Theoretical prediction of the electronic excited states and resonance Raman intensities in formamide from coupled cluster calculations

Electronic excitations and the resonance Raman spectrum of formamide were obtained from ab initio electron correlation calculations using the equation of motion coupled cluster (EOM-CCSD) method. Interpretation of the UV spectrum on the basis of calculated vertical excitation energies and oscillator strengths accounts for all experimental bands previously assigned. Our assignment, however, suggests an additional Rydberg band at about 7.4 eV which may be hidden under the main absorption. We also show that the Rydberg states appear pairwise, corresponding to n and π hole states, respectively. Using analytic derivative techniques, derivatives of the excited state energies with respect to normal coordinates of the ground state were calculated. Approximate resonance Raman intensities have been determined.     

Locally correlated equation-of-motion coupled cluster theory for the excited states of large molecules

We report an extension of the local correlation concept to electronically excited states via the equation-of-motion coupled cluster singles and doubles (EOM-CCSD) method. We apply the same orbital domain structure used successfully for ground-state CCSD by Werner and co-workers and find that the resulting localized excitation energies are in error generally by less than 0.2 eV relative to their canonical EOM-CCSD counterparts, provided the basis set is flexible and includes Rydberg-like functions. In addition, we account for weak-pair contributions efficiently using a correction to local-EOM-CCSD transition energies based on the perturbative (D) correction used with configuration interaction singles (CIS).     

Perturbation and SCF calculations for excited states

One can treat the linear variation calculation by the perturbation expansion; on the other hand, one can also relate the perturbed wave function for the mth state to the mth eigenvector and justify the upper bound nature of the perturbation calculations for excited states. One can also associate a special type linear variation wave function to the SCF calculation. The upper bound nature of the excited-state SCF calculation can then be accessed by the help of this special wave function.     

Relativistic calculations of ground and excited states of LiYb molecule for ultracold photoassociation spectroscopy studies

We report a series of quantum-chemical calculations for the ground and some of the low-lying excited states of an isolated LiYb molecule by the spin-orbit multistate complete active space second-order perturbation theory (SO-MS-CASPT2). Potential energy curves, spectroscopic constants, and transition dipole moments (TDMs) at both spin-free and spin-orbit levels are obtained. Large spin-orbit effects especially in the TDMs of the molecular states dissociating to Yb((3)P(0,1,2)) excited states are found. To ensure the reliability of our calculations, we test five types of incremental basis sets and study their effect on the equilibrium distance and dissociation energy of the ground state. We also compare CASPT2 and CCSD(T) results for the ground state spectroscopic constants at the spin-free relativistic level. The discrepancies between the CASPT2 and CCSD(T) results are only 0.01 ? in equilibrium bond distance (R(e)) and 200 cm(-1) in dissociation energy (D(e)). Our CASPT2 calculation in the supermolecular state (R=100 a.u.) with the largest basis set reproduces experimental atomic excitation energies within 3% error. Transition dipole moments of the super molecular state (R=100 a.u.) dissociating to Li((2)P) excited states are quite close to experimental atomic TDMs as compared to the Yb((3)P) and Yb((1)P) excited states. The information obtained from this work would be useful for ultracold photoassociation experiments on LiYb.     

Ground and excited states calculations of 7-phenylamino-substituted coumarins

A theoretical calculation of the ground and first excited states of two 7-phenylamino-substituted coumarin compounds are performed. In order to study the effect of phenyl substituted in amino group and fluorine atoms substituted in methyl group, 7-amino-4-methyl coumarin (C120) and 7-amino-4-(trifluoromethyl) coumarin (C151) were also studied. The geometries of the ground state and the first ground state were optimized using density function theory and configuration interaction singles levels of theory. Molecular orbitals (MO) of the ground and first excited states of the four coumarin compounds were obtained to explain the change of the structures. ZINDO and TD-DFT methods with different basis sets were applied to predict the UV absorption spectra. The solvent effect had also been taken into account using self-consistent isodensity polarized continuum model. The predicted spectra are in agreement with the experimental data.     

