Harmonic Vibrational Frequency Calculations Research Articles

The impact of solvation on the structure and electric field strength in Li+GlyGly complexes.

To scrutinise the impact of electric fields on the structure and vibrations of biomolecules in the presence of water, we study the sequential solvation of lithium diglycine up to three water molecules with cryogenic infrared action spectroscopy. Conformer-specific IR-IR spectroscopy and H2O/D2O isotopic substitution experiments provide most of the information required to decipher the structure of the observed conformers. Additional confirmation is provided by scaled harmonic vibrational frequency calculations using MP2 and DFT. The first water molecule is shown to bind to the Li+ ion, which weakens the electric field experienced by the peptide and as a consequence, also the strength of an internal NH⋯NH2 hydrogen bond in the diglycine backbone. The strength of this hydrogen bond decreases approximately linearly with the number of water molecules as a result of the decreasing electric field strength and coincides with an increase in the number of conformers observed in our spectra. The addition of two water molecules is already sufficient to change the preferred conformation of the peptide backbone, allowing for Li+ coordination to the lone pair of the terminal amine group.

Analytic gradients for relativistic exact-two-component equation-of-motion coupled-cluster singles and doubles method.

A first implementation of analytic gradients for spinor-based relativistic equation-of-motion coupled-cluster singles and doubles method using an exact two-component Hamiltonian augmented with atomic mean-field spin-orbit integrals is reported. To demonstrate its applicability, we present calculations of equilibrium structures and harmonic vibrational frequencies for the electronic ground and excited states of the radium mono-amide molecule (RaNH2) and the radium mono-methoxide molecule (RaOCH3). Spin-orbit coupling is shown to quench Jahn-Teller effects in the first excited state of RaOCH3, resulting in a C3v equilibrium structure. The calculations also show that the radium atoms in these molecules serve as efficient optical cycling centers.

Ab initio investigation of the competition of pnicogen, halogen, and hydrogen bonds resulting from the interactions between cyanophosphine and hypohalous acids.

The complexes formed as a result of the interactions between cyanophosphine (CP, H2PCN) and hypohalous acid molecules (HOX, X = F, Cl, Br, and I) were studied by employing ab initio computations conducted at the MP2/aug-cc-pVTZ level. Three types of complexes were acquired (I, II, and III) as a result of the (O∙∙∙P) pnicogen bond, the (N∙∙∙H) hydrogen bond, and the (N∙∙∙X) halogen bond interaction, respectively. The results of harmonic vibrational frequency calculations with no imaginary frequencies confirmed the structures as minima. In addition, given the interaction energy of the complexes, hydrogen bond complexes of structure II have the highest stability compared to other structures. In all studied complexes, the strength of the interactions depended on the electronegativity of the halogen atoms. The characteristics and nature of the whole three types of complexes were examined and evaluated with natural bond orbital (NBO), atom in molecules (AIM), molecular electrostatic potential (MEP) maps, non-covalent interaction (NCI) index, and electron density difference (EDD) analyses. The optimization of all complexes and corresponding monomers was conducted through the ab initio method, employing the MP2 level along with the aug/cc-pVTZ basis set for all atoms, except for the iodine (I) atom, for which the aug-cc-pVTZ (PP) basis set was employed. Subsequent frequency calculations were executed to ascertain the minimum energy state of the complexes at the MP2 level and the aug/cc-pVTZ basis set, utilizing Gaussian09 software. The MEP maps of the monomers were generated using the analysis-surface suite (WFA-SAS) software package. To probe the orbital interactions within the studied complexes, NBO analysis was performed employing NBO software. The assessment of bond nature, topological features, and electron density values at critical points for the studied complexes was undertaken using AIMAll software. The NCI index was derived utilizing Multiwfn software, and its three-dimensional representation was rendered using VMD software.

Quantitative Structure-Activity Relationship (QSAR) Modelling of Indomethacin Derivatives Using Regression Analysis.

