystal X-ray diffraction results of compound 1 (Crystal data for C18H13NO4 (M = 307.29 g/mol): Monoclinic, space group P21/c (no. 14), a = 11.399(5) Å, b = 5.876(5) Å, c = 21.859(5) Å, β = 91.060(5)°, V = 1463.9(14) Å3, Z = 4, T = 293(2) K, μ(MoKα) = 0.100 mm-1, Dcalc = 1.394 g/cm3, 13555 reflections measured (3.58° ≤ 2Θ ≤ 56.98°), 3669 unique (Rint = 0.0235) which were used in all calculations. The final R1 was 0.0444 (>2sigma(I)) and wR2 was 0.1506 (all data)), which are in good conformity with each other. Normal modes of vibrational frequencies of compounds 1-5 acquired from density-functional theory (DFT) method coincided with the experimental ones. The 1H and 13C chemical shifts of compounds 1-5 have been calculated by GIAO method and the results have been compared with the experimental ones. The first-order hyperpolarizability and their related properties of the novel molecules 1-5 are calculated computationally. The other parameters like natural bond orbital, zero-point vibrational energy, EHOMO, ELUMO, heat capacity and entropy have also been discussed.

Solvation of Potassium 5-Hydroxy Pentanoyl Trifluoroborate Salt in Aqueous Environment by Using FT-Raman and UV-Visible Spectra

The hydration process of potassium 5-hydroxypentanoyltrifluoroborate salt, K[C5H9BF3O2] and its 5-hydroxypentanoyltrifluoroborate [C5H9BF3O2]- anion have been studied by combining the experimental FT-Raman and ultraviolet-visible spectra in aqueous solution with hybrid B3LYP/6-311++G** calculations. Solvent effects have been considered with the self-consistent reaction field (SCRF) and solvation (SM) models. Here, the structures of [C5H9BF3O2].[H2O]n clusters of anion, with n from 1 to 5 implicit water molecules, were proposed in order to study the number of water molecules that could hydrate the anion. Calculations were performed in the gas phase and an aqueous solution to observe the effect of the medium on the dipole moment and volume values. Calculated solvation energies for all clusters were corrected by zero-point vibrational energy (ZPVE), non-electrostatic terms and by basis set superposition energy (BSSE). The dipole moment of salt in solution (10.19 D) suggests that the number of water molecules that could hydrate the anion vary between 3 and 4, in total agreement with the observed and predicted bands in the UV-Vis spectra for the salt and these two clusters in water between 180 and 400 nm. Comparisons among experimental and predicted Raman spectra show clearly the hydration effect because the bands attributed to OH, BF3 and C=O groups are shifted in solution, while, the predicted Raman spectra for all clusters in solution show strong changes in the intensities of many bands, in accordance with the corresponding experimental one. Evidently, the hydration occurs on the OH, BF3 and C=O groups.

Thermochemical Trends in Carbon Chain Molecules HC2kH/HC2k-1H (k = 1-6) Studied by Explicitly Correlated CCSD(T)-F12b Composite Methods.

We present a composite procedure based on explicitly correlated CCSD(T)-F12 calculations for accurate energetic predictions for carbon chain molecules HCnH encompassing both the even (HC2kH) and odd series (HC2k-1H), with the shorter members playing a key role in the evolution of cosmic carbon compounds in both circumstellar envelopes and interstellar medium. This approach considers the contributions of core-valence correlation, scalar relativistic effect, spin-orbit coupling, and zero-point vibrational energy in an additive manner. The computed ionization energies demonstrate outstanding agreement (±0.07 eV) up to a chain size of k = 6 and the literature heats of formation for k ≤ 2 are reproduced with "chemical accuracy" of 1 kcal mol-1. Among the various corrections included, the importance of core-valence correlation effect has been highlighted in the thermochemical calculations for carbon chain growth. The thermochemical trend toward infinite length is also highlighted by extrapolation of ionization energy and triplet-singlet splitting at the CCSD(T) level for k up to 15. The correlation between the end-group effect and the even-odd parity effect observed for HCnH chains has been established with the aid of intrinsic bond orbital localization.

