Choice of Optimal Shift Parameter for the Intruder State Removal Techniques in Multireference Perturbation Theory

An extensive critical evaluation of intruder state removal techniques (aka shift techniques) applicable to multireference perturbation theory (MRPT) shows that the magnitude of the shift parameter σ does not influence the spectroscopic parameters of diatomics to a significant degree, provided that the shift is chosen to be sufficiently large. In such case, typical variation of spectroscopic parameters over a wide range of shift parameters is smaller than 0.005 Å for equilibrium distances, 30 cm^–1 for harmonic vibrational frequencies, and 0.1 eV for dissociation energies. It is found that large values of σ not only remove intruder states but they also bring the MRPT energies and properties closer to experimental values. The presented analysis allows us to determine optimal values of the shift parameters to be used in conjunction with various versions of MRPT; these values are recommended to replace the <i>ad hoc</i> values of σ suggested in MRPT manuals in calculations for diatomics. Transferability of the optimal shift parameters to larger molecular systems and to other basis sets than aug-cc-pVTZ is anticipated but remains to be formally established

Dispersion-Corrected DFT Struggles with Predicting Three-Body Interaction Energies

We demonstrate that the dispersion-corrected density functional theory (DFT-D) schemes fall short of predicting reliable three-body interaction energies. This concerns also a popular variant of DFT-D called the “many-body dispersion” (MBD) method, which might seem surprising in the light of the fact that its name contains the very phrase “many-body”. The main reason for the inaccuracy of the three-body interaction energies in the DFT-D schemes can be attributed to internal deficiencies of the standard DFT functionals that the existing “-D” methods are incapable of correcting since the main problems emerge from the terms not related to the dispersion component. At present, it seems that none of the a posteriori dispersion techniques are able to predict accurately the total interaction energy for a supermolecular system together with its simultaneous decomposition into the many-body components. On the other hand, if one is interested only in the three-body interaction energies, we propose an adjustment to the MBD approach that achieves good accuracy in conjunction with the supermolecular MP2

Convergence in the Evolution of Nanodiamond Raman Spectra with Particle Size: A Theoretical Investigation

Structural characterization of nanodiamonds by vibrational spectroscopy requires knowledge of the factors determining the spectra. Raman spectroscopy is widely used to detect the diamond phase in nanodiamond powders and films, but several spectral features are still poorly understood. Here we present a theoretical study of the evolution of diamond hydrocarbon Raman spectra with increasing size, from the adamantane molecule to ∼3 nm large tetrahedral and octahedral particles of Td symmetry, containing up to about 1000 carbon atoms. The self-consistent-charge density functional tight-binding method (SCC-DFTB) was used for the calculation of harmonic first-order Raman spectra. We demonstrate very good agreement with Raman spectra computed by standard density functional theory (DFT) for the smaller model systems. The evolution of the Raman patterns is smooth, and convergence to the bulk limit could clearly be observed in case of the acoustic vibrational modes (ωA = 0 cm−1). We found a simple relationship between nanodiamond size and vibrational frequency, which is analogous to the corresponding equation for the radial breathing mode of single-walled carbon nanotubes. The T2 modes of octahedral diamond hydrocarbons coalesce faster to the bulk optical vibrational mode (in experiment, ωO = 1332 cm−1) than those of tetrahedral particles, consistent with the fact that the bulk/surface ratio is more favorable for octahedral particles. Our simulations unequivocally show that controversial Raman features around 500 and 1150 cm−1 do not originate from the nanodiamond crystals, and that the nanocrystal shape plays an important role in the appearance of the Raman spectra even in the 3 nm domain

Comparison of Geometric, Electronic, and Vibrational Properties for Isomers of Small Fullerenes C₂₀−C₃₆^†

We employ the self-consistent-charge density-functional tight-binding (SCC−DFTB) method for computing geometric, electronic, and vibrational properties for various topological isomers of small fullerenes. We consider all 35 five- and six-member rings containing isomers of small fullerenes, C20, C24, C26, C28, C30, C32, C34, and C36, as first part of a larger effort to catalog CC distance distributions, valence CCC angle distributions, electronic densities of states (DOSs), vibrational densities of states (VDOSs), and infrared (IR) and Raman spectra for fullerenes C20−C180. Common features among the fullerenes are identified and properties characteristic for each specific fullerene isomer are discussed

Vibration–rotation interactions in H₂, HD and D₂ : centrifugal distortion factors and the derivatives of polarisability invariants

