The NMR indirect nuclear spin–spin coupling constant of the HD molecule

We present new calculated and experimental values of the NMR indirect nuclear spin–spin coupling constant in HD. In the quantum-chemical ab initio calculations, the full configuration-interaction (FCI) method is used, yielding an equilibrium value of 41.22?Hz in the basis-set limit. Adding a calculated zero-point vibrational correction of 1.89?Hz and a temperature correction of 0.20?Hz at 300?K, we obtain a total calculated spin–spin coupling constant of J _FCI(HD)?=?43.31(5)?Hz at 300?K. This result is within the error bars of the experimental gas-phase NMR value, J _exp(HD)?=?43.26(6)?Hz, obtained by extrapolating values measured in HD–He mixtures to zero density.     

Highly accurate excited-state energies from direct computation of the 2-electron reduced density matrix by the anti-Hermitian contracted Schrödinger equation

ABSTRACT

Directly solving for the 2-electron reduced density matrix (2-RDM) via the anti-Hermitian contracted Schrödinger equation (ACSE) enables computations for excited states energies without the N-electron wave function. Of particular interest are excitations and dissociation curves that exhibit strong multi-reference correlation effects. The ground and excited states of the molecules HF, H₂O, and N₂ are examined at both equilibrium and non-equilibrium geometries to compare the ability of the ACSE and widely used ab initio techniques to treat strong multi-reference electron correlation. Calculations are performed with double-ζ basis sets for calibration with full configuration interaction (FCI). Multi-reference second-order perturbation theory (MRPT2) and the ACSE both provide qualitative precision with respect to FCI data, although the ACSE's capability to include higher order correlation effects permits near-FCI accuracy for ground and excited states and excitation energies.     

Influence of broken-pair excitations on the exact pair wavefunction

Doubly occupied configuration interaction (DOCI), the exact diagonalisation of the Hamiltonian in the paired (seniority zero) sector of the Hilbert space, is a combinatorial cost wave function that can be very efficiently approximated by pair coupled cluster doubles (pCCD) at mean-field computational cost. As such, it is a very interesting candidate as a starting point for building the full configuration interaction (FCI) ground state eigenfunction belonging to all (not just paired) seniority sectors. The true seniority zero sector of FCI (referred to here as FCI₀) includes the effect of coupling between all seniority sectors rather than just seniority zero, and is, in principle, different from DOCI. We here study the accuracy with which DOCI approximates FCI₀. Using a set of small Hubbard lattices, where FCI is possible, we show that DOCI ～ FCI₀ under weak correlation. However, in the strong correlation regime, the nature of the FCI₀ wavefunction can change significantly, rendering DOCI and pCCD a less than ideal starting point for approximating FCI.     

Towards the assignment of the REMPI spectrum of Ph2O using CIS and TD-DFT methods

Tentative assignment of the low-lying vibrational features of the first electronic excited singlet-state S₁ of diphenyl ether (Ph₂O), obtained from resonance-enhanced multiphoton ionisation (REMPI) spectroscopy, is performed using CIS and time-dependent density functional theory (TD-DFT) methods. The potential energy surfaces, regarding the rotation of the phenyl rings relatively to the C–O–C plane, are obtained at the B3LYP/6-31G(d) level of theory, for the ground-state of neutral and cationic Ph₂O and for its first excited singlet state. The torsional barriers of the ground state of diphenyl ether were studied by means of quantum-chemical perturbations of increasing accuracy and an extrapolation to the complete basis set limit and full configuration interaction (FCI) was performed through the use of correlation consistent basis sets and the continued fraction method. The first adiabatic ionisation energy (AIE) of the twist conformer is computed at 8.60 eV in the FCI limit, much higher than the experimental results of Terlouw et al. (8.09±0.03 eV) and Paiva et al. (7.8±0.1 eV). The B3LYP result of 7.82 eV is, however, in reasonable agreement with the result of Paiva et al. The first singlet excitation energy for the twist conformation is found to be 5.5 eV at the CIS/6-311++G(d,p) level of theory. Some features of the experimental REMPI spectrum, previously obtained by one of the authors, are explained and a new insight on the ionisation energy of diphenyl ether is presented.     