Indomethacin is a non-steroidal anti-inflammatory drug (NSAID) used for medication to reduce fever, spondylitis, or shoulder pain. It mainly works by the inhibition of prostaglandins, the endogenous signaling molecules. Fifteen indomethacin derivatives have been analyzed in relation to their physicochemical and molecular properties. Two-dimensional (2D) structures of fifteen indomethacin derivatives were drawn using the ACD Lab Chem Sketch version. Most of the topological parameters, such as wiener index (W), mean wiener index (Wa), Balaban indices (J), Balaban centric index (BAC), and molecular connectivity (χ), were calculated by using E Dragon software. The most common molecular file formats accepted in E-Dragon software were SMILES notations created online by Babel software and 2D structures of various derivatives, which were converted into 3D optimized structures using online CORINA, provided by Molecular Networks GMBH. 3D structures of compounds were also drawn on Gauss View software for calculations of various density functional theory (DFT) based quantum chemical descriptors, such as total energy (TE), softness (S), hardness (η), chemical potential (μ), highest occupied molecular orbital energy (HOMO), and lowest unoccupied molecular orbital energy (LUMO). All species were fully optimized in the gas phase with a 6-31+G* basis set. The harmonic vibrational frequency calculations were used to confirm that the optimized structures were minima, as characterized by positive vibrational frequencies. Combinations of various descriptors, such as D, ID, IOR, Log P, Mr, Mv, Mw, Pc, BAC, Pz, St, W, Wa, 0χ, 1χ, 2χ,3χ,4χ, 5χ, and Xeq have been found to be significant for modeling of activity. QSAR model no. 2: pIC50= -20.605 (±6.600) IOR - 0.747 (±0.454) I1 -5.083 (±3.478) Xeq + 51.647 optimized with empirical parameters with high statistical quality (R= 0.921, R2=0.848) was found to be the best model obtained. The QSAR model obtained suggests that substituents with a lesser value of the index of refraction and less electronegative groups were favourable for the activity, whereas indomethacin derivatives with a CH2CH2NHCONH (CH2)3ONO2 group at R1 position were unfavourable for the activity. The results were critically discussed based on regression data and cross-validation techniques. Pogliani factor Q and the results of the LOO (leave-one-out) method confirmed the reliability and predictability of the proposed models that could be highly beneficial for the future designing of new analogues with higher potency.

Molecular Geometries and Vibrational Contributions to Reaction Thermochemistry Are Surprisingly Insensitive to the Choice of Basis Sets.

Calculation of molecular geometries and harmonic vibrational frequencies are pre-requisites for thermochemistry calculations. Contrary to conventional wisdom, this paper demonstrates that quantum chemical predictions of the thermochemistry of many gas and solution phase chemical reactions appear to be very insensitive to the choice of basis sets. For a large test set of 80 diverse organic and transition-metal-containing reactions, variations in reaction free energy based on geometries and frequencies calculated using a variety of double and triple-zeta basis sets from the Pople, Jensen, Ahlrichs, and Dunning families are typically less than 4 kJ mol-1, especially when the quasiharmonic oscillator correction is applied to mitigate the effects of low-frequency modes. Our analysis indicates that for many organic molecules and their transition states, high-level revDSD-PBEP86-D4 and DLPNO-CCSD(T)/(aug-)cc-pVTZ single-point energies usually vary by less than 2 kJ mol-1 on density functional theory geometries optimized using basis sets ranging from 6-31+G(d) to aug-pcseg-2 and aug-cc-pVTZ. In cases where these single-point energies vary significantly, indicating sensitivity of molecular geometries to the choice of basis set, there is often substantial cancellation of errors when the reaction energy or barrier is calculated. The study concludes that the choice of basis set for molecular geometry and frequencies, particularly those considered in this study, is not critical for the accuracy of thermochemistry calculations in the gas or solution phase.

Design of derivatives of FOX-7-based new four-member heterocyclic insensitive high energy density molecules: a theoretical prospectives

Theoretical analysis of the novel, insensitive and high-energy density compounds based on the 1,1-dinitro-2,2-diamino-ethylene (FOX-7) moiety is presented here. In order to better serve as a prospective insensitive, high-energy molecule, a few novel heterocyclic four-member compounds were developed. The atoms in molecule (AIM) calculations have been used to estimate the stability of the C-NO2 bond as well as the covalent nature of the bonds. Using the Gaussian-16 quantum chemistry software, the electronic structure computations have been retrieved at the B3LYP level of theory with an aug-ccpVDZ basis set. It was discussed the impact sensitivity, thermal stability, detonation characteristics, harmonic vibrational frequency calculations, natural bond orbital calculations, the optimised structure of these molecules and more. The crystal density, activation energy for the nitro (C-NO2) to nitrito (C-ONO) transformation during the first stage of thermal breakdown, and the C-NO2 bond dissociation energy with BSSE correction of these molecules have been comprehensively investigated. These newly modelled compounds have been discovered to exhibit comparable detonation characteristics to those of FOX-7, which implies that they should be synthesised in a lab by experienced experimentalists.

Geometry optimizations with spinor-based relativistic coupled-cluster theory.

