Calculations of overtone NIR and NIR-VCD spectra in the local mode approximation: Camphor and Camphorquinone

We present a method to calculate near-infrared (NIR) and NIR-vibrational circular dichroism (NIR-VCD) spectra up to the second CH-stretching overtone region in the local mode approximation. Atomic polar tensors and atomic axial tensors are first evaluated by DFT methodology for all CH stretching coordinates with systematic positive and negative displacements off-equilibrium and therefrom anharmonic dipole moment functions are constructed by polynomial interpolations. No adjustable parameters are employed up to this point. Rotational and dipole strengths are finally calculated by evaluating transition moments of Morse-type wave-functions. The method is applied to the case of Camphor and Camphorquinone, for which relevant differences in the vibrational circular dichroism (VCD) data are observed, which are predicted by our approach. Further steps are still to be made for a more complete treatment: the ab initio evaluation of mechanical anharmonicity and the introduction of mechanical and electrical coupling between local modes.     

Far- and mid-infrared of crystalline 2,2'-bithiophene: ab initio analysis and comparison with infrared response

Infrared intramolecular vibrations and lattice modes in the crystalline phase of 2,2'-bithiophene (2T) are investigated using the direct method combined with density functional theory (DFT)-based total energy calculations. For the first time, the far- and mid-infrared responses have been calculated from the Gamma-point modes and the Born effective charge tensors of the 2T crystalline phase. The relative good agreement between the calculated and experimental infrared spectra allows us to assign the origin of the main features of the experimental spectra, which is of particular interest in the far-infrared domain. These assignments are useful for understanding all the properties of the 2T crystalline phase in which phonon-phonon and electron-phonon interactions play an important role.     

Spectral theory of anisotropic fluids

The spectral theory of symmetric viscoelastic fluids with arbitrary anisotropy, which is based on the generalized Maxwell relaxation law, is developed. A feature of the proposed approach is the use of a spectral (canonical) representation of tensors that describe the anisotropic properties of fluids. Simple special cases of the spectra of viscosity and relaxation-time tensors are considered. The orientation dynamics of anisotropic fluids is discussed. A theory of generation of eigenmodes that are related to stress relaxation is developed. On the basis of the spectral theory, the possibility of the existence of soft (zero energy) modes in anisotropic fluids with deep anisotropy is considered. The proposed theory opens up new alternatives for classifying anisotropic fluids.     

Anharmonic effects in IR, Raman, and Raman optical activity spectra of alanine and proline zwitterions

The difference spectroscopy of the Raman optical activity (ROA) provides extended information about molecular structure. However, interpretation of the spectra is based on complex and often inaccurate simulations. Previously, the authors attempted to make the calculations more robust by including the solvent and exploring the role of molecular flexibility for alanine and proline zwitterions. In the current study, they analyze the IR, Raman, and ROA spectra of these molecules with the emphasis on the force field modeling. Vibrational harmonic frequencies obtained with 25 ab initio methods are compared to experimental band positions. The role of anharmonic terms in the potential and intensity tensors is also systematically explored using the vibrational self-consistent field, vibrational configuration interaction (VCI), and degeneracy-corrected perturbation calculations. The harmonic approach appeared satisfactory for most of the lower-wavelength (200-1800 cm(-1)) vibrations. Modern generalized gradient approximation and hybrid density functionals, such as the common B3LYP method, provided a very good statistical agreement with the experiment. Although the inclusion of the anharmonic corrections still did not lead to complete agreement between the simulations and the experiment, occasional enhancements were achieved across the entire region of wave numbers. Not only the transitional frequencies of the C-H stretching modes were significantly improved but also Raman and ROA spectral profiles including N-H and C-H lower-frequency bending modes were more realistic after application of the VCI correction. A limited Boltzmann averaging for the lowest-frequency modes that could not be included directly in the anharmonic calculus provided a realistic inhomogeneous band broadening. The anharmonic parts of the intensity tensors (second dipole and polarizability derivatives) were found less important for the entire spectral profiles than the force field anharmonicities (third and fourth energy derivatives), except for a few weak combination bands which were dominated by the anharmonic tensor contributions.     

