The valence electronic excited states of trans-1,3-butadiene and trans,trans-1,3,5-hexatriene from generalized valence bond and configuration interact

Self-consistent ab initio generalized valence bond (GVB) and configuration interaction (Cl) calculations are presented for the ground and valence electronic excited states of trans-1,3-butadine and all trans-1,3,5-hexatrine. Previous workers have suggested that (all trans) polyenes exhibit a parity-forbidden valence excited state (2¹ A_g at an energy just below that of the first dipole-allowed (1¹ B_u) state. We find such valence excited electronic states for butadiene (ΔE = 7.06 eV) and hexatriene (ΔE = 5.87 eV), but in both cases the excitation energy is considerably higher than the dipole-allowed transitions (zero-zero transitions at 5.95 eV and 4.95 eV, respectively). The lower two triplet states are found at 3.35 eV and 5.08 eV for butadie and at 2.71 eV and 4.32 eV in hexatrine, in good agreement with experimental values (3.2–3.3 eV and 4.92 eV for butadiene and 2.66 eV and 4.1–4.2 eV for hexatrine). Considering the states formed by removing one electron from the π space we found ion states at 8.95 eV and 11.40 eV for butadiene and at 8.33 eV, 10.53 eV, and 11.60 eV for hexatriene, in godo agreement with experimental results (9.0 eV and 11.5 eV for butadiene and 8.45 eV, 10.43 eV and 11.6 eV for hexatriene).     

Ab initio study of the ground and lower-lying excited electronic states of NiX2 and FeX2 (X=F,Cl, Br,I) molecules

The ground and lower-lying excited electronic states of FeX₂ and NiX₂ (X=F, Cl, Br, I) molecules are systematically investigated by ab initio method at the complete active space self-consistent field (CASSCF) and multiconfigurational quasi-degenerate second-order perturbation (MCQDPT2) levels of theory. It is concluded that the dynamic electron correlation has to be taken into account in the prediction of the properties for such kind of molecules. The equilibrium bond lengths r_e(M–X), force constants and harmonic vibrational frequencies are calculated for the ground and lower-lying excited electronic states. The spin-orbit coupling (SOC) effects are analysed.     

Implementation of molecular symmetry in valence bond calculation

A novel strategy for the construction of many-electron symmetry-adapted wave function is proposed for ab initio valence bond (VB) calculations and is implemented for valence bond self-consistent filed (VBSCF) and breathing orbital valence bond (BOVB) methods with various orbital optimization algorithms. Symmetry-adapted VB functions are constructed by the projection operator of symmetry group. The many-electron symmetry-adapted wave function is expressed in terms of symmetry-adapted VB functions, and thus the VB calculations can be performed with the molecular symmetry restriction. Test results show that molecular symmetry reduces the computational cost of both the iteration numbers and CPU time. Furthermore, excited states with specific symmetry can be conveniently obtained in VB calculations by using symmetry-adapted VB functions.     

Pseudopotential approach of the electronic structure in clusters: application to Alkali Halides and Rare Gases

We examine here the use of pseudopotentials in limit cases where only a very small number of electrons (much less than the usual number of valence electrons), eventually excited, can be singled out and considered as active to determine the electronic structure. Two applications are considered. The first one concerns the family of nonstoechiometric ionic clusters for which only the excess electrons are active. The relevance and accuracy of such ab initio determined pseudopotentials is illustrated on Na_nF_n-1 clusters which are treated as one-electron systems. The second application concerns excited states of neutral rare gas clusters Rg _n ^* . In this case, the excited electron may be coupled to different core states and a resonant hole-particle treatment involving e-Rg and e-Rg ⁺ pseudopotentials is presented.     

Geometries, electronic structures, and excited states of UN2, NUO+, and UO 2 2+ : a combined CCSD(T), RAS/CASPT2 and TDDFT study

The ground- and excited-state geometries and electronic structures of the isoelectronic series of molecules UN₂, NUO⁺, and UO ₂ ²⁺ are investigated by using relativistic density functional theory (DFT) and ab initio wavefunction theory (WFT). Scalar relativistic and spin?Corbit-coupled quantum chemical methods at the CASPT2, RASPT2, CCSD(T), DFT and TDDFT levels are applied. Relativistic effects as elucidated by Pekka Pyykk? play an important role in these uranium compounds, in particular for the excited states. The three molecular species exhibit significantly different spectroscopic properties, concerning their excitation energies, bond lengths and vibrations. Density functional approaches yield qualitatively correct results for the ground states and the valence????U.7s,6d excited states. However, the performance of TDDFT for valence????U.5f type excitations (in particular of UN₂ and NUO⁺) is less satisfactory, indicating the importance of the self-interaction correction for such excitations.     

