Calculation of excited‐state ionization potential for boron‐like sequence

Excited‐state ionization potentials for boron‐like sequence with Z = 5–19 are studied systematically, using the weakest bound electron potential model theory (WBEPM theory) and iso‐spectrum‐level series conception. Nonrelativistic ionization energy is derived from the theory. Relativistic effects are included in the Breit–Pauli approximation. Comparison of the calculated excited‐state ionization potential with available experimental data is carried out for 1s²2s²2p ²P, 1s²2s²3s ²S_1/2, 1 s²2s²3p ²P, 1s²2s²3d ²D_5/2, 1s²2s²4d ²D_5/2, 1s²2s²5d ²D_5/2, and 1s²2s²6d ²D_5/2 series. The present results depart from experimental results by no more than 0.133 eV for all 81 results for which experimental data are available. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

Conductor‐like screening model for relaxed excited states: Implementation in the semiempirical method MSINDO

Two approaches to treat solvent polarization and reorientation effects for excited states of molecules and surfaces have been implemented in the recently developed MSINDO‐sCIS method (Gadaczek, Krause, Hintze, Bredow, J. Chem. Theory Comput. 2011, 7, 3675). They allow for an efficient calculation of analytical energy gradients and hence open the opportunity to investigate fluorescence effects or photochemical reactions in solution for large molecules that are difficult to treat with high‐level methods. Both approaches are based on the conductor‐like screening model (COSMO) (Klamt and Schüürmann, J. Chem. Soc., Perkin Trans. 1993, 2, 799) in combination with the configuration interaction singles (CIS) method (Foresman, Head‐Gordon, Pople, and Frisch, J. Phys. Chem. 1992, 96, 135). The paper gives a brief outline of the theoretical background. As a first application, solvent shifts of three well‐studied, environment‐sensitive fluorescent dyes (Kucherak, Didier, Mély, and Klymchenko, J. Phys. Chem. Lett. 2010, 1, 616) have been calculated and compared with experimental results and standard time‐dependent density functional theory. A statistical evaluation of MSINDO‐COSMO‐sCIS is provided for a set of 39 molecules suggested recently by Jacquemin et al. (Jacquemin, Planchat, Adamo, and Mennucci, J. Chem. Theory Comput. 2012, 8, 2359). Calculated vertical and adiabatic excitation energies and fluorescence energies are compared to experimental data. © 2014 Wiley Periodicals, Inc.     

Low‐lying singlet excited states of isocyanogen

Recent photofragment fluorescence excitation (PHOFEX) spectroscopy experiments have observed the ùA″ singlet excited state of isocyanogen (CNCN) for the first time. The observed spectrum is not completely assigned and significant questions remain about the excited states of this system. To provide insight into the energetically accessible excited states of CNCN, optimized geometries, harmonic vibrational frequencies, and excitation energies for the first three singlet excited states are determined using equation‐of‐motion coupled‐cluster theory with singles and doubles (EOM‐CCSD) and correlation‐consistent basis sets. Additionally, excited state coupled‐cluster methods which approximate the contributions from triples (CC3) are utilized to estimate the effect of higher‐order correlation on the energy of each excited state. For the ùA″ state, our best estimate for T₀ is about 42,200 cm^?1, in agreement with the experimentally estimated upper limit for the zero‐point level of 42,523 cm^?1. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

On orthogonality constrained multiple core‐hole states and optimized effective potential method