High-Level ab Initio Predictions for the Ionization Energies, Bond Dissociation Energies, and Heats of Formation of Vanadium Methylidene, Vanadium Methyl Species, and Their Cations (VCH2/VCH2+, VCH3/VCH3+).

The ionization energies of VCH2 and VCH3, the various 0 K bond dissociation energies (D0s) in their neutrals and cations, and their respective heats of formation at 0 and 298 K are computed by the single-reference, wave function-based CCSDTQ/CBS procedure. The core of the composite method is the approximation to the complete basis set (CBS) limit at the coupled cluster (CC) level which includes up to full quadruple excitations. The zero-point vibrational energy, core-valence correlation, spin-orbit coupling, and scalar relativistic effects have their contributions incorporated in an additive manner. For the species in the current study, this protocol requires geometry optimizations and harmonic frequency calculations practically no higher than the CCSD(T)/aug-cc-pwCVTZ and CCSD(T)/aug-cc-pVTZ levels, respectively. The present calculations successfully predict D0(V+-CH3) = 2.126 eV and D0(V+-CH2) = 3.298 eV in remarkable agreement with the data recently measured by a spin-orbit state selected V+ + CH4 collision experiment (Phys. Chem. Chem. Phys. 2021, 23, 273-286). The good accord encourages the use of CCSDTQ/CBS protocol in thermochemical predictions of various feasible product channels identified in methane activation by transition metal species.

The torsional states of methyl hydroperoxide molecule calculated using anharmonic zero point vibrational energy

The 2D surfaces of potential energy, kinematic coefficients, components of the dipole moment, the heights of potential barriers, the energies of stationary torsional states, and the tunneling frequencies of hydroxyl and methyl groups in the methyl hydroperoxide molecule were calculated at MP2/CBS and CCSD(T)/Aug-cc-pVTZ levels of theory. Additionally, calculations of the 2D surface of zero point vibrational energy of the molecule in the harmonic and anharmonic approximations were performed at MP2/Aug-cc-pVTZ level of theory. The zero point vibrational energy calculated in two approximations is summed up with the potential energy of the methyl hydroperoxide molecule, calculated at two levels of theory, and the resulting four outcomes of the refined potential energy are used to calculate the energies of stationary torsional states and tunneling frequencies. The results obtained are compared with the experimental and theoretical data presented in the literature to evaluate the efficiency of taking into account the zero point vibrational energy when examining the internal rotation in molecules.

Heavy Water Models for Classical Molecular Dynamics: Effective Inclusion of Nuclear Quantum Effects.

Small differences in physical and chemical properties of H2O and D2O, such as melting and boiling points or pKa, can be traced back to a slightly stronger hydrogen bonding in heavy versus normal water. In particular, deuteration reduces zero-point vibrational energies as a demonstration of nuclear quantum effects. In principle, computationally demanding quantum molecular dynamics is required to model such effects. However, as already demonstrated by Feynmann and Hibbs, zero-point vibrations can be effectively accounted for by modifying the interaction potential within classical dynamics. In the spirit of the Feymann-Hibbs approach, we develop here two water models for classical molecular dynamics by fitting experimental differences between H2O and D2O. We show that a three-site SPCE-based model accurately reproduces differences between properties of the two water isotopes, with a four-site TIP4P-2005/based model in addition capturing also the absolute values of key properties of heavy water. The present models are computationally simple enough to allow for extensive simulations of biomolecules in heavy water relevant, for example, for experimental techniques such as NMR or neutron scattering.

Transformation of an Embedded Five-Membered Ring in Polycyclic Aromatic Hydrocarbons via the Hydrogen-Abstraction-Acetylene-Addition Mechanism: A Theoretical Study.