Non-LTE Argon-plasma Composition

In this paper theory of calculation of non-LTE plasma composition is presented. The calculations are conducted for argon plasma for temperature ranges from 500 K to 30, 000 K and T _e/T _h ratios from 1 to 10. The effect of different versions of the Saha equation, Debye length, lowering of ionisation energy and pressure correction on the argon-plasma composition is evaluated. It was concluded that the modified Saha equation could not be used for calculation of non-LTE plasma composition. Application of various Debye lengths can change the electron number density by 8%. The lowering of the ionisation energy decreases the electron number density by 18%. For LTE-plasma pressure correction has a negligible effect on the electron number density.     

Electron ionization rate in III–V ternary semiconductors

Theoretical calculations are presented for the ionization rate of electrons in III–V ternary semiconductor compounds considering alloy scattering and carrier-carrier interaction, in addition to optical phonon scattering and ionization scattering. However, alloy scattering is found to be a weak interaction. Fairly good agreement is obtained for Ga_1–x In _x As withx=0.14 and 0.53 with the experimental results and for Ga_0.5 Al_0.5 As with the existing theoretical result which used an indirect method. The alloy scattering potential has been taken in the form of energy band-gap difference. The calculations can be used for any ternary semi-conductor.     

Phase stability of Crn+ 1GaCn MAX phases from first principles and Cr2GaC thin‐film synthesis using magnetron sputtering from elemental targets

Ab‐initio calculations have been used to investigate the phase stability and magnetic state of Cr_{n+ 1}GaC_n MAX phase. Cr₂GaC (n = 1) was predicted to be stable, with a ground state corresponding to an antiferromagnetic spin configuration. Thin‐film synthesis by magnetron sputtering from elemental targets, including liquid Ga, shows the formation of Cr₂GaC, previously only attained from bulk synthesis methods. The films were deposited at 650 °C on MgO(111) substrates. X‐ray diffraction and high‐resolution transmission electron microscopy show epitaxial growth of (000?) MAX phase. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A general pseudopotential model for molecules with many valence electrons

Criteria are discussed for the practical application of ‘valence-electron only’ calculations aimed at simulating ab initio all-electron calculations on molecules containing heavy atoms with many core electrons. A theoretical model is outlined based on the use of pseudopotentials derived from atomic SCF calculations. The model has been used in calculations for NaH, Na₂, H₂S, S₂, H₂S₂, HCl, Cl₂ and NaCl, and has been tested by comparison with reference all-electron calculations. Most of these tests employ double-zeta basis sets and SCF wavefunctions, although polarization functions and complete valence-electron CI wavefunctions have been used in some cases. The model is generally successful for ground-state equilibrium structures, charge distributions and orbital energies.     

The nonlinear optical susceptibility and electro-optic tensor of ferroelectrics: first-principle study

The nonlinear optical properties of some ABO₃ materials (BaTiO₃, KNbO₃, LiTaO₃ and LiNbO₃) are studied by density functional theory (DFT) in the local density approximation (LDA) expressions based on first-principle calculations. Our goals are to give the details of the calculations for linear and nonlinear optical properties, including the linear electro-optic (EO) tensor for some ABO₃ structures with oxygen octahedral structures using first-principles methods. These results can then be used in the study of the physics of ferroelectrics, specifically, we present calculations of the second harmonic generation response coefficient X _ijk ⁽²⁾ (−2ω, ω, ω) over a large frequency range for ABO₃ crystals. The electronic linear EO susceptibility X _ijk ⁽²⁾ (−ω, ω,0) is also evaluated below the band gap. These results are based on a series of the LDA calculations using DFT. Results for X _ijk ⁽²⁾ (−ω, ω,0) are in agreement with experiments below the band gap. The results are compared with the theoretical calculations and the available experimental data.     

Refined shell-model matrix elements for muon-capture processes

Recently many shell-model calculations have been performed in order to extract the value of the ratio C _P/C _A in light nuclei. Most of these calculations fail to reproduce the value given by the partially conserved axial vector hypothesis, roughly 7. We show, that by using the effective transition operators, calculated by the perturbative techniques, this discrepancy can be, at least partly, solved. New angular correlation data for ²⁸Si is used for the extraction of C _P/C _A. In the case of ²⁰Ne, the capture rate data is used for extraction.     