Large shift and small broadening of Br2 valence band upon dimer formation with H2O: an ab initio study

Valence electronic excitation spectra are calculated for the H(2)O···Br(2) complex using highly correlated ab initio potentials for both the ground and the valence electronic excited states and a 2-D approximation for vibrational motion. Due to the strong interaction between the O-Br and the Br-Br stretching motions, inclusion of these vibrations is the minimum necessary for the spectrum calculation. A basis set calculation is performed to determine the vibrational wave functions for the ground electronic state and a wave packet simulation is conducted for the nuclear dynamics on the excited state surfaces. The effects of both the spin-orbit interaction and temperature on the spectra are explored. The interaction of Br(2) with a single water molecule induces nearly as large a shift in the spectrum as is observed for an aqueous solution. In contrast, complex formation has a remarkably small effect on the T = 0 K width of the valence bands due to the fast dissociation of the dihalogen bond upon excitation. We therefore conclude that the widths of the spectra in aqueous solution are mostly due to inhomogeneous broadening.     

Ab initio computations of spin-orbit interactions in polyatomic molecules. Splitting of sulfur LII,III states and singlet–triplet transitions in SO2

Spin-orbit interactions among the ground and the first few excited electronic states of SO₂, are computed with ab initio molecular wave functions and Gaussian atomic orbitals. All spin-other orbits contributions to the matrix elements are included. The computed intensity of the first singlet–triplet transition is found to be in broad agreement with experiment and sensitive to an extension of the configuration interaction expansion of molecular wave functions. Also, the splitting of sulfur L_{II ,III} states in SO₂ is derived as an example of large spin-orbit interactions among electronic states.     

Geometry and electronic structure of impurity-trapped excitons in Cs2GeF6:U4+ crystals. The 5f17s1 manifold

Excitons trapped at impurity centers in highly ionic crystals were first described by McClure and Pedrini [Phys. Rev. B 32, 8465 (1985)] as excited states consisting of a bound electron-hole pair with the hole localized on the impurity and the electron on nearby lattice sites, and a very short impurity-ligand bond length. In this work the authors present a detailed microscopic characterization of impurity-trapped excitons in U(4+)-doped Cs(2)GeF(6). Their electronic structure has been studied by means of relativistic ab initio model potential embedded cluster calculations on (UF(6))(2-) and (UF(6)Cs(8))(6+) clusters embedded in Cs(2)GeF(6), in combination with correlation methods based on multireference wave functions. The local geometry of the impurity-trapped excitons, their potential energy curves, and their multielectronic wave functions have been obtained as direct, nonempirical results of the methods. The calculated excited states appear to be significantly delocalized outside the UF(6) volume and their U-F bond length turns out to be very short, closer to that of a pentavalent uranium defect than to that of a tetravalent uranium defect. The wave functions of these excited states show a dominant U 5f(1)7s(1) configuration character. This result has never been anticipated by simpler models and reveals the unprecedented ability of diffuse orbitals of f-element impurities to act as electron traps in ionic crystals.     

A convenient decontraction procedure of internally contracted state-specific multireference algorithms

Internally contracted state-specific multireference (MR) algorithms, either perturbative such as CASPT2 or NEVPT2, or nonperturbative such as contracted MR configuration interaction or MR coupled cluster, are computationally efficient but they may suffer from the internal contraction of the wave function in the reference space. The use of a low dimensional multistate model space only offers limited flexibility and is not always practicable. The present paper suggests a convenient state-specific procedure to decontract the reference part of the wave function from a series of state-specific calculations using slightly perturbed zero-order wave functions. The method provides an orthogonal valence bond reading of the ground state and an effective valence Hamiltonian, the excited roots of which are shown to be relevant. The orthogonal valence bond functions can be considered quasidiabatic states and the effective valence Hamiltonian gives therefore the quasidiabatic energies and the electronic coupling among the quasidiabatic states. The efficiency of the method is illustrated in two case problems where the dynamical correlation plays a crucial role, namely, the LiF neutral/ionic avoided crossing and the F(2) ground state wave function.     