QM/MM calculation of protein magnetic shielding tensors with generalized hybrid-orbital method: a GIAO approach

A method to compute magnetic shielding tensors with generalized hybrid-orbital (GHO) QM/MM scheme is developed at the levels of Hartree-Fock and second-order M?ller-Plesset perturbation theory using gauge-including atomic orbitals. A feature of the GHO method is utilized to ensure gauge-origin independency of GHO shielding tensors in a simple way. The benchmark calculations indicate that the GHO method reproduced full-QM shielding constants nearly quantitatively for atoms not directly coupled to the GHO linking atoms. As an application to a realistic protein, carbon chemical shifts are calculated for the retinal chromophore in visual rhodopsin.     

Theoretical investigation of doubly resonant IR-UV sum-frequency vibrational spectroscopy of binaphthol chiral solution

The doubly resonant IR-UV sum-frequency vibrational spectroscopy (SFVS) of 1,1'-bi-2-naphthol (BN) solution and its dispersion spectra are analyzed and computed using the ZINDO//AM1 calculation and the direct approach of Raman scattering tensor calculation, which is based on calculations of Franck-Condon factors and on differentiation of the electronic transition moments with respect to the vibrational normal modes. The calculated results indicate that, for the most intense vibrational bands observed in the SFVS experiment, the calculated frequencies, symmetry, order, intensities, and pattern of the enhanced vibrational modes agree with experiment qualitatively, and due to the Franck-Condon progression, there are the doublet peaks in the corresponding resonant sum-frequency dispersion spectra. The polarization resonance Raman spectra of BN for the vibrational modes appearing in SFVS are also computed and associated with the experiment SFVS of BN. This direct evaluation approach of Raman tensors may provide a way of assigning the doubly resonant IR-UV SFVS.     

(13)C shielding tensors of crystalline amino acids and peptides: Theoretical predictions based on periodic structure models

Precise theoretical predictions of NMR parameters are helpful for the spectroscopic identification of complicated biological molecules, especially for the carbon shielding tensors in amino acids. The (13)C shielding tensors of various crystalline amino acids and peptides have been calculated using the gauge-including projector augmented wave (GIPAW) method based on two different periodic structure models, namely that deduced from available crystallographic data and that from theoretically optimized structures. The incorporation of surrounding lattice effects is found to be crucial in obtaining reliable predictions of (13)C shielding tensors that are comparable to the experimental data. This is accomplished by refining the experimental crystallographic data of the amino acids and peptides at the GGA/PBE level by which more accurate intramolecular C--H bond lengths and intermolecular hydrogen-bonding interactions are obtained. Accordingly, more accurate predictions of (13)C shielding tensors comparable to the experimental results (within a maximum deviation of +/-10 ppm) were achieved, rendering more explicit (13)C shielding tensors assignments for solid biological systems particularly for amino acids with multiple carboxyl carbons, such as asparagine, glutamine, and glutamic acid.     

Ab initio vibrational spectra and dielectric properties of carbonates: magnesite, calcite and dolomite

The equilibrium geometry, the Raman and IR vibrational spectra at the Γ point, TO–LO splitting, IR intensities, Born and dielectric tensors of magnesite MgCO₃, dolomite MgCa(CO₃)₂ and calcite CaCO₃ have been calculated with the periodic ab initio program CRYSTAL, by using an all-electron gaussian type basis set and the B3LYP hamiltonian. LO (longitudinal-optical) modes are computed by correcting the dynamical matrix through Born charges and high frequency dielectric tensors obtained from well localized Wannier functions and a saw-tooth computational scheme. The mean absolute difference between calculated and experimental frequencies (IR TO and LO and RAMAN) is as small as 6.9 cm⁻¹ for magnesite, 7.7 cm⁻¹ for dolomite and 8.5 cm⁻¹ for calcite. Calculated IR intensities are in semiquantitative agreement with experiment. The modes of the three compounds are compared through graphical animation available on the CRYSTAL web-site.     

Density Functional Theory Calculations of 95Mo NMR Parameters in Solid‐State Compounds

The application of periodic density functional theory‐based methods to the calculation of ⁹⁵Mo electric field gradient (EFG) and chemical shift (CS) tensors in solid‐state molybdenum compounds is presented. Calculations of EFG tensors are performed using the projector augmented‐wave (PAW) method. Comparison of the results with those obtained using the augmented plane wave + local orbitals (APW+lo) method and with available experimental values shows the reliability of the approach for ⁹⁵Mo EFG tensor calculation. CS tensors are calculated using the recently developed gauge‐including projector augmented‐wave (GIPAW) method. This work is the first application of the GIPAW method to a 4d transition‐metal nucleus. The effects of ultra‐soft pseudo‐potential parameters, exchange‐correlation functionals and structural parameters are precisely examined. Comparison with experimental results allows the validation of this computational formalism.     