Five-membered rings are constituents of many polycyclic aromatic hydrocarbons (PAHs), and their presence on the edges of large PAHs has been repeatedly observed experimentally. However, modern kinetic combustion models often do not consider the growth of PAHs through the transformation of the five-membered rings. In connection with the above, we carried out a theoretical study of the mechanism of hydrogen-abstraction-acetylene-addition (HACA) transformation of an embedded five-membered ring on the armchair PAH edge to a six-membered ring, considering cyclopenta[d,e,f]phenanthrene (4,5-methylenephenanthrene) as a prototype system for this process. The potential energy surface for the reactions of cyclopenta[d,e,f]phenanthrenyl radicals produced by direct H abstractions from cyclopenta[d,e,f]phenanthrene with acetylene has been compiled at the G3(MP2,CC)//B3LYP/6-311G(d,p) level of theory including zero-point vibrational energy corrections. The computed energies and molecular parameters were then used to solve the Rice-Ramsperger-Kassel-Marcus master equation in order to calculate the reaction rate at various pressures and temperatures, which were fitted to the modified Arrhenius equation for further kinetic modeling. The results show that the HACA transformation of the embedded five-membered ring to a six-membered ring is possible, albeit slow. The most viable reaction mechanism involves the R2 + C2H2 reaction, where the acetylene molecules add to a σ-radical in the six-membered ring adjacent to the five-membered ring via a low entrance barrier. The predominant product of R2 + C2H2 is predicted to be 3-ethynyl-4H-cyclopenta[def]phenanthrene Pr5 via immediate H elimination from the initial addition complex. Next, Pr5 undergoes H-assisted isomerization to 4aH-pentaleno[4,3,2,1-cdef]phenanthrene Pr4, and the latter adds a H-atom eventually forming the 1-pyrenylmethyl radical Pr3: R2 + C2H2 ⇆ 3-ethynyl-4H-cyclopenta[def]phenanthrene (Pr5) + H or 4aH-pentaleno[4,3,2,1-cdef]phenanthrene (Pr4) + H; Pr5 + H ⇆ Pr4 + H; Pr4 + H → 1-pyrenylmethyl (Pr3). This HACA sequence may be competitive with the methyl radical addition to the R1 radical formed by H abstraction from the CH2 group in the five-membered ring of cyclopenta[d,e,f]phenanthrene, which provides a pathway to pyrene following two H-atom losses. Relative contributions of the two mechanisms of the five- to six-membered ring transformation would strongly depend on the branching ratios of the R1 and R2 radicals produced by the H abstractions and the available concentration of C2H2 versus CH3 and hence differ in different flames.

Local electronic structure of dilute hydrogen in β−MnO2

The electronic and magnetic states of $\ensuremath{\beta}\text{\ensuremath{-}}{\mathrm{MnO}}_{2}$ in terms of hydrogen impurities have been investigated by the muon spin rotation technique combined with density-functional theory (DFT) calculations for muon as pseudohydrogen. We found that 85% of implanted muons are localized in the oxygen channels of the rutile structure and behave like interstitial protons (${\mathrm{Mu}}^{+})$ except those (7.6%) forming a charge-neutral state (${\mathrm{Mu}}^{0})$ at 2.3 K, which indicates that interstitial hydrogen acts like a shallow donor within less than 0.1 meV of ionization energy. The residual 15% of muons are attributed to those related to lattice imperfection as Mn vacancies. Detailed analyses combined with the DFT approach suggested that the muon is localized at the center of the oxygen channel due to its large zero-point vibration energy.

The Lennard-Jones Potential Revisited: Analytical Expressions for Vibrational Effects in Cubic and Hexagonal Close-Packed Lattices.

