Molecular Application of a State Specific Multi-Reference Brillouin-Wigner Perturbation Theory

The single reference second order Brillouin-Wigner perturbation theory recently developed,which eliminates its size-extensivity error,has been generalized to state-specific,multi-reference(SS-MR),BWPT2 providing a size-extensive correction to the electron correlation problem for systems that demand the use of a multi-reference function.Illustrative numerical tests of the size-extensivity corrections are made for widely used molecules in their ground states,which are pronounced multi-reference characteristics.We have implemented two-reference and three-reference cases for CH_2,BH and bond breaking process in the ground states of HF molecules.The results are compared with the rigorously size-extensive methods such as the M(?)ller-Plesset perturbation theory,i.e.,MP2,full configuration interaction(Full-CI) and allied methods using the same basis sets.     

On the performance of DFT/MRCI-R and MR-MP2 in spin–orbit coupling calculations on diatomics and polyatomic organic molecules

ABSTRACT

We have investigated the performance of different multi-reference quantum chemical methods with regard to electronic excitation energies and spin–orbit matrix elements (SOMES). Among these methods are two variants of the combined density functional theory and multi-reference configuration interaction method (DFT/MRCI and DFT/MRCI-R) and a multi-reference second-order Møller–Plesset perturbation theory (MR-MP2) approach. Two variants of MR-MP2 have been tested based on either Hartree–Fock orbitals or Kohn–Sham orbitals of the BH-LYP density functional. In connection with the MR-MP2 approaches, the first-order perturbed wave functions have been employed in the evaluation of spin–orbit coupling. To validate our results, we assembled experimental excitation energies and SOMES of eight diatomic and fifteen polyatomic molecules. For some of the smaller molecules, we carried out calculations at the complete active space self-consistent field (CASSCF) level to obtain SOMEs to compare with. Excitation energies of the experimentally unknown states were assessed with respect to second-order perturbation theory corrected (CASPT2) values where available. Overall, we find a very satisfactory agreement between the excitation energies and the SOMEs obtained with the four approaches. For a few states, outliers with regard to the excitation energies and/or SOMEs are observed. These outliers are carefully analysed and traced back to the wave function composition.     

Explorative computational study of the singlet fission process

Different ab initio methods, namely multi-reference and nonorthogonal configuration interaction techniques, are explored for their applicability in studying the singlet fission problem. It has been shown for 2-methyl-1,5-hexadiene that the ¹TT state can be identified using multi-reference techniques. The geometrical and vibrational properties of the ¹TT state are such that they can be approximated with those of the ⁵TT state. A proof of principle is given for the calculation of the singlet fission pathway driven by nuclear motion: efficient singlet fission can take place if the ¹TT and S₁ states are close in energy with a large non-adiabatic coupling matrix element at the S₁ geometry, and the energy of the S₀ state is well below that of the ¹TT state at the ¹TT geometry.

The nonorthogonal configuration interaction method was used to treat a tetracene trimer. It has been shown that the first excited states can be interpreted as delocalised states; interaction with charge-transfer base states plays an important role. The ¹TT states are localised on one pair of molecules. The electronic coupling between the diabatic S[n] and ¹TT[m] states is in the meV range, confirming previous estimates. The charge-transfer base states enhance the coupling between the S[1]/S[2] and ¹TT[2] excited states.     

The molecular structure and analytical potential energy function of HCO （X^2A＇）

In this paper the equilibrium structure of HCO has been optimized by using density functional theory （DFT）/ B3P86 method and CC-PVTZ basis. It has a bent （Cs, X^2A＇） ground state structure with an angle of 124.4095 °. The vibronic frequencies and force constants have also been calculated. Based on the principles of atomic and molecular reaction statics, the possible electronic states and reasonable dissociation limits for the ground state of HCO molecule have been determined. The analytic potential energy function of HCO （X^2A＇） molecule has been derived by using the many-body expansion theory. The contour lines are constructed, which show the static properties of HCO （X^2A＇）, such as the equilibrium structure, the lowest energies, etc. The potential energy surface of HCO （X^2A＇） is reasonable and very satisfactory.     

The electronic structure of the low lying sextet and quartet states of CrF and CrCl

The electronic structure of CrF and CrCl in X ⁶Σ⁺, ⁶Π, ⁶Δ, A⁶Σ⁺, ⁴Σ⁺, ⁴Π, and ⁴Δ states that correlate with the low lying ⁶S, ⁶D, and ⁴D states of Cr⁺ have been studied, using large atomic natural orbital (ANO) basis sets and a variety of ab initio methods, including multi-reference configuration interaction (MRCI) and coupled cluster with perturbative triples (RCCSD(T)). We include scalar relativistic effects perturbatively and also explore the consequence of correlating the 3s and 3p electrons on the transition metal. We report T _e, R _e,ω_e, as well as dipole moments, bond energies, and charge distributions and compare with the available experimental data as well as previous theoretical results.     

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.     