Development of analytic gradients for relativistic coupled-cluster singles and doubles augmented with a non-iterative triples [CCSD(T)] method using an all-electron exact two-component Hamiltonian with atomic mean-field spin-orbit integrals (X2CAMF) is reported. This enables efficient CC geometry optimizations with spin-orbit coupling included in orbitals. The applicability of the implementation is demonstrated using benchmark X2CAMF-CCSD(T) calculations of equilibrium structures and harmonic vibrational frequencies for methyl halides, CH3X (X = Br, I, and At), as well as calculations of rotational constants and infrared spectrum for RaSH+, a radioactive molecular ion of interest to spectroscopic study.

The conformational landscape of myrtenol: The structure of the hydroxymethyl group and its robustness upon hydration.

The conformational landscape of myrtenol (2-pinen-10-ol) and its robustness upon hydration were investigated theoretically and experimentally by employing a synergic combination of quantum chemical calculations and Fourier transform microwave spectroscopy coupled to a supersonic jet expansion. Relaxed potential energy surfaces have been carried out, and the lowest energy conformers of the monomer were found to be associated with different geometries of the hydroxymethyl group from those previously reported [Sedo et al., J. Mol. Spectrosc. 356, 32 (2019)]. Geometry optimizations and harmonic vibrational frequency calculations allowed characterization of the equilibrium structure of the possible conformers of myrtenol. Among the nine predicted structures, four have been observed, analyzed, and identified. The controversy on the geometry was solved with the deuteration of the hydroxyl group, which led to the determination of substitution (rs) geometry, in agreement with the present theoretical results. Interestingly, the four observed conformers exhibit the same orientation of OH as in the allyl alcohol molecule. Furthermore, hydrogen bonding linking myrtenol to water was studied. One monohydrate has been observed and identified. Non-covalent interactions and natural bond orbital analysis were performed to depict the interactions responsible for the stabilization of the observed structure. We conclude that the structure of the hydroxymethyl group is robust and does not change upon hydration.

Second-Order Analytic Derivatives for XYG3 Type of Doubly Hybrid Density Functionals: Theory, Implementation, and Application to Harmonic and Anharmonic Vibrational Frequency Calculations.

Analytic derivative methods in quantum chemistry are powerful tools for the calculation of molecular properties and simulation of chemical systems. While the derivatives of the well-established B2PLYP type of doubly hybrid (DH) density functionals can be generated by a straightforward combination between the Kohn-Sham density functional and the second-order perturbation theory (PT2), both of these two contributions have to be considered nonvariationally for the XYG3 type of DH functionals (xDHs). A total Lagrangian that includes both parts is therefore needed for the corresponding Z-vector equations for the first-order derivatives of xDHs. Starting from the differentiation of the Z-vector equations, a theory for the second-order derivatives for xDHs is developed here and is applied to the molecular harmonic and anharmonic vibrational frequency calculations. The results are generally of high quality, as compared to the well-established experimental and CCSD(T) counterparts. Further investigations on the fundamental frequency predictions prove the capability of the xDH functionals for an accurate calculation of spectroscopic properties for a wide range of medium-size molecules.

Single-Point Hessian Calculations for Improved Vibrational Frequencies and Rigid-Rotor-Harmonic-Oscillator Thermodynamics.

The calculation of harmonic vibrational frequencies (HVF) to interpret infrared (IR) spectra and to convert molecular energies to free energies is one of the essential steps in computational chemistry. A prerequisite for accurate thermostatistics so far was to optimize the molecular input structures in order to avoid imaginary frequencies, which inevitably leads to changes in the geometry if different theoretical levels are applied for geometry optimization and frequency calculations. In this work, we propose a new method termed single-point Hessian (SPH) for the computation of HVF and thermodynamic contributions to the free energy within the modified rigid-rotor-harmonic-oscillator approximation for general nonequilibrium molecular geometries. The key ingredient is the application of a biasing potential given as Gaussian functions expressed with the root-mean-square-deviation (RMSD) in Cartesian space in order to retain the initial geometry. The theory derived herein is generally applicable to quantum mechanical (QM), semiempirical QM, and force-field (FF) methods. Besides a detailed description of the underlying theory including the important back-correction of the biased HVF, the SPH approach is tested for reaction paths, molecular dynamics snapshots of crambin, and supramolecular association free energies in comparison to high-level density functional theory (DFT) values. Furthermore, the effect on IR spectra is investigated for organic dimers and transition-metal complexes revealing improved spectra at low theoretical levels. On average, DFT reference free energies are better reproduced by the newly developed SPH scheme than by conventional calculations on freely optimized geometries or without any relaxation.