Analytical formulas are derived for the zero-point vibrational energy and anharmonicity corrections of the cohesive energy and the mode Grüneisen parameter within the Einstein model for the cubic lattices (sc, bcc, and fcc) and for the hexagonal close-packed structure. This extends the work done by Lennard-Jones and Ingham in 1924, Corner in 1939, and Wallace in 1965. The formulas are based on the description of two-body energy contributions by an inverse power expansion (extended Lennard-Jones potential). These make use of three-dimensional lattice sums, which can be transformed to fast converging series and accurately determined by various expansion techniques. We apply these new lattice sum expressions to the rare gas solids and discuss associated critical points. The derived formulas give qualitative but nevertheless deep insight into vibrational effects in solids from the lightest (helium) to the heaviest rare gas element (oganesson), both presenting special cases because of strong quantum effects for the former and strong relativistic effects for the latter.

Concentration-dependent adsorption of organic contaminants by graphene nanosheets: quantum-mechanical models.

Adsorption is the key process in the expression of environmentally relevant physicochemical and toxicological properties of carbon nanomaterials. However, the adsorption of organic contaminants on to nanomaterials is a highly complex phenomenon, owing to the heterogeneity of adsorption sites, for example, on graphene surface as well as due to multiple factors operative during the adsorption, particularly, at the quantum-mechanical level. For predicting the concentration-dependent adsorption coefficients of organic contaminants by carbon nanomaterials, one option has been to rely on the existing linear-solvation energy relationship (LSER) models. The present work on the adsorption of aromatic and aliphatic organic contaminants by graphene nanosheets reveals that the existing LSER models are prone to failure when tested for internal and external validation using an external prediction set of compounds unknown to the model. As an alternative to the LSERs, the present work reports pure quantum-mechanical models developed using computational only quantum-mechanical descriptors. The reliability of the quantum-mechanical models was tested using state-of-the-art validation procedures employing an external prediction set of compounds. The proposed quantum-mechanical models reveal mean polarizability, zero-point vibrational energy, and its electron-correlation contribution to be the key descriptors in the prediction of adsorption coefficients of organic contaminants by graphene nanosheets.

Secondary kinetic deuterium isotope effects on unimolecular cleavage reactions: Zero-point vibrational energy and qualitative RRKM theory.

Secondary kinetic isotope effects arise as the result of transition-state zero-point vibrational energy differences. Unimolecular simple cleavage reactions of gas-phase ions in mass spectrometers allow detailed studies of isotope effects on competing reactions, particularly when examined in intramolecular competition experiments where interpretation requires very few simplifying assumptions. The zero-point energy differences reflect changes of isotope sensitive vibrational properties, and both α- and β-secondary deuterium isotope effects are related to the sp 3 → sp 2 hybridization changes that accompany bond cleavage. Deuterium substitution three bonds or more removed from the bond broken also gives rise to isotope effects, but their origin is less easily interpreted. The magnitude and variation of the observed effects depend not only on zero-point energy differences; a number of additional factors play a role. The influence of the critical energy, the excess energy, the size of the reactant, and the presence of competing reactions can be rationalized within a simple, qualitative RRKM framework. The distinction between kinetic and thermodynamic isotope effects is not always obvious.

Study of interacting mechanism of amino acid and Alzheimer's drug using vibrational techniques and computational method

The present work is undertaken to investigate the molecular interaction between Memantine (Alzheimer's drug) and DL-Alanine (amino acid) using DFT and vibrational spectroscopic methods, in particular, Fourier Transform Infrared Spectroscopy (FTIR) and Raman techniques. The DFT calculations of these molecules are carried out using the B3LYP/6–311 ++ G (d, p) level of theory. The experimental FTIR and Raman spectra of the molecules are compared to the respective DFT computed wavenumbers. A satisfactory agreement is obtained between experimental and computed wavenumbers. Further, HOMO-LUMO energy gap, Natural Bond Orbital (NBO) analysis, total energy, zero-point vibrational energy, Molecular Electrostatic Potential (MEP), chemical potential, hardness, ionization energy, global electrophilicity index, dipole moments, and first-order hyperpolarizabilities of the interacting state are reported and compared to the respective parameters of the individual states. The NBO analysis of the molecules indicates the transfer of charge between DL-Alanine and Memantine through NH•••O intermolecular hydrogen bonds. The molecular docking studies of the molecules are performed to investigate the binding affinity of the ligand with the 6DG7 receptor.

