Optimal double-configuration study of the lowest excited Π states of H2

Various levels of approximation (Hartree-Fock, configuration interaction and double-configuration Hartree-Fock method) are compared for extensive and limited exponent optimization of the atomic orbitals of the wavefunctions. The potential energy curves for the lowest-lying ¹ _u, ³ _u, ¹ _g, ³ _g states of the hydrogen molecule are presented. The shapes of the curves on the highest level of approximation, i.e. with the optimal double-configuration wavefunction, are basically in agreement with previous, more sophisticated and time-consuming work. The influence of the various approximations is also studied for several one-electron properties: charge distribution of the wavefunction along and perpendicular to the molecular axis, quadrupole moment and core attraction energy distribution. Differences arise to the work of Zemke et al. [1], who used a limited exponent optimization with a larger basis set, in the _g states where the orbitals are very diffuse. The differences concern magnitude and location of minima and maxima of potential curves, as well as considerable changes in one-electron properties which depend strongly on the spatial distribution of the orbitals.

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Zusammenfassung Verschiedene Approximationsstufen (Hartree-Fock, Konfigurationenwechselwirkung und Doppelkonfigurationen-Hartree-Fock-Methode) werden für ausgedehnte und begrenzte Exponentenoptimisierung von Atomorbitalen der Wellenfunktionen verglichen. Die Potentialkurven für die niedrigsten ¹ _u, ³ _u, ¹ _g, ³ _g Zustände des Wasserstoffmoleküls werden angegeben. Die Form der Kurven im Rahmen der besten Näherung, d. h. mit Doppelkonfiguration, stimmen im wesentlichen mit früheren aufwendigeren Rechnungen überein. Der Einfluß der verschiedenen Approximationen wird auch an einigen Einelektroneneigenschaften studiert: Ladungsverteilung der Wellenfunktion längs und senkrecht zur Molekülachse, Quadrupolmoment und Verteilung der Rumpfenergie. Unterschiede erscheinen zur Arbeit von Zemke et al. [1], die einen größeren Basissatz mit begrenzter Optimisierung verwandten, bei den _g Zuständen, wo die -Orbitale sehr diffus sind. Die Unterschiede betreffen Größe und Lage der Minima und Maxima der Potentialkurven sowie beträchtliche Änderungen in solchen Einelektroneneigenschaften, die stark von der räumlichen Verteilung der Orbitale abhängen.

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Résumé Comparaison de différents niveaux d'approximation (Hartree-Fock, interaction de configuration et Hartree-Fock à deux configurations) pour des optimisations étendues et limitées des orbitales atomiques de base. Calcul des courbes d'énergie potentielle pour les plus bas états ¹ _u, ³ _u, ¹ _g, ³ _g de la molécule d'hydrogène. Pour la fonction d'onde la plus raffinée: H.F. à deux configurations, la forme des courbes est en accord avec les résultats obtenus dans des travaux précédents plus complexes et plus coûteux. On étudie aussi l'influence des diverses approximations sur plusieurs propriétés monoélectroniques: distribution de charge le long de l'axe moléculaire et perpendiculairement à celui-ci, moment quadrupolaire et distribution de l'énergie d'attraction de coeur. On trouve des différences avec le travail de Zemke et al. (1), qui utilisent une plus grande base partiellement optimisée, pour les états _g où les orbitales sont très diffuses. Les différences concernent la grandeur et la position des extrema des courbes de potentiel, ainsi que des variations importantes des propriétés monoélectroniques qui dépendent fortement de la distribution spatiale des orbitales.

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On leave to: Institut für Theoretische Chemie, Universität Stuttgart.

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On leave to: Office of Computing Activities, National Science Foundation, Washington, D.C.     