Ab initio valence bond calculations. X. Vertical valence ionization potentials of allene and butatriene

The ground and vertical valence ionized states of allene and butatriene have been studied in the ab initio valence bond framework using the 6–31G basis set after contraction and introducing the core–valence shell separation. The final wave functions have been analyzed in terms of VB structures by means of population analysis.     

Electronic transition moment with spin‐orbit coupling of the molecular ion KRb+

By using the electronic wave functions obtained from an ab initio calculation, including the spin‐orbit coupling, the electronic transition moments have been investigated for two bound states of symmetry Ω = 1/2 and Ω = 3/2 of the molecular ion KRb⁺. Based on a canonical functions approach for the determination of the vibrational wave functions, the matrix elements have been calculated for the bound states considered for v = 0, 10, 20 with v′‐ v = 0, 1, 2, …, 6; by using the same canonical approach, the eigenvalues and abscissas of the corresponding turning points (r_min and r_max) have been investigated for these states that obtained from a theoretical ab initio calculation up to v = 105. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Valence : A Massively Parallel Implementation of the Variational Subspace Valence Bond Method

This work describes the software package, Valence , for the calculation of molecular energies using the variational subspace valence bond (VSVB) method. VSVB is an ab initio electronic structure method based on nonorthogonal orbitals. Important features of practical value include high parallel scalability, wave functions that can be constructed automatically by combining orbitals from previous calculations, and ground and excited states that can be modeled with a single configuration or determinant. The open-source software package includes tools to generate wave functions, a database of generic orbitals, example input files, and a library build intended for integration with other packages. We also describe the interface to an external software package, enabling the computation of optimized molecular geometries and vibrational frequencies. © 2019 Wiley Periodicals, Inc.     

Two-state model based on the block-localized wave function method

The block-localized wave function (BLW) method is a variant of ab initio valence bond method but retains the efficiency of molecular orbital methods. It can derive the wave function for a diabatic (resonance) state self-consistently and is available at the Hartree-Fock (HF) and density functional theory (DFT) levels. In this work we present a two-state model based on the BLW method. Although numerous empirical and semiempirical two-state models, such as the Marcus-Hush two-state model, have been proposed to describe a chemical reaction process, the advantage of this BLW-based two-state model is that no empirical parameter is required. Important quantities such as the electronic coupling energy, structural weights of two diabatic states, and excitation energy can be uniquely derived from the energies of two diabatic states and the adiabatic state at the same HF or DFT level. Two simple examples of formamide and thioformamide in the gas phase and aqueous solution were presented and discussed. The solvation of formamide and thioformamide was studied with the combined ab initio quantum mechanical and molecular mechanical Monte Carlo simulations, together with the BLW-DFT calculations and analyses. Due to the favorable solute-solvent electrostatic interaction, the contribution of the ionic resonance structure to the ground state of formamide and thioformamide significantly increases, and for thioformamide the ionic form is even more stable than the covalent form. Thus, thioformamide in aqueous solution is essentially ionic rather than covalent. Although our two-state model in general underestimates the electronic excitation energies, it can predict relative solvatochromic shifts well. For instance, the intense pi-->pi* transition for formamide upon solvation undergoes a redshift of 0.3 eV, compared with the experimental data (0.40-0.5 eV).     

Photoluminescence of oxygen-containing surface defects in germanium oxides: a theoretical study

Photoabsorption and photoluminescence properties of nonbridging oxygen -O-Ge[triple bond](NBO), -OO-Ge[triple bond] (peroxy radical), O=Ge=, and (O2)Ge= defects in germanium oxides have been investigated by high-level ab initio calculations. Geometry optimization for excited electronic states of model clusters simulating these defects was carried out at the complete-active-space self-consistent-field level, and relative energies were calculated by various methods including time-dependent density-functional theory, outer-valence Green's functions, equation-of-motion coupled cluster theory with single and double excitations, symmetry-adapted cluster configuration interaction, multireference second-order perturbation theory, and multireference configuration interaction. The results demonstrate that the considered excited states of the aforementioned defects normally exhibit large Stokes shifts and that, with few exceptions, UV photoabsorption is accompanied by red or IR photoluminescence.     