We report the correction factors for centrifugal distortion in Raman intensities for pure rotation (O0- and S0-branch) and vibration–rotation (O1- and S1-branch) transitions in the ground electronic state of H2, HD and D2. These factors are presented for 52 selected excitation wavelengths and for the initial rotational states, J=2−21. This data is useful in applications of intensity calibration of spectrometers and the spectroscopy of flames. The classical treatment of centrifugal distortion involved the expansion of polarisability anisotropy (γ) over the internuclear distance, while assuming the diatomic molecule behaves as a harmonic oscillator. Here, this approximation of polarisability invariants as a Taylor series expansion is tested, revealing that truncation up to the second-order derivatives of mean polarisability (α¯) and polarisability anisotropy (γ) gives faithful representations, yielding accurate expectation values with error 0.2%, for the ground rovibrational state and for the fundamental transition.</p

Testing the limitations of harmonic approximation in the determination of Raman intensities

Raman intensities in molecular spectra are usually computed within double harmonic approximation. This procedure relies on treating a vibrating molecule as a collection of harmonic oscillators and on the assumption that polarisability tensor invariants display linear variations around the molecular equilibrium geometry. This methodology, originally formulated by Placzek, constitutes the theoretical foundation for computing Raman intensities in standard quantum chemistry packages. However, the two assumptions underlying double harmonic approximation have not been sufficiently tested. In this work, we employed exact anharmonic ro-vibrational wave functions and distance-dependent polarisability invariants together with their harmonic approximants to investigate the discrepancies in Raman intensities of the fundamental transitions in 12 diatomic molecules, caused by double harmonic approximation. We found that: (i) the errors in total Raman intensities were between −8.2% and +9.5%, (ii) the largest discrepancy was observed for F2, where the polarisability invariants could not be adequately modelled by their linear approximants, and (iii) quantum chemical methods fail to predict reliable polarisability invariants at non-equilibrium molecular geometries; the associated errors in Raman intensities are huge and completely overshadow the shortcomings of double harmonic approximation. We communicate here an urgent need for developing accurate methods capable of computing reliable polarisabilities also at distorted geometries.</p

Theoretical Investigation of Molecular Properties of the First Excited State of the Phenoxyl Radical

A theoretical study of molecular, electronic, and vibrational properties of the first excited state of the phenoxyl radical, A 2B2, is presented. The calculated molecular geometries, vertical and adiabatic excitation energies, and harmonic vibrational frequencies are compared with analogous results obtained for the ground state. The calculated excitation energies correspond well to experimental data. The harmonic vibrational frequencies of the A 2B2 and the ground state are similar except for modes involving the vibrations of the CO bond

Theoretical Interpretation of the UV−vis Spectrum of the CS₂/Cl Complex in the Spectral Region 320−550 nm

Accurate multireference configuration interaction and time-dependent density functional calculations have been performed to interpret the experimental UV−vis spectrum of the CS2/Cl complex in the spectral region 320−550 nm. The molecular structure of the complex responsible for the previously observed UV−vis spectrum is recognized as ClSCS, not ClCS2. Two low-lying excited states of ClSCS, responsible for its optical absorption, have been identified and analyzed. Optical excitation of ClSCS leads to the excitation-specific bond elongation that may lead to photofragmentation of the molecule. In addition, experimental conditions for verifying the presence of ClCS2 are identified and detailed characterization of its optically active excited states with possible photofragmentation pathways is given

Spectral Evidence of Bevel-Gear-Type Rotation of Benzene around Br in Solid <i>p</i>‑H₂: Infrared Spectrum of the C₆H₆Br Radical

Whether the structure of C6H6X (X = halogen), an intermediate in the halogenation of benzene, is an open or a bridged form has been debated. We produced Br to react with C6H6 upon photolysis in situ of a Br2/C6H6/p-H2 matrix at 3.2 K. In contrast to the C6H6Cl σ-complex reported previously, the observed infrared spectrum indicates that C6H6Br is an open-form π-complex. Furthermore, lines of the two CH out-of-plane bending modes associated mainly with even- and odd-numbered carbons, predicted near 672 and 719 cm–1, merged into a broad line at 697.3 cm–1, indicating that these modes become nearly equivalent as Br migrates from one carbon atom to another. Quantum-chemical calculations support that the benzene ring performs a bevel-gear-type rotation with respect to Br. Observation of only trans-ortho- and trans-para-C6H6Br2 suggests that this gear-type motion allows the additional Br atom to attack C6H6Br only from the opposite side of the Br atom in C6H6Br

Relativistic Parametrization of the Self-Consistent-Charge Density-Functional Tight-Binding Method. 1. Atomic Wave Functions and Energies^†

A detailed treatment of a confined relativistic atom, needed as an initial step for the parametrization of the self-consistent-charge density-functional tight-binding method, is presented and discussed. The required one-component quantities, i.e., orbital energies, orbital wave functions, and Hubbard parameters, are obtained by weighted averaging of the corresponding numbers determined for the atomic spinors. The wave function and density confinement is achieved by introducing the Woods−Saxon potential in the atomic four-component Dirac−Kohn−Sham problem. The effect of the additional confining potential on energy eigenvalues and the shape of atomic wave functions and densities is discussed and numerical examples are presented for the valence spinors of carbon, germanium, and lead