An ab initio study of the lowest electronic states of yttrium dicarbide, YC2

The low-lying electronic states of yttrium dicarbide have been calculated using highly correlated wave functions and systematic sequences of correlation consistent basis sets. For the (2)A(1) ground electronic state, the near-equilibrium potential energy surface (PES) has been calculated using the coupled cluster method in conjunction with basis sets ranging in size from double to quintuple zeta. The relativistic effects have been taken into account by using pseudopotentials for the Y atom. After extrapolation to the complete basis set limit, additional corrections due to core-valence correlation and spin-orbit effects have also been included. The same approach has been followed for the (2)B(1), (2)B(2), and (2)A(2) states but only the C(2V) PESs have been considered in these cases. For the two (2)A(1) electronic excited states and, for comparison purposes, for the ground state, the multireference configuration interaction (MRCI) approach has been used in conjunction with double-zeta and triple-zeta basis sets for the construction of the PES. The molecular and spectroscopic properties predicted for the ground and excited states investigated in this work compare well with the available experimental data, particularly for the ground electronic state. The 0 K dissociation enthalpy of YC(2), DeltaH(Y-C2)(0 K), and its atomization enthalpy, SigmaD(0), are predicted to be 148.4 and 291.5 kcal/mol, respectively.     

Ab initio calculation of the lowest singlet and triplet states in CH2, CHF,CF2, and CHCH3

The lowest singlet and triplet states of the radicals CH₂, CHF, CF₂, and CHCH₃ have been investigated both in SCF and IEPA approximation (“independent electron pair approach” to account for electron correlation). The SCF calculations yield triplet ground states for CH₂, CHF, and CHCH₃, and a singlet ground state for CF₂. Electron correlation stabilizes the singlet state by about 14 kcal/mole with respect to the triplet for all four radicals leading to a singlet ground state also for CHF. The final triplet-singlet energy separations are 10, 6, ?11, ?47 kcal/mole for CH₂, CHCH₃, CHF, CF₂, respectively. Values for equilibrium bond angles, ionization potentials and bond energies are also given.     

Configuration-Interaction study of lower excited states of O2: Valence and rydberg characters of the two lowest 3Σu − states

Configuration-interaction calculations, with an extended basis, are carried out on the ground and lower excited states of O₂ and O₂⁺ at and near the equilibrium internuclear distance (R = 2.3 a.u.) of the ground state of O₂. Particular attention has been paid to the two lowest ³Σ_u^? states, and the mixing of the valence and Rydberg characters in these states are studied. The lowest ³Σ_u^? state is a Rydberg-type state for R < 2.3 a.u., but becomes valence-type for R ? 2.3 a.u. The second ³Σ_u^? state, which is 1.6 eV above the lowest ³Σ_u^? at R = 2.3 a.u., changes its character from Rydberg to valence, valence to Rydberg, and then to valence again when R increases from 1.9 to 3.1 a.u. Satisfactory agreement between the calculated and experimental vertical excitation energies is obtained.     

Semidiffuse states of diatomic molecules: Configuration interaction studies of the lowest 2Σ+ and 2Δ states of NS,SiF, and CCl

It has been shown by ab initio configuration-interaction methods that the lowest ²Σ⁺ states of NS and SiF are ‘semidiffuse’ states, like the B ²Σ⁺ state of PO. The lowest ²Σ⁺ state of CCl also appears to be semidiffuse, although here the situation is not so clear. Semidiffuse states require diffuse orbitals in the wavefunction, but they are not Rydberg states. The second ²Σ⁺ state of each molecule is shown to be the lowest ns Rydberg state, whereas the third ²Σ⁺ state is a valence state for NS and CCl, and a 4po Rydberg state for SiF. The lowest ²δ state of each molecule derives from the 7σ → 3π valence configuration. Comparison with available experimental information shows, in general, good agreement.     

