Rovibrational momentum densities of diatomic molecules in the rigid rotor-harmonic oscillator approximation

The rigid rotor-harmonic oscillator model in the momentum representation is used to examine the rovibrational momentum density of a diatomic molecule. The effects on this function of rotational and vibrational excitation, thermal averaging, and nuclear spin statistics are exhibited in calculations on N₂ and thehydrogen halides, and a brief comparison with electron momentum densities is made.     

Calculation of argon trimer rovibrational spectrum

Rovibrational spectra of Ar3 are computed for total angular momenta up to J=6 using row-orthonormal hyperspherical coordinates and an expansion of the wave function on hyperspherical harmonics. The sensitivity of the spectra to the two-body potential and to the three-body corrections is analyzed. First, the best available semiempirical pair potential (HFDID1) is compared with our recent ab initio two-body potential. The ab initio vibrational energies are typically 1-2 cm-1 higher than the semiempirical ones, which is related to the slightly larger dissociation energy of the semiempirical potential. Then, the Axilrod-Teller asymptotic expansion of the three-body correction is compared with our newly developed ab initio three-body potential. The difference is found smaller than 0.3 cm-1. In addition, we define approximate quantum numbers to describe the vibration and rotation of the system. The vibration is represented by a hyper-radial mode and a two-degree-of-freedom hyperangular mode, including a vibrational angular momentum defined in an Eckart frame. The rotation is described by the total angular momentum quantum number, its projection on the axis perpendicular to the molecular plane, and a hyperangular internal momentum quantum number, related to the vibrational angular momentum by a transformation between Eckart and principal-axes-of-inertia frames. These quantum numbers provide a qualitative understanding of the spectra and, in particular, of the impact of the nuclear permutational symmetry of the system (bosonic with zero nuclear spin). Rotational constants are extracted from the spectra and are shown to be accurate only for the ground hyperangular mode.     

Momentum density and molecular geometry. Bent BH 2 − and linear BH 2 +

Based on a special form of the molecular virial theorem, the recently proposed method of momentum density for interatomic interactions is here applied to the problem of molecular geometry. Two molecules BH ₂ ^– and BH ₂ ⁺ , which have the same nuclear framework but favor respectively bent and linear conformations, are comparatively studied. Using an approximate Hartree-Fock momentum density, the total molecular energy (including the nuclear repulsion) is partitioned into orbital components, and a geometry correlation diagram is derived. An atom-bond partitioning of the total energy is also examined based on the one- and two-center decomposition of the momentum density.     

Anharmonic Vibrational Signatures of DNA Bases and Watson-Crick Base Pairs

Changes of molecular structure and associated charge distributions, and changes of anharmonic vibrational parameters from DNA base monomers to the Watson-Crick base pairs, have been investigated at the density functional theory level. Through examination of the NH2, N H, and C=O stretching vibrational modes that are involved in the multiple H-bonds in the base pairs, sensitivity of their diagonal and off-diagonal anharmonicities, as well as anharmonic vibrational couplings, to the structure change are predicted. Our results reveal the intrinsic connection between the anharmonic vibrational potentials, H-bonding, and electrostatic interactions in DNA bases.     

Zero-point vibrational effects on proton shieldings: functional-group contributions from ab initio calculations.

We investigate the effects of zero-point vibrational motion on the nuclear magnetic shielding constants of a large number of organic molecules. The vibrational corrections include anharmonic contributions from the potential energy surface and harmonic contributions from the curvature of the property surface. Particular attention is paid to vibrational corrections to hydrogen shielding constants where we show that vibrational corrections may be substantial, ranging from about +0.50 to -0.70 ppm, and thus demonstrating that ignoring these effects may give errors in the chemical shifts by more than 1 ppm in certain extreme cases. These effects can therefore not be neglected when comparing calculated results with experiment, not even for the chemical shifts. However, we also demonstrate that the vibrational corrections to the hydrogen shieldings are to a large extent transferable from one molecule to another. We have tabulated functional vibrational corrections to the hydrogen shieldings, based on results for more than 35 molecules. Unfortunately, no similar transferability has been observed for the vibrational corrections to shielding constants of other nuclei such as carbon, nitrogen, or oxygen.     