On the equivalence of conformational and enantiomeric changes of atomic configuration for vibrational circular dichroism signs

We study systematically the vibrational circular dichroism (VCD) spectra of the conformers of a simple chiral molecule, with one chiral carbon and an "achiral" alkyl substituent of varying length. The vibrational modes can be divided into a group involving the chiral center and its direct neighbors and the modes of the achiral substituent. Conformational changes that consist of rotations around the bond from the next-nearest neighbor to the following carbon, and bond rotations further in the chain, do not affect the modes around the chiral center. However, conformational changes within the chiral fragment have dramatic effects, often reversing the sign of the rotational strength. The equivalence of the effect of enantiomeric change of the atomic configuration and conformational change on the VCD sign (rotational strength) is studied. It is explained as an effect of atomic characteristics, such as the nuclear amplitudes in some vibrational modes as well as the atomic polar and axial tensors, being to a high degree determined by the local topology of the atomic configuration. They reflect the local physics of the electron motions that generate the chemical bonds rather than the overall shape of the molecule.     

Structure and dynamics of homoleptic beryllocenes: a solid-state 9Be and 13C NMR study

The correlation between anisotropic 9Be NMR (quadrupolar and chemical shielding) interactions and the structure and dynamics in [Cp2Be], [Cp2*Be], and [(C5Me4H)2Be] is examined by solid-state 9Be NMR spectroscopy, as well as by ab initio and hybrid density functional theory calculations. The 9Be quadrupole coupling constants in the three compounds correspond well to the relative degrees of spherical ground-state electronic symmetry of the environment about beryllium. Theoretical computations of NMR interaction tensors are in excellent agreement with experimental values and aid in understanding the origins of NMR interaction tensors and their correlation to molecular symmetry. Variable-temperature (VT) 9Be and 13C NMR experiments reveal a highly fluxional structure in the condensed phase of [Cp2Be]. In particular, the pathway by which the Cp rings of [Cp2Be] 'invert' coordination modes is examined in detail using hybrid density functional theory in order to inspect variations of the 9Be NMR interaction tensors. The activation energy for the 'inversion' process is found to be 36.9 kJ mol(-1) from chemical exchange analysis of 13C VT CP/MAS NMR spectra. The low-temperature (ca. -100 degrees C) X-ray crystal structures of all three compounds have been collected and refined, and are in agreement with previously reported structures. In addition, the structure of the same Cp2Be crystal was determined at 20 degrees C and displays features consistent with increased intramolecular motion, supporting observations by 9Be VT NMR spectroscopy.     

Intensity‐Carrying Modes in Raman and Raman Optical Activity Spectroscopy

We describe a quantum‐chemical approach for the determination of modes with maximum Raman and Raman optical activity (ROA) intensity by maximizing the intensities with respect to the Raman and Raman optical activity intensity, respectively, which is shown to lead to eigenvalue equations. The intensity‐carrying modes are in general hypothetical modes and do not directly correspond to a certain normal mode in the spectrum. However, they provide information about those molecular distortions leading to intense bands in the spectrum. Modes with maximum Raman intensity are presented for propane‐1,3‐dione, propane‐1,3‐dionate, and Λ‐tris(propane‐1,3‐dionato)cobalt(III). Moreover, the mode with highest ROA intensity is examined for this chiral cobalt complex and also for the (chiral) amino acid L ‐tryptophan. The Raman and ROA high‐intensity modes are an optimal starting guess for intensity‐tracking calculations, in which selectively normal modes with high Raman or ROA intensity are converged. We present the first Raman and ROA intensity‐tracking calculations. These reveal a high potential for large molecules, for which the selective calculation of normal modes with high intensity is desirable in view of the large computational effort required for the calculation of Raman and ROA polarizability property tensors.     