多参考组态相互作用方法计算研究XOn(X=S,Cl；n=0,±1)的解析势能函数和光谱常数

采用从头计算的多参考组态相互作用方法和含扩散基的3个基组aug-cc-PVXZ (X=D,T,Q) 计算了SO和ClO分子及其分子离子的势能曲线，确定了平衡几何结构、离解能，并采用Feller拟合递推方法得到了基函数为无穷大计算水平值. 确定了SO^－，ClO⁺，ClO^-分子离子的基态. 通过Murrell-Sorbie势能函数和最小二乘法拟合得到了解析势能函数. 基于所得的势能函数，通过解核运动的薛定谔方程得到振 关键词： 多参考组态相互作用 势能曲线 解析势能函数 光谱常数     

Excited state geometry optimisation using Fock-space multi-reference coupled cluster method

The Fock-space multi-reference coupled cluster method is used for the geometry optimisation of the low-lying excited states of the molecules. Molecular geometries of the carbon monohydride cation (CH)⁺, water (H₂O), ozone (O₃) and formaldehyde (HCHO) in their low-lying excited states are optimised. Excited state gradients are calculated using finite field multi-reference coupled cluster method. We compare our results with other theoretical and/or experimental results, wherever available.     

Structure and bonding of the (C6H6)+ 2 radical

To elucidate the relative stability of various structures of the benzene dimer cation radical, (C₆H₆)⁺ ₂ in its ground and low-lying excited states, ab initio complete active space self-consistent field (CASSCF), multi-reference singly and doubly excited configuration interaction (MRSDCI), and multi-reference coupled pair approximation (MRCPA) calculations were performed. Full optimization was performed at the CASSCF level for various structures of the dimer cation, followed by MRSDCI and MRCPA calculations. It was found that the global minimum of the cation is at a slipped C_2h sandwich structure but there are some other sandwich structures with almost the same stability, being within about kcal mol^?1. T-shape structures are less stable than the sandwich structures, by more than 5 kcal mol^?1 by MRCPA calculations. Low lying electronic excited states in various structures are also discussed.     

Raman scattering in amorphous boron

Raman scattering measurements have been performed at room temperature in thin film evaporated amorphous B and B_0.91C_0.09. The amorphous B spectrum indicates density of states features similar to those observed in infrared absorption as well as lower frequency scattering attributed to acoustic plus optic-like modes. The addition of C to amorphous B broadens the spectrum and shifts the lowest frequency peak to higher frequencies. A comparison of the amorphous B and broadened crystalline β-B Raman spectra indicates a number of similarities in peak frequencies that are consistent with similar short range order in both materials.     

Dynamics of Electronic States and Magnetoabsorption in 3D Topological Insulators in a Quantizing Magnetic Field

Quantum states have been calculated analytically; the dynamics of a wave packet in a magnetic field has been investigated, and the optical absorption coefficient has been calculated for surface states in 3D topological insulators of the Bi₂Te₃ family. We have detected a qualitative effect of the hexagonal warping of the spectrum on the structure of wavefunctions at the Landau levels, its manifestation in the features of the wave packet dynamics in a quantizing magnetic field, as well as in the frequency dependence of the optical absorption coefficient, in which new peaks that are absent in the isotropic model of the spectrum appear depending on the polarization of the incident wave. The effects considered here can be manifested in the optical and transport experiments with topological insulators, which makes it possible to determine the parameters of their band structure.     

A CASCI-MRMP method based on Kohn—Sham orbitals

Kohn-Sham orbitals are used in the previously proposed CASCI-MRMP scheme (a multi-reference M?ller-Plesset (MRMP) method with a complete active space configuration interaction (CASCI) reference function). That is, the CASCI wave function was constructed using the Kohn-Sham orbitals and used as a reference function of the MRMP to incorporate the remaining dynamical correlation. The scheme was applied to the potential curves of the ground and low-lying excited states of N₂, the potential curve of the ground state of CO, the barrier height of the H₂CO → H₂ + CO reaction, the valence π-π? and Rydberg excited states of benzene, and the low-lying excited states of ozone. Good agreement between the theory, experiment, and some benchmark calculations was obtained. The various orbitals which are investigated here do not give very different results. Rather, the choice of active space makes a considerable difference, and in particular the perturbation calculation is proved to be very important.     

The electronic structure of ZrSe32

The energy bands of the semiconductor ZrSe₃ have been evaluated using the KKR method. The general features of the electronic structure are expected to pertain to other transition metal trichalcogenides which have similar trigonal prismatic coordination. The calculated density of states agrees well with X-ray photoemission spectra for the valence band. The joint density of states has been evaluated and is discussed in terms of optical measurements.     

A study of the valence shell photoionisation dynamics of CH3CN and CF3CN

Valence shell angle resolved photoelectron spectra of CH₃CN and CF₃CN have been recorded in the photon energy range 14–120 eV, thereby allowing asymmetry parameters and branching ratios to be derived. The carbon and nitrogen K-shell photoabsorption spectra of these two molecules exhibit features ascribed to shape resonantly enhanced transitions. Energy dependent variations observed in the asymmetry parameters and branching ratios provide evidence of shape resonances influencing the valence shell photoionisation dynamics. In addition to the main lines associated with single-hole states, complex satellite structure appears in the inner valence region of the photoelectron spectrum due to many-electron effects. The experimental spectra have been interpreted using previously reported ionisation energies and spectral intensities obtained from Green's function calculations.     