Molecular dipole static polarisabilities and hyperpolarisabilities of conjugated oligomer chains calculated with the local π-electron coupled cluster theory

A new semi-empirical π-electron local coupled cluster theory has been developed to calculate static dipole polarisabilities and hyperpolarisabilities of extended π-conjugated systems. The key idea of the approach is the use of the ethylene molecular orbitals as the orbital basis set for π-conjugated compounds (the method is termed the Covalent Unbonded Molecules of Ethylene method, cue). Test calculations of some small model organic conjugated compounds demonstrate high accuracy of the version of the cue local coupled cluster theory developed in this work in comparison with the π-electron full configuration interaction (FCI) method. Calculations of different conjugated carbon-based oligomer chains (polyenes, polyynes, polyacenes, polybenzocyclobutadiene, etc.) demonstrate fast convergence (per π-electron) of the polarisability and hyperpolarisability values in the calculations when more classes of orbital excitations are included in the coupled cluster single and double (CCSD) excitation operator. The results show qualitatively correct dependence on the system size.     

Calculations with the CNDO method on clusters of silver atoms

An attempt has been made to explore the applicability of the complete neglect of differential overlap (CNDO) method for investigating clusters of silver atoms. A new parametrization for silver has been obtained by comparing charge distributions, as well as local and total density of states, from CNDO calculations with those from the X_α scattered wave (X_αSW) method for an Ag₇ cluster which represents a fragment of the silver lattice. These parameters have then been used for making CNDO calculations on four further clusters of the same type, namely Ag₆, Ag₁₀, Ag₁₃ and Ag₁₉, and the results are compared with previous X_αSW calculations. These CNDO calculations give d-band widths in broad agreement with those from the X_αSW method. The most significant difference is that the CNDO method gives less localization on central atoms with high coordination numbers than is found from the X_αSW calculations. It is suggested that this apparent deficiency of the CNDO calculations may be less serious when the clusters are being used for modelling part of a solid metal rather than for specifically investigating the properties of small particles.     

On the ‘expanded local mode’ approach applied to the methane molecule: isotopic substitutions CH3D ←CH4 and CHD3 ←CH4

Operator perturbation theory and the symmetry properties of the axially symmetric XYZ₃ (C_3v) type molecules are used for the determination of the spectroscopic parameters in the form of functions of structural parameters and parameters of the intramolecular potential function. Several relations between sets of spectroscopic parameters of these molecules are obtained. The ‘expanded local mode’ model and the general isotopic substitution theory are used to estimate the relations between spectroscopic parameters of CH₃D and CHD₃, on one hand, and with the T_d symmetric isotopic species, CH₄, on the other hand. Test calculations with the isotopic relations show that even without including prior information about the CH₃D and CHD₃ species, numerical results of calculations are in a good agreement both with experimental data and with results of ab initio calculations.     

(2 + 1) Resonance enhanced multiphoton ionization of hydrogen chloride in a pulsed supersonic jet: Vacuum wavenumbers of rotational lines with detailed band analysis for excited electronic states of HCl

A comprehensive study of the excited electronic states of HCl is reported. Using resonance enhanced multiphoton ionization ((2 + 1) REMPI) and time-of-flight mass spectrometry (TOFMS) over 120 band systems are analyzed. Supersonic jet techniques are used to prepare rotationally cold species for laser spectroscopy in the 77 000 to 96 000 cm⁻¹ region. At least 50 new electronic states are characterized as well as several features only tentatively assigned previously. A long vibrational progression consisting of 29 vibrational levels of the deeply bound V¹Σ⁺(0⁺) valence/ion-pair state is studied. We also extend the identification and analysis to high vibrational levels of low-lying Rydberg states. The assignments of [²Π_i] Rydberg state complexes are evaluated in terms of spin-orbit coupling and united-atom calculations. In several band systems, the spectra exhibit anomalous rotational line intensities and broadened linewidths which are consistent with predissociation. Multiphoton ionization with mass spectrometry permits the investigation of isotope effects as well as the appearance of fragment species associated with repulsive potential curves.     