Ab initio molecular orbital calculations of the energetic,structural, vibrational and electronic properties of some hydrogen bonded complexes of water,ammonia and hydroxylamine

Recently published results of some ab initio molecular orbital calculations on 10 hydrogen bonded homodimers and heterodimers of water, ammonia and hydroxylamine have been analysed. The properties discussed include the interaction energies, the structural parameters of the hydrogen bonded fragments, RAH⋯B, the vibrational properties (wavenumbers of the bonded AH-stretching and RAH-bending vibrational modes, and their shifts, and the wavenumbers of the highest frequency intermolecular modes of the complexes), and the atomic polar tensors, their invariants, and the Mulliken charges of the bonded hydrogen atoms. It is concluded that such complexes are stabilized by hydrogen bonds of the OH⋯N, OH⋯O and NH⋯N type, listed in decreasing order of strength. The complexes tend to form preferentially open (more or less linear) structures, followed by large cyclic structures, in which ring strain is minimized, and finally small cyclic structures, in which ring strain is more important.     

Evaluation of electronic correlation contributions for optical tensors of large systems using the incremental scheme

A new method is developed to calculate the optical tensors of large systems based on available wave function correlation approaches (e.g., the coupled cluster ansatz) in the framework of the incremental scheme. The convergence behaviors of static first- and second-order polarizabilities with respect to the order of the incremental expansion are examined and discussed for the model system Ga(4)As(4)H(18). The many-body increments of optical tensors originate from the dipole-dipole coupling effects and the corresponding contributions to the incremental expansion are compared among local domains with different distances and orientations. The weight factors for increments of optical tensors are found to be tensorial in accordance with the structural symmetry as well as the polarization and the external electric field directions. The long-term goal of the proposed approach is to incorporate the sophisticated molecular correlation methods into the accurate wave function calculation of optical properties of large compounds or even crystals.     

Gaussian induced dipole polarization model

A new induced dipole polarization model based on interacting Gaussian charge densities is presented. In contrast to the original induced point dipole model, the Gaussian polarization model is capable of finite interactions at short distances. Aspects of convergence related to the Gaussian model will be explored. The Gaussian polarization model is compared with the damped Thole-induced dipole model and the point dipole model. It will be shown that the Gaussian polarization model performs slightly better than the Thole model in terms of fitting to molecular polarizability tensors. An advantage of the model based on Gaussian charge distribution is that it can be easily generalized to other multipole moments and provide effective damping for both permanent electrostatic and polarization models. Finally, a method of parameterizing polarizabilities is presented. This method is based on probing a molecule with point charges and fitting polarizabilities to electrostatic potential. In contrast to the generic atom type polarizabilities fit to molecular polarizability tensors, probed polarizabilities are significantly more accurate in terms of reproducing molecular polarizability tensors and electrostatic potential, while retaining conformational transferability.     

Automatic fitting procedures for EPR spectra of disordered systems: matrix diagonalization and perturbation methods applied to fluorocarbon radicals

Two types of automatic fitting procedures for EPR spectra of disordered systems have been developed, one based on matrix diagonalization of a general spin Hamiltonian, the other on 2nd order perturbation theory. The first program is based on a previous Fortran code complemented with a newly written interface in Java to provide user-friendly in and output. The second is intended for the special case of free radicals with several relatively weakly interacting nuclei, in which case the general method becomes slow. A least squares' fitting procedure utilizing analytical or numerical derivatives of the theoretically calculated spectrum with respect to the g- and hyperfine structure (hfs) tensors was used to refine those parameters in both cases. 'Rigid limit' ESR spectra from radicals in organic matrices and in polymers, previously studied experimentally at low temperature, were analyzed by both methods. Fluorocarbon anion radicals could be simulated, quite accurately with the exact method, whereas automatic fitting on, e.g. the c-C(4)F(8)(-) anion radical is only feasible with the 2nd order approximative treatment. Initial values for the (19)F hfs tensors estimated by DFT calculations were quite close to the final. For neutral radicals of the type XCF(2)CF(2)* the refinement of the hfs tensors by the exact method worked better than the approximate. The reasons are discussed. The ability of the fitting procedures to recover the correct magnetic parameters of disordered systems was investigated by fittings to synthetic spectra with known hfs tensors. The exact and the approximate methods are concluded to be complementary, one being general, but limited to relatively small systems, the other being a special treatment, suited for S=1/2 systems with several moderately large hfs.     