Computational and infrared spectroscopic investigations of N-substituted carbazoles.

The carbazole moiety is a commonly identified structural motif in the high-molecular-weight components of petroleum, known as asphaltenes. Detailed characterization of carbazoles is important for understanding the structure of asphaltenes and addressing challenges in the areas of heavy oil recovery, transportation, upgrading, and oil spills, arising from asphaltene properties and composition. In this work we study carbazole and the four N-substituted carbazoles 9-methylcarbazole, 9-ethylcarbazole, 9-vinylcarbazole and 9-phenylcarbazole. Experimental far- and mid-infrared spectra of these five carbazoles are measured using transmission and photoacoustic techniques. The molecular structures of the monomers and the respective dimers, optimized at the ωB97X-D/6-311++G(d,p) level of the density functional theory (DFT), are subjected to harmonic vibrational frequency calculations. The effect of changing substituents on the N-H bond, π-π stacking distances, and angles between monomers within the dimers, in addition to intermolecular interactions, is investigated. Noncovalent interaction analysis is employed to highlight the areas of attractive and repulsive interactions in the dimers. Thermochemistry calculations show that the formation of dimers of all carbazoles is spontaneous at 298 K. Comparison of the calculated vibrational spectra of these compounds with experimental spectra indicates that the existence of both monomers and dimers must be invoked to account for the observed bands in the infrared spectra. Excellent correlations between the experimentally-determined and calculated harmonic vibrational energies are obtained, with an experimental-to-calculated scaling factor of 0.95-0.96. These findings highlight the coupled computational-experimental approach for the interpretation of vibrational spectra and are essential for improving the spectroscopic characterization of N-substituted carbazoles.

Visible-Light-Driven Anti-Markovnikov Hydrocarboxylation of Acrylates and Styrenes with CO 2

Light-driven carbon dioxide (CO2) capture and utilization is one of the most fundamental reactions in Nature. Herein, we report the first visible-light-driven photocatalyst-free hydrocarboxylation ...

Efficient Computation of Free Energy Contributions for Association Reactions of Large Molecules.

Modern density functional theory (DFT) methods are capable of providing accurate association energies for supramolecular systems and even protein-ligand complexes. However, the calculation of the essential harmonic vibrational frequencies needed to obtain free energies is often too computationally demanding. In this work, the corresponding thermostatistical contributions are computed in the well-established (modified) rigid-rotor-harmonic-oscillator approximation with structures and frequencies taken from low-cost quantum chemical methods, namely, GFN2-xTB and PM6-D3H4. Additionally, a recently developed new general force field (GFN-FF) is tested for this purpose. DFT reference values for 59 complexes composed of three standard noncovalent and supramolecular benchmark sets (S22, L7, and S30L) are used in the evaluation. Overall, the accuracy of the low-cost methods is remarkable with typical deviations of only 0.5-2 kcal mol-1 (5-10%) from the DFT reference values. In particular, the performance of the GFN-FF is promising considering the acceleration of 5 and 2-3 orders of magnitude compared to DFT and GFN2-xTB, respectively. This opens new perspectives for computing thermodynamic properties of, e.g., biomacromolecules as shown, for example, for the binding of retinol and rivaroxaban in protein complexes consisting of ≤4700 atoms.

The Moving-Grid Effect in the Harmonic Vibrational Frequency Calculations with Numeric Atom-Centered Orbitals.

When using atom-centered integration grids, the portion of the grid that belongs to a certain atom also moves when this atom is displaced. In the paper, we investigate the moving-grid effect in the calculation of the harmonic vibrational frequencies when using all-electron full-potential numeric atomic-centered orbitals as the basis set. We find that, unlike the first-order derivative (i.e., forces), the moving-grid effect plays an essential role for the second-order derivatives (i.e., vibrational frequencies). Further analysis reveals that the predominantly diagonal force constant terms are affected, which can be bypassed efficiently by invoking translational symmetry. Our approaches have been demonstrated in both finite (molecules) and extended (periodic) systems.

Uncontracted core Pople basis sets in vibrational frequency calculations

AbstractThe effects that uncontracting the core 1s basis functions in the Pople basis sets have on the calculation of harmonic vibrational frequencies, scaling factors, and anharmonic frequencies are examined for a selection of hybrid and meta‐hybrid density functional theory methods across a wide range of molecules. Median improvements of around half a wavenumber indicate that uncontracting the core functions provides modest improvements for harmonic calculations. The importance of these core functions is found to increase when using meta‐hybrid or anharmonic methods. The core functions are also found to be particularly important for several types of vibrational coordinate, including some carbonyl and carbon‐nitrogen stretching modes, where interaction between the uncontracted 1s functions and triple‐ζ 2s functions appear to play a significant role. Extra core functions are also particularly important for anharmonic second‐order perturbation theory calculations involving alkyne molecule bending modes, where individual transitions can change by as much as 230 wavenumbers.