Tritium adsorption and desorption on/from nuclear graphite edge by a first-principles study

The removal of tritium from irradiated nuclear graphite is one of the key targets of nuclear graphite decontamination. Here, we employ first principle density functional theory (DFT) to study its adsorption and molecular desorption on the most common edges and their reconstructions. The calculated adsorption energy ranges from −2.6 to - 5 eV, depending on the edge structure and the hydrogenation level, and are much larger than on the bulk of graphite. The hydrogenation level increases with the increase of hydrogen partial pressure, and drops rapidly at high temperature. The pathways to fully saturated edges are then determined for each edge variant and the activation energy (Eac) for molecular desorption computed by properly accounting for vibrational zero-point energy corrections (ΔEZPE). Our results showed that, there are three different stages for the desorption of hydrogen isotopes from nuclear graphite, namely stage 1 (200–300 °C), stage 2 (500–700 °C), stage 3 (1000–1100 °C). Our results can provide a theoretical basis for the tritium removal experiment from nuclear graphite.

DFT Investigation of Hydrogen Atom Abstraction from NHC-Boranes by Methyl, Ethyl and Cyanomethyl Radicals-Composition and Correlation Analysis of Kinetic Barriers.

Understanding the hydrogen atom abstraction (HAA) reactions of N-heterocyclic carbene (NHC)-boranes is essential for extending the practical applications of boron chemistry. In this study, density functional theory (DFT) computations were performed for the HAA reactions of a series of NHC-boranes attacked by •CH2CN, Me• and Et• radicals. Using the computed data, we investigated the correlations of the activation and free energy barriers with their components, including the intrinsic barrier, the thermal contribution of the thermodynamic reaction energy to the kinetic barriers, the activation Gibbs free energy correction and the activation zero-point vibrational energy correction. Furthermore, to describe the dependence of the activation and free energy barriers on the thermodynamic reaction energy or reaction Gibbs free energy, we used a three-variable linear model, which was demonstrated to be more precise than the two-variable Evans–Polanyi linear free energy model and more succinct than the three-variable Marcus-theory-based nonlinear HAA model. The present work provides not only a more thorough understanding of the compositions of the barriers to the HAA reactions of NHC-boranes and the HAA reactivities of the substrates but also fresh insights into the suitability of various models for describing the relationships between the kinetic and thermodynamic physical quantities.

Torsional States and Tunneling Probability in HOSOH, DOSOD, and DOSOH Molecules Analyzed at the CBS Limit.

Torsional vibrations of a sulfoxylic acid molecule (HOSOH) and its two deuterated isotopologues were analyzed for the first time. Harmonic and anharmonic calculations of the vibrational frequencies of the trans- and cis-conformers were performed. More rigorous consideration of the torsional vibrations was made based on 2D potential energy and kinematic coefficient surface calculations. These calculations were made at the MP2/cc-pVTZ and MP2/cc-pVQZ levels of theory, and then the results were extrapolated to the complete basis set limit. The 2D surface of the zero-point vibrational energy of a sulfoxylic acid molecule was calculated at the MP2/cc-pVTZ level of theory in anharmonic approximation and taken into account. The energies of the torsional states were found by numerical solution of the vibrational Schrödinger equation of the restricted dimensionality using the Fourier method. 2D surfaces of the dipole moment components were calculated too. Using all these data, the torsional IR spectra of the trans- and cis-conformers of the HOSOH, DOSOD, and DOSOH molecules were also modeled at different temperatures.

Full-quantum descriptions of molecular systems from constrained nuclear-electronic orbital density functional theory.