Spin‐orbit ZORA and four‐component Dirac–Coulomb estimation of relativistic corrections to isotropic nuclear shieldings and chemical shifts of noble gas dimers

Hartree–Fock and density functional theory with the hybrid B3LYP and general gradient KT2 exchange‐correlation functionals were used for nonrelativistic and relativistic nuclear magnetic shielding calculations of helium, neon, argon, krypton, and xenon dimers and free atoms. Relativistic corrections were calculated with the scalar and spin‐orbit zeroth‐order regular approximation Hamiltonian in combination with the large Slater‐type basis set QZ4P as well as with the four‐component Dirac–Coulomb Hamiltonian using Dyall's acv4z basis sets. The relativistic corrections to the nuclear magnetic shieldings and chemical shifts are combined with nonrelativistic coupled cluster singles and doubles with noniterative triple excitations [CCSD(T)] calculations using the very large polarization‐consistent basis sets aug‐pcSseg‐4 for He, Ne and Ar, aug‐pcSseg‐3 for Kr, and the AQZP basis set for Xe. For the dimers also, zero‐point vibrational (ZPV) corrections are obtained at the CCSD(T) level with the same basis sets were added. Best estimates of the dimer chemical shifts are generated from these nuclear magnetic shieldings and the relative importance of electron correlation, ZPV, and relativistic corrections for the shieldings and chemical shifts is analyzed. © 2015 Wiley Periodicals, Inc.     

Non-muffin-tin MS Xα total energies for H2, C2, N2 and CO

NMT (non-muffin-tin) MS Xα calculations for the ground state potential curves are reported for the molecules H₂, C₂, N₂, and CO. These calculations include corrections linear and second order in the NMT charge density and show great improvement over the MT (muffin-tin) curves. With these corrections, somewhat better agreement with experiment is also found. A comparison is made between tne Xα and the local spin density (LSD approximations for the H₂ and CO molecules.     

Theoretical characterization of hydrogen pentoxide,H2O5

Following our investigations on hydrogen polyoxides, herein we employed coupled cluster theory in conjunction with Dunning's correlation consistent basis sets and density functional theory to study HOOOOOH (H₂O₅). The infrared spectra of H₂O₅ and its three deuterated isotopologues, as well as those of the five single‐substituted ¹⁸O isotopologues are discussed in detail. Internal valence coordinates were employed to classify the vibrational modes. The Raman activity is reported to help in the identification of hydrogen pentoxide. The suggested enthalpy of formation is ΔH_f,298° (HOOOOH) = 1.4 ± 1.5 kcal/mol. This value includes corrections for relativistic and core‐valence effects as well as anharmonic corrections to Zero‐point energy corrections. © 2013 Wiley Periodicals, Inc.     

Zero-point vibrational corrections to isotropic hyperfine coupling constants in polyatomic molecules

The present work addresses isotropic hyperfine coupling constants in polyatomic systems with a particular emphasis on a largely neglected, but a posteriori significant, effect, namely zero-point vibrational corrections. Using the density functional restricted-unrestricted approach, the zero-point vibrational corrections are evaluated for the allyl radical and four of its derivatives. In addition for establishing the numerical size of the zero-point vibrational corrections to the isotropic hyperfine coupling constants, we present simple guidelines useful for identifying hydrogens for which such corrections are significant. Based on our findings, we critically re-examine the computational procedures used for the determination of hyperfine coupling constants in general as well as the practice of using experimental hyperfine coupling constants as reference data when benchmarking and optimizing exchange-correlation functionals and basis sets for such calculations.     

Hydrogen-bonded and van der Waals complexes studied by a Gaussian density functional method. The case of (HF)2, ArHCl and Ar2HCl systems

Summary Linear combination of Gaussian-type orbitals local spin density calculations (LCGTO-LSD) have been performed to further test the applicability to the method of hydrogen-bonded and van der Waals systems. The calculated minimum energy structures and binding energies for the (HF)₂, ArHCl and Ar₂HCl complexes are presented. In addition, the harmonic vibrational frequencies are reported for (HF)₂. The results show that by using nonlocal corrections and increasing the number of radial points in the grid, the calculated parameters are close to experimental ones and provide some encouraging evidence for the reliable use of density functional theory for these complex systems.     

Nonadiabatic Corrections To The Vibrational Energies Of The Hydrogen Molecule

The nonadiabatic corrections to the vibrational levels of H₂ and D₂ are evaluated for the X¹∑⁺_g state by taking into account the coupling with the E, F¹∑⁺_g electronic state. The computed corrections diminish the existing discrepancy between the experimental and theoretical vibrational quanta by about 20%.     