A complete and self-consistent evaluation of XPS spectra of TiN

The electron configuration in single crystalline (sc-)titanium nitride (TiN) has been quantitatively studied using angle resolved X-ray photoelectron spectroscopy (AR-XPS). All samples were fabricated and transferred in situ so that only minimal surface contaminations were observed. The residual oxygen contamination was separated from the bulk information by extrapolating angle resolved measurements. Special attention is given to the quantitative evaluation of the spectra based on basic principles. Shake-up features are observed on core level lines and appear due two final ionized states. The ratio of this shake-up and the main Ti 2p energy line are investigated in this paper. In order to quantify this shake-up a precise evaluation is required. Here we present an approach to evaluate the XPS spectra of the Ti 2p photoemission line in TiN in a self-consistent manner that accounts for all features observable in an energy window of 80 eV. The evaluation considers the appropriate Tougaard background correction, shake-up features as well as surface and bulk plasmons. The ratio of the Ti 2p_1/2 and Ti 2p_3/2 and the corresponding peaks in the energy loss features fulfill the requirements given by quantum mechanics. The energy loss ΔE due to the shake-up process and the shake-up ratio have been determined quantitatively for oxygen-free bulk titanium nitride. The origin of the shake-up, its intensity and energy difference ΔE are explained by a two electron excitation process.     

Fast particle emission from CO2 laser produced plasmas

Spatial distributions and spectra of non thermal particles emitted from CO₂ laser aluminum plasmas have been recorded. With laser fluxes greater than 10¹³ W/cm² ions with MeV maximum kinetic energy have been detected as well as fast electrons in the range of 50 to 500 keV. The results are discussed in terms of resonant absorption as a function of different parameters s such as laser flux and angle of incidence.     

A multi-reference CI study of the low-lying valence and Rydberg states of CF3 radical

Highly correlated calculations at the multi-reference configuration interaction levels including singles and doubles excitations (MR-CISD) and extensivity corrections (MR-CISD?+?Q) have been performed to study some low-lying valence and Rydberg states of the CF₃ radical. Our highest level results (at the MR-CISD?+?Q level) yield the following energy ordering: 3s (7.90?eV)?2A₂ (8.61?eV)?π (8.72?eV)?z (8.73?eV). MR-CISD results indicate transitions of similar intensities from the ground to the following three final states, in the following order: 3p_π?>?3p_z?>?3s. It has also been found that the aforementioned Rydberg states should be responsible for visible emissions and correspond to transitions between bound states. Therefore, it is suggested that the lack of vibrational structure in the visible band of parent systems (e.g. CF₃Cl) may be due to a transition from a bound to an unbound state of the parent molecule.     

Ab initio multi-reference configuration interaction of the low-lying states of the AsP molecule

Nine low-lying electronic states of the AsP molecule, including Σ , Ⅱ, and △ symmetries with singlet, triplet, and quintet spin multiplicities, are studied using multi-reference configuration interaction method.The potential energy curves and the spectroscopic constants of these nine states are determined, and compared with the experimental observed data as well as other theoretical works available at present.Three quintet states are reported for the first time.Furthermore, the analytical potential energy functions of these states are fitted using Murrell-Sorbie function and least square fitting method.     

Electronic structure and optical properties of ordered compounds potassium tantalate and potassium niobate and their disordered alloys

The electronic energy band structure, site and angular momentum decomposed density of states (DOS) of cubic perovskite oxides KNbO₃ and KTaO₃ have been obtained from a first principles density functional based full potential linearized augmented plane wave (FLAPW) method within a generalized gradient approximation (GGA). The total DOS in valence region is compared with the experimental photo-emission spectra (PES). The calculated DOS is in good agreement with the experimental energy spectra and the features in the spectra are interpreted by comparison with the projected density of states (PDOS). The valence band PES is mainly composed of Nb-4d/Ta-5d and O 2p states in KNbO₃ and KTaO₃, respectively. Using the PDOS and the band structure we have analyzed the inter-band contribution to the optical properties of these materials. The real and imaginary parts of the dielectric function have been calculated and compared with experimental data. They are found to be in a reasonable agreement. The role of band structure on the optical properties have been discussed.     

Conformation and phonon dispersion in trans-1,4-polybutadiene

Phonon dispersion studies for trans-l,4-polybutadiene (TPBD) are reported. The change in profile of the dispersion curves as a function of the ═CH─CH₂─ dihedral angle φ has been obtained in order to find the geometry of the polymer that gives the best interpretation of the spectra. It is found for φ = 71°. The regions of high density of states obtained from the dispersion curves for an isolated chain have been used to explain the features of the spectra. Some of these, which were earlier attributed to interchain interactions, in fact arise due to intrachain interactions. Prominent features of the dispersion curves are discussed and heat capacity, derived therefrom, is reported. Calculations have also been performed for unsaturated C-deuterated and fully deuterated TPBD samples to check the validity of the force field and assignments.