We develop a full-quantum formulation of constrained nuclear-electronic orbital density functional theory (cNEO-DFT). This formulation deviates from the conventional Born-Oppenheimer framework, and all nuclei and electrons are treated on an equal footing within the molecular orbital picture. Compared to the conventional DFT, the ground state energy in full-quantum cNEO-DFT inherently includes all vibrational zero-point energies. We also derived and implemented the analytic gradient of the full-quantum cNEO-DFT energy with respect to the quantum nuclear expectation positions. With the analytic gradient, the geometry optimizations are performed, which naturally include the nuclear quantum effects and describe the geometric isotope effects. The full-quantum cNEO-DFT is tested on a series of small molecules and the transition states of two hydrogen transfer reactions. The results are compared with those from conventional DFT, DFT-VPT2, and NEO-DFT with only key protons treated quantum mechanically. It is found that the nuclear quantum effects have notable impacts on molecular equilibrium geometries and transition state geometries. The full-quantum cNEO-DFT can be a promising method for describing the nuclear quantum effects in many chemical processes.

A matrix completion algorithm to recover modes orthogonal to the minimum energy path in chemical reactions.

Structured statistical methods are promising for recovering or completing information from noisy and incomplete data with high fidelity. In particular, matrix completion exploits underlying structural properties such as rank or sparsity. Our objective is to employ matrix completion to reduce computational effort associated with the calculation of multiple quantum chemical Hessians, which are necessary for identification of temperature-dependent free energy maxima under canonical variational transition state theory (VTST). We demonstrate proof-of-principle of an algebraic variety-based matrix completion method for recovering missing elements in a matrix of transverse Hessian eigenvalues constituting the minimum energy path (MEP) of a reaction. The algorithm, named harmonic variety-based matrix completion (HVMC), utilizes the fact that the points lying on the MEP of a reaction step constitute an algebraic variety in the reaction path Hamiltonian representation. We demonstrate that, with as low as 30% random sampling of matrix elements for the largest system in our test set (46 atoms), the complete matrix of eigenvalues can be recovered. We further establish algorithm performance for VTST rate calculations by quantifying errors in zero-point energies and vibrational free energies. Motivated by this success, we outline next steps toward developing a practical HVMC algorithm, which utilizes a gradient-based sampling protocol for low-cost VTST rate computations.

Accessible approaches for vibrational zero point energy calculation of organoboron compounds

In this paper, two empirical approaches were used to calculate vibrational zero-point energies (ZPEs) of organoboron compounds. Firstly, the contribution of boron atom has been determined and incorporated in the Schulman and Disch empirical formula. For the second approach, the bond contributions of BH, BC, BO, BCl, BN, BF and BB were determined and introduced to our empirical formula already established. A comparison of results obtained for 120 organoboron compounds with the reported available values and those obtained using HF/6-31G* method, indicates the reliability of the empirical employed approaches to reproduce vibrational zero-point energies of organoboron compounds.

Heavy-Atom Tunneling in Semibullvalenes: How Driving Force, Substituents, and Environment Influence the Tunneling Rates.

The Cope rearrangement of selectively deuterated isotopomers of 1,5‐dimethylsemibullvalene 2 a and 3,7‐dicyano‐1,5‐dimethylsemibullvalene 2 b were studied in cryogenic matrices. In both semibullvalenes the Cope rearrangement is governed by heavy‐atom tunneling. The driving force for the rearrangements is the small difference in the zero‐point vibrational energies of the isotopomers. To evaluate the effect of the driving force on the tunneling probability in 2 a and 2 b, two different pairs of isotopomers were studied for each of the semibullvalenes. The reaction rates for the rearrangement of 2 b in cryogenic matrices were found to be smaller than the ones of 2 a under similar conditions, whereas differences in the driving force do not influence the rates. Small curvature tunneling (SCT) calculations suggest that the reduced tunneling rate of 2 b compared to that of 2 a results from a change in the shape of the potential energy barrier. The tunneling probability of the semibullvalenes strongly depends on the matrix environment; however, for 2 a in a qualitatively different way than for 2 b.