Expanded electronic states of the fluorine molecule

Potential curves of electronically excited states of F₂ with an expanded outer orbital have been calculated using a modified frozen core technique: The ionic core has been described with a two-determinant wave function and for the excited states a mixing of configurations with different cores has been employed. An investigation of the valence shell states of F₂ is presented and potential curves for a singly excited as well as a doubly excited V-state of ¹Σ_u⁺ symmetry have been calculated. Further a low lying two-configuration state resulting from simultaneous excitation to a valence and a Rydberg orbital is predicted.     

Electronic band structure and chemical bonding in the new antiperovskites AsNMg3 and SbNMg3

The electronic properties of the new Mg-based antiperovskites AsNMg₃ and SbNMg₃ are investigated within the ab initio local-density full-potential LMTO-GGA method. Both compounds are ionic wide-gap semiconductors with a direct energy gap at Γ of 1.332 eV for AsNMg₃ and an indirect energy gap (Γ→M transitions) of 0.623 eV for SbNMg₃. The valence bands are composed mainly of N 2p and (As,Sb) np states. There is some covalent mixing between Mg-N and Mg-(As,Sb) valence states. The equilibrium values of lattice constants and the bulk modulus were also obtained.     

An analysis of the topology of the electron charge density and the reactant–product electronic structure variation along the intrinsic reaction coordinate

In this work the topology of the electron charge density and the variations in the reactant and product electronic structures are analyzed along the Fukui intrinsic reaction coordinate (IRC). The systems studied are the ionic and the Menschutkin S_N2 reactions. This study is performed at ab initio RHF and MP2 levels, and density functional level, employing the B3LYP functional. The basis set in all cases is of split valence type and includes diffuse and polarization functions in nonhydrogen atoms 6‐31+G*. As a measure of the variations of reactant and product electronic structures, we calculate at the RHF level, the overlap integral between the total wavefunction and the wavefunction based on the reactant (or product) localized fragment orbitals. This integral can be interpreted, in Hilbert space, as the cosine of the angle between the vector representing the electronic structure of the molecule in each point of the IRC and that of reactant (or product) electronic structure. The calculated molecular properties were analyzed in light of the valence bond approach, and qualitative differences were noted depending on the property studied. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

A Valence Bond Study of the Low‐Lying States of the NF Molecule

The electronic structures of the three lowest‐lying states of NF are investigated by means of modern valence bond (VB) methods such as the VB self‐consistent field (VBSCF), breathing orbital VB (BOVB), and VB configuration interaction (VBCI) methods. The wave functions for the three states are expressed in terms of 9–12 VB structures, which can be further condensed into three or four classical Lewis structures, whose weights are quantitatively estimated. Despite the compactness of the wave functions, the BOVB and VBCI methods reproduce the spectroscopic properties and dipole moments of the three states well, in good agreement with previous computational studies and experimental values. By analogy to the isoelectronic O₂ molecule, the ground state ³Σ^? possesses both a σ bond and 3‐electron π bonds. However, here the polar σ bond contributes the most to the overall bonding. It is augmented by a fractional (19 %) contribution of three‐electron π bonding that arises from π charge transfer from fluorine to nitrogen. In the singlet ¹Δ and ¹Σ⁺ excited states the π‐bonding component is classically covalent, and it contributes 28 % and 37 % to the overall bonding picture for the two states, respectively. The resonance energies are calculated and reveal that π bonding contributes at least 24, 35 and 42 kcal mol^?1 to the total bonding energies of the ³Σ^?, ¹Δ and ¹Σ⁺ states, respectively. Some unusual properties of the NF molecule, like the equilibrium distance shortening and bonding energy increasing upon excitation, the counterintuitive values of the dipole moments and the reversal of the dipole moments as the bond is stretched, are interpreted in the light of the simple valence bond picture. The overall polarity of the molecule is very small in the ground state, and is opposite to the relative electronegativity of N vs F in the singlet excited states. The values of the dipole moments in the three states are quantitatively accounted for by the calculated weights of the VB structures.