Hydrogen bonds in crystalline D-alanine: diffraction and spectroscopic evidence for differences between enantiomers

Enantiomeric amino acids have specific physiological functions in complex biological systems. Systematic studies focusing on the solid-state properties of d-amino acids are, however, still limited. To shed light on this field, structural and spectroscopic studies of d-alanine using neutron powder diffraction, polarized Raman scattering and ab initio calculations of harmonic vibrational frequencies were carried out. Clear changes in the number of vibrational modes are observed as a function of temperature, which can be directly connected to variations of the N-D bond lengths. These results reveal dissimilarities in the structural properties of d-alanine compared with l-alanine.

Harmonic Vibrational Frequencies: Approximate Global Scaling Factors for TPSS, M06, and M11 Functional Families Using Several Common Basis Sets.

We propose new approximate global multiplicative scaling factors for the DFT calculation of ground state harmonic vibrational frequencies using functionals from the TPSS, M06, and M11 functional families with standard correlation consistent cc-pVxZ and aug-cc-pVxZ (x = D, T, and Q), 6-311G split valence family, Sadlej and Sapporo polarized triple-ζ basis sets. Results for B3LYP, CAM-B3LYP, B3PW91, PBE, and PBE0 functionals with these basis sets are also reported. A total of 99 harmonic frequencies were calculated for 26 gas-phase organic and nonorganic molecules typically found in detonated solid propellant residue. Our proposed approximate multiplicative scaling factors are determined using a least-squares approach comparing the computed harmonic frequencies to experimental counterparts well established in the scientific literature. A comparison of our work to previously published global scaling factors is made to verify method reliability and the applicability of our molecular test set.

Implementation of Molecular Gradients for Local Hybrid Density Functionals Using Seminumerical Integration Techniques.

We present the first implementation of the derivative of the local hybrid exchange-correlation energy with respect to the displacement of nuclei in a Gaussian-type atomic basis set. This extends a recent efficient implementation of local hybrid functionals for self-consistent Kohn-Sham and linear-response TDDFT calculations into the TURBOMOLE program package. In contrast to seminumerical schemes for global exact-exchange admixtures and to the related SCF and TDDFT implementations of local hybrid functionals, additional analytical integrals have to be evaluated at each grid point in the case of molecular gradients. The overall efficiency of the present scheme is improved through prescreening with the density matrix (P-junctions), as well as with spherical overlap estimates (S-junctions). Comparative timings for structure optimizations with local vs global hybrid functionals are discussed while gauging the accuracy for S- and P-junctions using varying thresholds. Local hybrids are furthermore assessed for structure optimization and harmonic vibrational frequency calculations (using numerical second derivatives) of a selection of test systems, comparing with experimental data and some widely used density functionals.

DFT studies on the vibrational and electronic spectra of acetylsalicylic acid

The following is a theoretical and experimental study on the vibrational and electronic properties of acetylsalicylic acid (ASA). Vibrational information was obtained by FT-IR and Raman spectroscopy which agree well with harmonic vibrational frequency calculations. The calculations were carried out using density functional theory B3LYP methods with 6-311G** and LANL2DZ basis sets. The vibrational assignments were calculated by Gaussview. Absorption UV-Vis experiments of ASA reveal three maximum peaks at 203, 224 and 277 nm, which are in agreement with calculated electronic transitions using TD-B3LYP/6-311G**.

A combined ab initio and Franck–Condon simulation study of the photodetachment spectra of the HCBr− anion

Geometry optimization and harmonic vibrational frequency calculations have been performed on the X˜2A″ state of HCBr−, and X˜1A′ and a˜3A″ states of HCBr. The term energy and electron affinity of HCBr were calculated and extrapolated to the complete basis set limit. The Duschinsky matrix and displacement vector were calculated at the CCSD(T)/aug-cc-pVQZ level. The normal mode mixing effects played a minor role and can be neglected for the HCBr(X˜1A′)–HCBr−(X˜2A″) photodetachment. Spectral simulations involved the HCBr(X˜1A′)–HCBr−(X˜2A″) and HCBr(a˜3A″)–HCBr−(X˜2A″) photodetachments were carried out on HCBr− at CCSD(T)/aug-cc-pVQZ level, respectively.