An attempt to construct a multiple core‐hole state within the optimized effective potential (OEP) methodology is presented. In contrast to the conventional Δ‐self‐consistent field method for hole states, the effects of removing an electron is achieved using some orthogonality constraints imposed on the orbitals so that a Slater determinant describing a hole state is constrained to be orthogonal to that of a neutral system. It is shown that single, double, and multiple core‐hole states can be treated within a unified framework and can be easily implemented for atoms and molecules. For this purpose, a constrained OEP method proposed earlier for excited states (Glushkov and Levy, J. Chem. Phys. 2007, 126, 174106) is further developed to calculate single and double core ionization energies using a local effective potential expressed as a direct mapping of the external potential. The corresponding equations, determining core‐hole orbitals from a one‐particle Schrödinger equation with a local potential as well as correlation corrections derived from the second‐order many‐body perturbation theory are given. One of the advantages of the present direct mapping formulation is that the effective potential, which plays the role of the Kohn–Sham potential, has the symmetry of the external potential. Single and double core ionization potentials computed with the presented scheme were found to be in agreement with data available from experiment and other calculations. We also discuss core‐hole state local potentials for the systems studied. © 2012 Wiley Periodicals, Inc.     

Variational treatment on the energy of the He‐sequence ground state with weakest bound electron potential model theory

The concept of spin–orbital of the weakest bound electron is described used to construct the antisymmetric wave function of atomic or ionic systems within weakest bound electron potential model theory (WBEPM theory). The total energies of He‐sequence (Z = 2–9) in the ground states is calculated with a variational method. The effect of fixed orbital approximation is discussed quantitatively. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Quantum bifurcation in a coulombic‐like potential

Because of the lack of nonlinear dynamics, up to now no bifurcation phenomenon in its original sense has been discovered directly in quantum mechanical systems. Based on the formalism of complex‐valued quantum mechanics, this article derives the nonlinear Hamilton equations from the Schrödinger equation to provide the necessary mathematic framework for the analysis of quantum bifurcation. This new approach makes it possible to identify quantum bifurcation by the direct evidence of the sudden change of fixed points and their surrounding trajectories. As a practical application of the proposed approach, we consider the quantum motion in a Coulombic‐like potential modeled by V(r) = A/r² ? B/r, where the first term describes the centrifugal trend and the second deals with the Coulombic attraction. As the bifurcation parameter evolves, we demonstrate how local and global bifurcations in quantum dynamics can be identified by inspecting the changes of fixed points and their surrounding trajectories. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Theoretical study on regularity of changes in quantum defects in Rydberg state series of many‐valence electron atoms within WBEPM theory

Within the scheme of the weakest bound electron potential model theory, the regularity of changes in quantum defects in 40 “spectrum‐level‐like series” of several many‐valence electron atoms of the third period was studied. The n–δ curves of the 40 spectrum‐level‐like series could be classified into three types; for all such series the quantum defects δ could be expanded as a polynomial of the principal quantum number n in a spectrum‐level‐like series. With regularity, the level energies of high Rydberg states in a series can be predicted accurately. By carefully studying and explaining the three types of 40 n–δ curves, the conclusion was reached: the type of the n–δ curve, i.e., the regularity of changes in quantum defects in a spectrum‐level‐like series, was determined by both the energy level and the azimuthal quantum number l of the weakest bound electron. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 232–237, 2001     

Unexpected properties of non‐autoionizing doubly excited states of the H2 molecule

We present accurate calculations of the non‐autoionizing and doubly excited states of the H₂ molecule using full configuration interaction with Hartree–Fock molecular orbitals and Heitler–London atomic orbitals. We consider the united atom configurations from He(2p2p) up to He(2p8g) and dissociation products from H₂(2p + 2p) up to H₂(2p + 6?). Born–Oppenheimer calculations are carried out with extended and optimized Slater‐type orbitals for a total of 40 states, 10 for each symmetry, covering the internuclear distances from the united atom to dissociation, which, for some states, is reached beyond 100 a₀. Occurrences of repulsive states cleanly interlaced between bound states with many vibrational levels are reported. Some of the potential minima are deep enough to accommodate many vibrational levels (up to 50). Noteworthy large equilibrium minima, like R_eq = 46.0 a₀ in the state dissociating as (2p + 6h) and with 18 vibrational levels. The occurrence of vertical excitations from the singly excited manifolds is analyzed. Several states present double minima generated by avoided crossings, some with a strong ionic character. © 2016 Wiley Periodicals, Inc.     