An ab initio calculation of the rotational-vibrational energies in the electronic ground state of NH2

We have calculated ab initio the three-dimensional potential-energy surface of the NH₂ molecule at 145 nuclear geometries spanning energy ranges of about 18 000 cm^-1 for the NH stretch and 12 000 cm^-1 for the bend. The ab initio configuration-interaction calculations were done using the multireference MRD-CI method. The calculated equilibrium configuration has NH bond length r _e = 1·0207 Å and bond angle α = 103·1°. The rotational-vibrational energies for ¹⁴NH₂, ¹⁴NHD and ¹⁴ND₂ were calculated variationally using the Morse-oscillator rigid-bender internal-dynamics Hamiltonian. For ¹⁴NH₂ we calculate that υ₁ = 3267 (3219) cm^-1, υ₂ = 1462 (1497) cm^-1 and υ₃ = 3283 (3301) cm^-1, where experimental values are given in parentheses.     

Ab initio study of the ground and excited states of hydrogen sulphide using SCF and CI calculations

Results from ab initio SCF and CI calculations on the ground state and low-lying valence and Rydberg states of H₂S are reported. A double ξ basis of contracted gaussian functions augmented by polarization and diffuse 3d, 4s and 4p functions is used for the calculations. The geometries of various excited states are studied by means of SCF calculations. The first observed band in the absorption spectrum is predicted to arise from the overlapping of transitions from the 2b₁ orbital to a Rydberg 4s and strongly bent valence upper state. The calculations support the assignment of other spectral features to transitions from the 2b₁ to components of the Rydberg 3d and 4p orbitals.     

Quantum chemical calculations of the structural influence on electronic properties in TiO2 nanocrystals

ABSTRACT

Quantum chemical calculations for two TiO₂ nanoparticle cluster models (rutile–(TiO₂)_n with n = 20, and anatase–(TiO₂)_n with n = 92), selected to represent different nanoparticle size regimes, are used to elucidate structural influences on the electronic properties. Structural and electronic properties were obtained using a variety of computational methods and structure optimisation schemes, including a comparison of results for several different density functional theory functionals, as well as complementary Hartree–Fock and semi-empirical calculations. The results demonstrate a strong dependence of electronic properties, such as the optical band gap of importance for photoelectrochemical and photocatalytic applications, on the structure of the nanocrystal. From a methodological point of view, the calculations also provide useful information of broader significance about the viability of different computational schemes to efficiently obtain reliable computational results for intrinsically nanostructured materials.     

Local structure of technologically modified g-GeS2: resonant Raman and absorption edge spectroscopy combined with ab initio calculations

We have used resonant Raman and absorption edge spectroscopy together with first-principle calculations in order to study the structure of GeS₂ glasses (g-GeS₂). The glasses were prepared under different melt temperatures and cooling rates, which are shown to significantly influence the g-GeS₂ structure at the nano-scale. The combined use of Raman spectroscopy and ab initio calculations reveals the origin of the molecular level electronic structure and its connection to the interesting technological features of the g-GeS₂. Local structure within the glasses is discussed in terms of atomic Ge _n S _m clusters. The band gaps computed for these clusters and their correlation to the experimental band gaps and the possible formation of band tail states are also discussed.     

Study of parameters of the angular distribution of photoelectrons in the relativistic quadrupole approximation

Relativistic calculations of differential cross sections for photoionization are performed and the behavior of parameters β, γ, and δ describing the angular distribution of photoelectrons in the quadrupole approximation is studied. The calculations were carried out for a number of atoms for kinetic energies of photoelectrons E _k ≈50 000 eV. The electronic wave functions of the initial and final states are calculated by the Dirac-Fock method taking into account the exchange interaction and a hole produced in the atomic shell upon photoionization. The dependence of parameters β, γ, and δ on the physical assumptions used in the calculations is studied. Comparison with nonrelativistic calculations shows that relativistic values of the nondipole parameters γ and δ can be substantially different even at low energies of photoelectrons. Our calculations of nondipole parameters γ and δ for the 2p-shell of the Kr atom better agree with the recent experimental data than nonrelativistic calculations performed earlier taking approximately into account the exchange interaction and neglecting a hole.     

Influence of the special features of atomic structure of Si24 and MeSi24 (Me = Na or K) nanoparticles on their electron properties

The influence of atomic structure of silicon nanoparticles on the distribution of total and partial state densities in the valence and conductivity bands as well as on the valence band and gap widths is analyzed based on the calculated geometrical and electron structure of the Si ₂₄ and MeSi ₂₄ (Me = Na or K) clusters. Semi-empirical AM1 and PM3 methods are used for calculations. The adequacy of calculations is confirmed by their comparison with the available experimental data. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 46–51, February, 2006.