Quantum Monte Carlo calculations for ground and excited states

A brief overview of the diffusion quantum Monte Carlo method is given. We illustrate the application to ground‐state calculations by a study of the relative stability of carbon clusters near the crossover to fullerene stability, thereby determining the smallest stable fullerene. The application to excited states is illustrated via a study of excitonic states in small hydrogenated silicon clusters. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Ab initio calculations of triplet excited states and potential-energy surfaces of vinyl chloride: insights into spectroscopy and photodissociation dynamics

The equilibrium geometries and harmonic vibrational frequencies of three low-lying triplet excited states of vinyl chloride have been calculated using the state-averaged complete active space self-consistent field (CASSCF) method with the 6-311++G(d,p) basis set and an active space of four electrons distributed in 13 orbitals. Both adiabatic and vertical excitation energies have been obtained using the state-averaged CASSCF and the multireference configuration-interaction methods. The potential-energy surfaces of six low-lying singlet states have also been calculated. While the 3(pi, pi*) state has a nonplanar equilibrium structure, the 3(pi, 3s) and 3(pi, sigma*) states are planar. The calculated vertical excitation energy of the 3(pi, pi*) state is in agreement with the experiment. The singlet excited states are found to be multiconfigurational, in particular, the first excited state is of (pi, 3s) character at the planar equilibrium structure, of (pi, sigma*) as the C-Cl bond elongates, and of (pi, pi*) for highly twisted geometries. Avoided crossings are observed between the potential-energy surfaces of the first three singlet excited states. The absorption spectra of vinyl chloride at 5.5-6.5 eV can be unambiguously assigned to the transitions from the ground state to the first singlet excited state. The dissociation of Cl atoms following 193-nm excitation is concluded to take place via two pathways: one is through (pi, sigma*) at planar or nearly planar structures leading to fast Cl atoms and the other through (pi, pi*) at twisted geometries from which internal conversion to the ground state and subsequent dissociation produces slow Cl atoms.     

Lithium cluster anions: photoelectron spectroscopy and ab initio calculations

Structural and energetic properties of small, deceptively simple anionic clusters of lithium, Li(n)(-), n = 3-7, were determined using a combination of anion photoelectron spectroscopy and ab initio calculations. The most stable isomers of each of these anions, the ones most likely to contribute to the photoelectron spectra, were found using the gradient embedded genetic algorithm program. Subsequently, state-of-the-art ab initio techniques, including time-dependent density functional theory, coupled cluster, and multireference configurational interactions methods, were employed to interpret the experimental spectra.     

Preliminary calculations on excited states of the oxygen molecule

It is well known that the energy interval separating ³ _u ^– and ³ _u ⁺ states of O₂, as given by the conventional ASMO method, is too large. In order to resolve this difficulty, removal of the equivalence restrictions usually employed in the orbital theory is proposed. Thus the orbital exponent of one antibonding _g MO is allowed to take a different value from the other _g's. Variational calculations show that the resulting outermost orbital is much more diffuse than the others. This model of a single diffuse orbital brings about a considerable energy lowering for the ³ _u ^– state and thus the agreement of the ³ _u ^– - ³ _u ⁺ interval with experiment is improved.

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Zusammenfassung Die konventionelle ASMO-Theorie liefert bekanntlich eine viel zu große Differenz der Terme ³ _u ^– und ³ _u ⁺ von O₂, weswegen der Vorschlag gemacht wird, die üblicherweise vorgenommene Äquivalenz-Einschränkung fallen zu lassen. Der Orbital-Exponent eines lockernden MO's kann von dem der übrigen _g's abweichen. Rechnungen zeigen, daß das äußerste MO viel diffuser als die anderen ist und daß die Energie des ³ _u ^– -Zustandes beträchtlich erniedrigt wird.

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Résumé La séparation entre les états ³ _u ^{– 3} _u ⁺ de O₂ donnée par la méthode ASMO conventionnelle est connue pour être trop grande. Afin de résoudre cette difficulté la levée des restrictions d'équivalence ordinairement utilisées est proposée. Ainsi l'exposant orbital d'une des orbitales moléculaires antiliantes _g peut prendre une valeur différente de celui de l'autre orbitale antiliante _g. Des calculs variationnels montrent que l'orbitale la plus haute ainsi obtenue est beaucoup plus diffuse que les autres. Ceci a pour effet de diminuer considérablement l'énergie de l'état ³ _u ^– , améliorant la séparation entre les états ³ _u ^– et ³ _u ⁺ .