Nuclear momentum distribution in solid and liquid HF from ab initio calculation

A calculation of nuclear momentum distribution of liquid and solid hydrogen fluoride was performed. In both systems, density functional theory generalized gradient approximation functional of Perdew, Burke, and Ernzerhof was used for the calculation: for liquid hydrogen fluoride, using an atom centered basis set for an isolated molecule with optimized geometry, and for solid hydrogen fluoride using plane-wave basis sets on optimized orthorhombic crystal cell. For liquid hydrogen fluoride, a semiclassical approach was adopted with the vibrational contribution to momentum distribution obtained from the density functional theory calculation and translational and rotational contributions calculated classically. Nuclear momentum distribution in the solid hydrogen fluoride was calculated entirely quantum mechanically using phonon dispersion and vibrational density of states calculated in the framework of plane-wave density functional theory. Theoretical results were contrasted with recently obtained results of Compton (deep inelastic) neutron scattering on liquid and solid hydrogen fluoride. In case of liquid hydrogen fluoride, almost a perfect agreement between theory and experiment was achieved within the harmonic Born-Oppenheimer approximation. For the solid system under investigation, the harmonic approximation leads to small (4%) overestimation of the square root of the second moment indicating that neutron Compton scattering technique is sensitive to proton delocalization due to hydrogen bonding in solid hydrogen fluoride.     

Vibrational analysis of free and hydrogen bonded complexes of nicotinamide and picolinamide

Harmonic and anharmonic vibrations of free nicotinamide (NIA) and picolinamide (PIA) molecules together with their hydrogen bonded complexes H₂O–NIA and H₂O–PIA have been studied by means of density functional method. The calculation results of the vibrational spectra of free molecules have been investigated and are compared to the available experimental spectra. The vibrational wavenumbers of both molecules have also been calculated by polarizable continuum model (PCM) that represents the solvent as a polarizable continuum and places the solute in a cavity within the solvent (water is chosen as the solvent in this study). The results of PCM calculations and the H₂O–NIA, H₂O–PIA complexes, are used to investigate the H-bonding interactions of both molecules with the water molecule. The harmonic wavenumbers have been scaled by proper factors obtained by comparing the observed versus calculated wavenumbers and it is shown that anharmonic corrections on the vibrational spectra provided a better agreement between the observed and calculated wavenumbers compared to the results obtained by scaling factor method.     

Improving on equilibrium isotropic nuclear shielding constants

Isotropic nuclear shielding constants at the equilibrium molecular structure σ_eq and zero‐point vibrational corrections (ZPVCs) to σ_eq are evaluated using the B3LYP/aug‐cc‐pVTZ level of theory, as well as the KT2/aug‐cc‐pVTZ level of theory. Various scaling factors and systematic corrections are obtained by linear regression to experimental shielding constants. Comparisons of the scaled and systematically corrected equilibrium and vibrationally averaged shielding constants reveal that, at the 99% confidence level, the ZPVCs via second‐order perturbation theory do not improve the agreement of B3LYP/aug‐cc‐pVTZ and KT2/aug‐cc‐pVTZ calculated shielding constants with experiment. This holds true when the same analysis is applied to CCSD(T)/aug‐cc‐pCV[TQ]Z calculated σ_eq of Teale et al. [Journal of Chemical Physics 2013, 138, 024111]. In addition, at the 99% confidence level, B3LYP/aug‐cc‐pVTZ and KT2/aug‐cc‐pVTZ scaled and systematically corrected shielding constants are found to be statistically no different from CCSD(T)/aug‐cc‐pCV[TQ]Z calculated σ_eq. The use of scaling factors and systematic corrections could thus provide a cheaper but yet reasonably accurate alternative for the study of nuclear shielding constants of larger systems.     

A complete shape characterization for molecular charge densities represented by Gaussian-type functions

An algorithm for a detailed 3-D characterization of the shapes of molecular charge distributions is implemented, tested and applied for a family of AB₂ molecules. The characterization is performed by computing a number of topological invariants (“shape groups”) associated with a continuum of molecular surfaces: the complete family of all electronic isodensity contours for the given molecules. These shape groups (the homology groups of truncated surfaces derived from isodensity contours) depend continuously on two parameters: a density value defining the density contour, and a reference curvature value, to which the local curvatures of the isodensity contours are compared. The electronic charge distribution is modeled by means of Gaussian-type functions. The method employs an explicit form of the charge density function in order to compute the curvature properties for the molecular surfaces analytically, from which the shape groups are derived by the algorithm. No visual inspection is required for the characterization and comparison of shapes of molecular charge densities, as these are done algorithmically by the computer. However, visual inspection of the results of the shape analysis is a possible option. For a given molecule, in a given nuclear configuration, the technique provides a two-dimensional shape map, displaying the distribution of shape groups as a function of the local curvature and the level set value (the value of the charge density at the contour). The computer program GSHAPE performs the analysis of shape maps automatically. This feature makes it potentially useful in the context of computer-aided drug design, where unbiased, automated shape characterization methods are valuable tools. As examples, several two-dimensional shape maps for simple systems are discussed. The changes induced in these maps by a change in the nuclear geometry, as well as by the changes of the nuclear charge, are also analyzed. The method is applicable to large biomolecules of interest if charge density information is available.     