Analytic energy gradient in combined time-dependent density functional theory and polarizable force field calculation

Formulas for evaluating analytic energy gradient are derived for combined time-dependent density functional theory (TDDFT) and polarizable force field methods that incorporate dipole polarizability tensors and linearly induced point dipoles. The Z-vector method for determining relaxed one-particle difference density matrix in regular TDDFT methods is extended to include induced dipoles. The analytic gradient of the mutual polarization energy of the force field and the TDDFT excited state can be formulated by using the TDDFT difference density-induced dipoles and the transition state density-induced dipoles. All the forces and torques involving induced dipoles can be efficiently evaluated using standard electrostatic formulas as if the induced dipoles were permanent dipoles. The formulas are given in the most general form and are applicable to various flavors of polarizable force fields. Implementation and tests with a polarizable five-point water model show that the formulas are rigorous. The carbonyl vibration modes and infrared spectrum intensities of a cluster formed by acetone and two water molecules are studied.     

Time-dependent density functional theory for calculating origin-independent optical rotation and rotatory strength tensors

An approach to calculate origin-independent electronic chiroptical property tensors using time-dependent density functional theory (TDDFT) and gauge-including atomic orbital (GIAO) basis sets is evaluated. Computations of origin-dependent optical rotation tensors and of rotatory strengths needed to simulate circular dichroism spectra are presented. The optical rotation tensor computations employ solutions of coupled perturbed Kohn-Sham equations for a dynamic electric field and a static magnetic field. Because the magnetic field is time independent, the GIAO treatment is somewhat simplified compared to a previously reported method, at some added computational cost if hybrid functionals are employed. GIAO rotatory strengths are also calculated, using transition density matrices from a standard TDDFT excitation energy module. A new implementation in the NWChem quantum chemistry package is employed for representative computations of origin-invariant chiroptical response tensors for methyloxirane, norbornenone, and the ketosteroid androstadienone. For the steroid molecule the vibrational structure of the CD spectrum is modeled explicitly by using calculated Franck-Condon factors. The agreement with experiment is favorable.     

Modeling NMR chemical shift: A survey of density functional theory approaches for calculating tensor properties

The NMR chemical shift, a six-parameter tensor property, is highly sensitive to the position of the atoms in a molecule. To extract structural parameters from chemical shifts, one must rely on theoretical models. Therefore, a high quality group of shift tensors that serve as benchmarks to test the validity of these models is warranted and necessary to highlight existing computational limitations. Here, a set of 102 13C chemical-shift tensors measured in single crystals, from a series of aromatic and saccharide molecules for which neutron diffraction data are available, is used to survey models based on the density functional (DFT) and Hartree-Fock (HF) theories. The quality of the models is assessed by their least-squares linear regression parameters. It is observed that in general DFT outperforms restricted HF theory. For instance, Becke's three-parameter exchange method and mpw1pw91 generally provide the best predicted shieldings for this group of tensors. However, this performance is not universal, as none of the DFT functionals can predict the saccharide tensors better than HF theory. Both the orientations of the principal axis system and the magnitude of the shielding were compared using the chemical-shift distance to evaluate the quality of the calculated individual tensor components in units of ppm. Systematic shortcomings in the prediction of the principal components were observed, but the theory predicts the corresponding isotropic value more accurately. This is because these systematic errors cancel, thereby indicating that the theoretical assessment of shielding predictions based on the isotropic shift should be avoided.     

Combined first-principles computational and experimental multinuclear solid-state NMR investigation of amino acids

13C, 14N, 15N, 17O, and 35Cl NMR parameters, including chemical shift tensors and quadrupolar tensors for 14N, 17O, and 35Cl, are calculated for the crystalline forms of various amino acids under periodic boundary conditions and complemented by experiment where necessary. The 13C shift tensors and 14N electric field gradient (EFG) tensors are in excellent agreement with experiment. Similarly, static 17O NMR spectra could be precisely simulated using the calculation of the full chemical shift (CS) tensors and their relative orientation with the EFG tensors. This study allows correlations to be found between hydrogen bonding in the crystal structures and the 17O NMR shielding parameters and the 35Cl quadrupolar parameters, respectively. Calculations using the two experimental structures for L-alanine have shown that, while the calculated isotropic chemical shift values of 13C and 15N are relatively insensitive to small differences in the experimental structure, the 17O shift is markedly affected.