     

Millimeter-wave spectrum of ClCN observed in a DC glow discharge and ab initio calculations

The ground state (v=0) millimeter-wave rotational spectrum of cyanogen chloride (ClCN) and some of its isotopic species have been investigated in the frequency region: 40.0–75.0 GHz. ClCN was produced by DC discharge through a mixture of 3-chlorobenzonitrile and tri-chloroethylene. The millimeter-wave spectrometer used is a source-modulated system combined with a free space glass discharge cell. Millimeter-wave radiation has been produced using a frequency multiplier, the fundamental radiation source being klystrons. The quadrupole hyperfine structures of ³⁵Cl and ³⁷Cl have been resolved, measured and analyzed. Finally, internuclear distances of ClCN have been determined using the Kraitchman's equation and compared with the previously reported values. Satisfactory agreements between the DFT-B3LYP/6-311++g(3d,3p) calculations and experimental values were found for internuclear distances and dipole moment. Based on the results of ab initio calculations at the MP4 level, ClCN was found to have a bent structure in the first excited electronic state.     

Static electric properties of LiH: explicitly correlated coupled cluster calculations

Explicitly correlated MBPT-R12 and coupled cluster [up to CCSD(T)-R12] methods have been used in calculations of various (vibrationless) electrical properties for the LiH molecule, including the dipole and quadrupole moments, dipole and quadrupole polarizability tensors, dipole hyperpolarizability tensors, and the second dipole hyperpolarizability tensors. Generally, with extension of the basis set the R12 method did not lead to faster convergence for the calculated properties towards the basis limit. Nevertheless, R12 calculations serve as useful indicators to judge the reliability of the results, and substantially help in determining the accuracy. Results obtained with the 11s8p6d5f/9s8p6d5f basis and CCSD(T)-R12 calculated within this work should be close to the basis set limit. Received: 8 June 1998 / Accepted: 23 July 1998 / Published online: 7 October 1998     

Role of doubly excited states in calculations of optical activity

It is shown that doubly excited states play an important role in calculations of the optical activity of molecules with well-conjugated electron systems, such as the DNA bases. In some significant cases it is necessary to include a large number of excited states in the configuration interaction (CI ) to obtain a reliable, converging result. A new version of the CNDO/OPTIC method, which includes doubly excited states in the CI , is proposed. As an application, the electric transition moments in different pyrimidines are considered. The calculated results agree with experimental data and results obtained from ab initio calculations and INDO calculations using doubly excited states in the CI .     

Transition strengths and first-order properties of excited states from local coupled cluster CC2 response theory with density fitting

A new ab initio method for calculating transition strengths and orbital-unrelaxed first-order properties of singlet ground and excited states of extended molecular systems is presented. It is based on coupled cluster response theory at the level of the CC2 model with local approximations introduced to the doubles-excitation part of the wave function. Density fitting is employed for the calculation of the electron repulsion integrals, so that--with the exception of doubles amplitudes--only three-indexed objects do occur in the formalism. The new method was tested by performing calculations for a set of various molecules and excited states and by comparing the results with corresponding canonical (nonlocal) calculations. It turned out that for calculating transition strengths and properties of excited states the ordinary Boughton-Pulay domains are insufficient in numerous cases. To circumvent this problem a new scheme for extending domains is proposed, which is based on the solution of the coupled perturbed localization and Hartree-Fock equations. When such extended domains are used, a satisfactory agreement between canonical and local results is achieved.     