Semiempirical method for extracting electron molecule cross sections from experimental data: CF4 as an example

A semiempirical method is described for calculating electron-molecule interaction potential, electron density, and elastic and vibrational inelastic cross sections using experimental data.CF ₄ was considered as un example. Experimental data from IR and Raman spectra, molecular property calculations (dipole matrix elements, polarizability, distance between atoms in molecule), beam measurements of total, momentum transfer, and differential cross sections, and swarm data (diffusion and drift veolcity) are used for extracting the interaction potential, the molecule electron density, avid the differential cross sections. Electron energy distribution functions, drift velocity, and characteristic energy are calculated with the obtained differential e-CF ₄ cross sections lierAr/CF ₄ mixtures.     

Calculating molecular vibrational spectra beyond the harmonic approximation

We present a new approach for calculating anharmonic corrections to vibrational frequency calculations. The vibrational wavefunction is modelled using translated Hermite functions thus allowing anharmonic effects to be incorporated directly into the wavefunction whilst still retaining the simplicity of the Hermite basis. We combine this new method with an optimised finite-difference grid for computing the necessary third and fourth nuclear derivatives of the energy. We compare our combined approach to existing anharmonic models—vibrational self-consistent field theory (VSCF), vibrational perturbation theory (VPT), and vibrational configuration interaction theory (VCI)—and find that it is more cost effective than these alternatives. This makes our method well-suited to computing anharmonic corrections for frequencies in medium-sized molecules. Contribution of the Mark S. Gordon 65th Birthday Festschrift Issue.     

Charge state of metal atoms on oxide supports: a systematic study based on simulated infrared spectroscopy and density functional theory

A long standing question in the study of supported clusters of metal atoms in the properties of metal–oxide interfaces is the extent of metal–oxide charge transfer. However, the determination of this charge transfer is far from straight forward and a combination of different methods (both experimental and theoretical) is required. In this paper, we systematically study the charging of some adsorbed transition metal atoms on two widely used metal oxides surfaces [α-Al₂O₃ (0001) and rutile TiO₂ (110)]. Two procedures are combined to this end: the computed vibrational shift of the CO molecule, that is used as a probe, and the calculation of the atoms charges from a Bader analysis of the electron density of the systems under study. At difference from previous studies that directly compared the vibrational vawenumber of adsorbed CO with that of the gas phase molecule, we have validated the procedure by comparison of the computed CO stretching wavenumbers in isolated monocarbonyls (MCO) and their singly charged ions with experimental data for these species in rare gas matrices. It is found that the computational results correctly reproduce the experimental trend for the observed shift on the CO stretching mode but that care must be taken for negatively charged complexes as in this case there is a significative difference between the total charge of the MCO complex and the charge of the M atom. For the supported adatoms, our results show that while Cu and Ag atoms show a partial charge transfer to the Al₂O₃ surface, this is not the case for Au adatoms, that are basically neutral on the most stable adsorption site. Pd and Pt adatoms also show a significative amount of charge transfer to this surface. On the TiO₂ surface our results allow an interpretation of previous contradictory data by showing that the adsorption of the probe molecule may repolarize the Au adatoms, that are basically neutral when isolated, and show the presence of highly charged Au^δ+–CO complexes. The other two coinage metal atoms are found to significatively reduce the TiO₂ surface. The combined use of the shift on the vibrational frequency of the CO molecule and the computation of the Bader charges shows to be an useful tool for the study the charge state of adsorbed transition metal atoms and allow to rationalize the information coming from complementary tools.     

Photodissociation spectrum of CH3I+ prepared by multiphoton ionization

Two-photon resonant multiphoton ionization has been used to prepare rotationally cooled and selected CH₃I⁺ ions with controlled vibrational and electronic distributions. These ions are photodissociated by a second laser. The highly simplified photodissociation spectrum displays a clear dissociation threshold as well as bands hidden in earlier spectra. The data suggests corrections to previously determined vibrational constants.