Density functional calculations on triply excited states of lithium isoelectronic sequence

Triply excited states of many-electron atomic systems are characterized by the presence of strong electron correlation, closeness to more than one threshold, and degeneracy with many continua; therefore, they offer unusual challenges to theoretical methodologies. In the present article, we computed with reasonable accuracy all the n=2 intrashell triply excited states (2s²2p ²P; 2s2p^{2 2}D, ⁴P, ²P, ²S; and 2p^{3 2}D, ²P, ⁴S) of three-electron atomic systems (Z=2, 3, 4, 6, 8, 10) by using a density functional formalism developed recently in our laboratory, based on the nonvariational Harbola–Sahni exchange potential in conjunction with a parametrized local Wigner and Lee–Yang–Parr correlation potentials. Nonrelativistic energies and densities are obtained by solving a Kohn–Sham-type differential equation. The calculated results are compared with available experimental and other theoretical data. The 2p³(⁴S)→1s2p²(⁴P) transition wavelength for the isoelectronic series is also computed. The overall good agreement of our results with the literature data indicates the reliability of the present density functional methodology for excited states of many-electron systems. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 65 : 317–332, 1997     

Computation of ionization and various excited state energies ofhelium and helium‐like quantum dots

In the effective mass approximation, we calculated the wave functions and some energy states of helium and helium‐like quantum dots (QDs) with impurity charges Z = 0, 1, 2, 3, and 4. In addition, we carried out the ionization energies of these QDs as a function of dot radius, and we investigated the influence of impurity on the ionization energy. We utilized the method that is a combination of quantum genetic algorithm (QGA) and Hartree‐Fock Roothaan (HFR). The results are in a good agreement with literature results. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Features of the fluorine‐substituted acetaldehydes dynamics in the low‐lying electronic states: Quantum mechanical study of the CHF2CHO molecule lowest excited singlet state

The potential energy surface (PES) for the CHF₂CHO molecule in the excited S₁ state is calculated by the CASSCF method. The features of the 1‐ and 2‐D cross‐sections of PES are considered in comparison with those of the relative molecules. The vibrational frequencies are calculated in harmonic approximation and the vibrational energy levels for the inversion motion of the carbonyl fragment CCH_aO and for the torsion motion of the CHF₂‐top are calculated in anharmonic approximation by the 1‐ and 2‐D variational methods. The calculated data are compared with the experimental ones. The problems of the experimental data interpretation are considered. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Ritz variational method for the high‐lying nonautoionizing doubly excited 1,3Fe states of two‐electron atoms

Energy eigenvalues of nonautoionizing doubly excited states originating from 2pnf ( ) configuration of two‐electron atoms have been calculated by expanding the basis set in explicitly correlated Hylleraas coordinates under the framework of Ritz variational method. A detailed discussion on the evaluation of correlated basis integrals is given. The energy eigenvalues of a number of these doubly excited states are being reported for the first time especially for the high lying states. The effective quantum numbers ( ) for the states mentioned above have been calculated by using the theory of quantum defect.     

Time-dependent Hartree-Fock calculations for the excited ‘S’ states of lithium isoelectronic sequence

Time-dependent HF (RPA) calculations have been performed to estimate the transition energies and excited state wavefunctions of Li, Be⁺, B²⁺ and C³⁺ for the transitions 1s ²2s ² S 1s ² ns ² S (n = 3,4, ... 8). The excitation energies and excited state wavefunctions are extracted from the position of the poles of a linearised variational functional. The excitation energies are in excellent agreement with those obtained spectroscopically. The excited state wavefunctions are utilised to find the matrix elements of different operators and the cusp values.     

Molecular electric properties in electronic excited states: multipole moments and polarizabilities of H2O in the lowest1 B 1 and3 B 1 excited states

Summary The dipole and quadrupole moments and the dipole polarizability tensor components are calculated for the¹ B ₁ and³ B ₁ excited states of the water molecule by using the complete active space (CAS) SCF method and an extended basis set of atomic natural orbitals. The dipole moment in the lowest¹ B ₁ (0.640 a.u.) and³ B ₁ (0.416 a.u.) states is found to be antiparallel to that in the ground electronic state of H₂O. The shape of the quadrupole moment ellipsoid is significantly modified by the electronic excitation to both states investigated in this paper. All components of the excited state dipole polarizability tensor increase by about an order of magnitude compared to their values in the ground electronic state. The present results are used to discuss some aspects of intermolecular interactions involving molecules in their excited electronic states.     