The excited states and vibronic spectroscopy of diphenyldiacetylene and diphenylvinylacetylene

Laser induced fluorescence (LIF) excitation scans and dispersed fluorescence (DFL) spectra have been recorded for two four-carbon α,ω-diphenyl systems, diphenyldiacetylene (DPDA, φ-C≡C-C≡C-φ) and trans-diphenylvinylacetylene (DPVA, φ-CH≡CH-C≡C-φ) as isolated molecules cooled in a supersonic expansion. While these molecules have similar conjugation length, they exhibit strikingly different vibronic spectroscopy and photophysics. The near-UV LIF excitation spectrum of diphenyldiacetylene has its electronic origin at 32,158 cm(-1), and a strong progression in the C≡C stretch (2156 cm(-1)). All transitions are inherently broad, with widths of ~30 cm(-1) fwhm or greater. The S(1) origin DFL spectrum is composed of sharp transitions with Franck-Condon activity mirroring that in the excitation spectrum, and broad emission shifted well to the red ascribable to phosphorescence on the μs timescale. Using ab initio calculations, it is possible to show that DPDA exists as a single, planar conformer with D(2h) symmetry. In contrast, trans-diphenylvinylacetylene shows intense sharp transitions in both LIF and DFL spectra with an S(0)-S(1) origin of 31,183.2 cm(-1) and long progressions involving the in-plane fundamentals ν(53) (bridge-phenyl bending) and ν(51) (bridge-phenyl stretch). A sharp reduction in fluorescence yield in DPVA occurs within 300 cm(-1) of the S(1) origin. Possible causes for the photophysical processes occurring in the two molecules are discussed.     

Second-derivative method: Application to vibrational spectroscopy in excited electronic states

The second-derivative method, which has been known to be useful for finding peaks overlapped in a broad band, is applied to u.v. and visible absorption bands to derive vibrational frequencies in excited electronic states of molecules in solution. By using this method, much better estimates of vibrational frequencies are possible for Franck—Condon active modes than can be made from the absorption spectrum itself. Computational procedure and the results obtained for trans-1,3,5-hexatriene, azulene, pyrazine and anthracene are described with remarks about the effectiveness and limitations of the second-derivative method.     

Ab initio calculations of electronically excited states of cyano-substituted polyacetylene cations

The transition energies for the lowest energy pi --> pi* electronic excitations are calculated with the complete active space self-consistent field method (CASSCF) and with the complete active space second-order perturbation theory method (CASPT2) for the linear cyano-substituted polyacetylene cations, H-Cn-CN+, n = 4-11, and NC-Cn-CN+, n = 2-10. These systems are models for an important class of interstellar species. We demonstrate the utility of the theoretical calculations in assigning the experimental spectra.     

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     

Quantum chemical ab initio calculations for excited states of F IV

Quantum chemical ab initio calculations have been performed for the ground state and for several excited states of the F³⁺ ion (F IV). Three levels of accuracy have been used: Frozen-core SCF calculations (FRC-SCF) to determine orbital energies ε _nl and quantum defects δ _l for excited Rydberg orbitalsnl; frozen-core SCF followed by CI calculations (FRC-CI) which account for multiplet splittings and configuration mixings, and multi-configuration coupled-electron-pair approximation (MC-CEPA) calculations which include dynamic correlation effects. The accuracy of the calculated excitation energies is in the order of 5000 cm^?1 at the FRC-CI level and in the order of 500 cm^?1 at the MC-CEPA level. This latter error amounts to about 0.1% for excitation energies in the range of 400000 to 600000 cm^?1. The MC-CEPA calculations have been performed for 17 experimentally known states and for 14 experimentally unknown states, in particular for the configurations 2s2p ² (² D)3s, 2s 2p ²(² S)3s, 2s ² 2p 4p, and 2s ² 2p 5p.     

Addition by subtraction in coupled cluster theory. II. Equation-of-motion coupled cluster method for excited, ionized, and electron-attached states based on the nCC ground state wave function

New iterative double and triple excitation corrections to the equation-of-motion coupled cluster (EOM-CC) based upon the recently developed nCC methods [Bartlett and Musia?, J. Chem. Phys. 125, 204105-1 (2006)] are applied to excitation energies (EEs), ionization potentials (IPs), and electron affinities (EAs). The methods have been tested by the evaluation of the vertical EEs, IPs, and EAs for Ne, BH, CH(2), H(2)O, N(2), C(2), CH(+), CO, and C(2)H(4) compared to full configuration interaction, EOM-CCSD, EOM-CCSDT, and experimental data.