Radial and angular correlations in doubly excited states: A time‐dependent perturbation approach

The time‐dependent variation perturbation theory (TDVPT) was applied to estimate separately the effect of radial and angular correlations in the doubly excited states of two‐electron systems. Test calculations were performed for the transitions 1s² : ¹S^e→2s² : ¹S^e for H⁻ and 1s² : ¹S^e→ns² : ¹S^e (n=2,…,5) for He, Li⁺, Be²⁺, and B³⁺. Transition energies to various doubly excited states were estimated using radially correlated basis sets as well as with basis sets which take care of both radial and angular correlations. Angular correlation is taken care of by incorporating higher angular momentum basis sets in the expansion of the perturbed wave functions. The excitation energy is lower in all the cases, indicating the correct behavior. Overall improvement of the results is observed when angular correlation is included. The effect of angular correlation, however, diminishes rapidly with increase of the nuclear charge. This has been demonstrated explicitly for the lowest doubly excited transitions in the highly stripped ions Al¹¹⁺, Si¹²⁺, P¹³⁺, S¹⁴⁺, and Cl¹⁵⁺. © 1999 John Wiley & Sons, Inc. Int J Quant Chem 76: 99–104, 2000     

An ab initio study of excited states of guanine in the gas phase and aqueous media: Electronic transitions and mechanism of spectral oscillations

Ground state geometries of the four tautomeric forms keto‐N9H, keto‐N7H, enol‐N9H, and enol‐N7H of guanine were optimized in the gas phase at the RHF level using a mixed basis set consisting of the 4‐31G basis set for all the atoms except the nitrogen atom of the amino group for which the 6‐311+G* basis set was used. These calculations were also extended to hydrogen‐bonded complexes of three water molecules with each of the keto‐N9H (G9‐3W) and keto‐N7H (G7‐3W) forms of guanine. Relative stabilities of the four above‐mentioned tautomers of guanine as well as those of G9‐3W and G7‐3W complexes in the ground state in the gas phase were studied employing the MP2 correlation correction. In aqueous solution, relative stabilities of these systems were studied using the MP2 correlation correction and polarized continuum model (PCM) or the isodensity surface polarized continuum model (IPCM) of the self‐consistent reaction field (SCRF) theory. Geometry optimization in the gas phase at the RHF level using the 6‐31+G* basis set for all atoms and the solvation calculations in water at the MP2 level using the same basis set were also carried out for the nonplanar keto‐N9H and keto‐N7H forms of guanine. Thus, it is shown that among the different tautomers of guanine, the keto‐N7H form is most stable in the gas phase, while the keto‐N9H form is most stable in aqueous solution. It appears that both the keto‐N9H and keto‐N7H forms of guanine would be present in the ground state, particularly near the aqueous solution–air interface. Vertical excitation and excited state geometry optimization calculations were performed using configuration interaction involving single electron excitation (CIS). It is found that the absorption spectrum of guanine would arise mainly due to its keto‐N9H form but the keto‐N7H form of the same would also make some contribution to it. The enol‐N9H and enol‐N7H forms of the molecule are not expected to occur in appreciable abundance in the gas phase or aqueous media. The normal fluorescence spectrum of guanine in aqueous solution with a peak near 332 nm seems to originate from the lowest singlet excited state of the keto‐N7H form of the molecule while the fluorescence of oxygen‐rich aqueous solutions of guanine with a peak near 450 nm appears to originate from the lowest singlet excited state of the keto‐N9H form of the molecule. The origin of the slow damped spectral oscillation observed in the absorption spectrum of guanine has been explained. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 826–846, 2000