A CASPT2 study of the valence and lowest Rydberg electronic states of benzene and phenol

Summary The valence excited states and the 3s, 3p, and 3d (united atom) Rydberg states of benzene and phenol have been obtained by the CASPT2 method, which computes a second-order perturbation correction to complete active space self-consistent field (CASSCF) energies. All non-zero dipole oscillator strengths are also computed, at the CASSCF level. For benzene, 16 singlet and 16 triplet states with excitation energies up to ca. 7.86 eV (63 400 cm^–1) are obtained. Of these, 12 singlet and three triplet energies are experimentally known well enough to allow meaningful comparison. The average error is around 0.1 eV. The highest of these singlet states (2¹ E_2g) is the highest valence * state predicted by elementary -electron theory. Its energy is then considerably lower than has been suggested from laser flash experiments, but in perfect agreement with a reinterpretation of that experiment. For phenol, 27 singlet states are obtained, in the range 4.53–7.84 eV (63 300 cm^–1). Only the lowest has a well-known experimental energy, which agrees with the computed result within 0.03 eV. The ionization energy is in error by 0.05 eV.     

The intermolecular potentials of the O2-O2 dimer: a detailed ab initio study of the energy splittings for the three lowest multiplet states

Intermolecular potentials for the three lowest multiplet states (singlet, triplet and quintet) of the O(2)((3)Sigma)-O(2)((3)Sigma) dimer have been investigated in detail by means of high level ab initio calculations. The methods used include MRCI, ACPF, CASPT2, using different active spaces and basis sets. The results for the quintet state are compared with benchmark CCSD(T) calculations. As expected, the former methods do not account accurately for dispersion interactions, although the CASPT2 method performs better than the CI based ones. On the other hand, it is shown that highly correlated methods are necessary to accurately describe the splittings among the multiplet states. We propose to obtain singlet and triplet interaction potentials by combining CCSD(T) quintet potentials and multiconfigurational singlet-quintet and triplet-quintet splittings, respectively. The calculated splittings are quite stable regarding the method employed, except for the well region of the singlet and triplet states within the rectangular configuration, which corresponds to the absolute minima of these multiplet states. Nevertheless, we have been able to assess adequate upper and lower bounds to the interaction potential for this particular region.     

On the lowest electronic states of the C2F radical

The adiabatic energy surfaces of the lowest three electronic states [²(²A′ and ²A′)] and ²Σ⁺[²A′] of the C₂F radical were investigated by the Hartree-Fock multiconfiguration self-consistent field (HF—MCSCF) ab initio method using a large set of atomic natural orbitals (ANO) and an extended configuration space, and the results were shown to be in agreement with the predictions of valence theory for this radical. The electronic ground state was found to have a bent equilibrium structure, hence contradicting the Walsh rule which predicts for the isoelectronic molecules a ² linear state. The three states were found to be nearly degenerate and the potential energy surfaces of the two lowest electronic states exhibit an avoided crossing at an energy ∼2000 cm⁻¹ above the ground-state minimum, lower than the highest vibrational fundamental. The strong adiabatic interaction which is responsible for the ordering of the electronic states and their equilibrium geometry involves not only the bending coordinate as normally found for Renner-Teller pairs of states, but also the C—C stretching coordinate, due to the near degeneracy of the ²Σ⁺ and the ² lowest electronic states at linear geometries. © 1996 John Wiley & Sons, Inc.     

A study of interaction in the lowest singlet and triplet states of H2

The potential energy curves of the ground state and the first excited state of H₂ are examined in terms of the electronic force acting on each nucleus. The results reveal the detailed course of events that occur when two hydrogen atoms with parallel and antiparallel electron spins approach one another from a large internuclear separation.     

Ab initio study of the structure and conformations of 2-fluoroethanal in the ground and lowest excited electronic states

The structure of the conformationally flexible 2-fluoroethanal molecule (CH₂FCHO, FE) in the ground (S₀) and lowest excited triplet (T₁) and singlet (S₁) electronic states was investigated by ab initio quantum-chemical methods. The FE molecule in the S₀ state was found to exist as two conformers, viz., as cis (the F—C—C—O angle is 0°) and trans (the F—C—C—O angle is 180°) conformers. On going both to the T₁ and S₁ states, the FE molecule undergoes substantial structural changes, in particular, the CH₂F top is rotated with respect to the core and the carbonyl CCHO fragment becomes nonplanar. The potential energy surfaces for the T₁ and S₁ states are qualitatively similar, viz., six minima in each of the excited states of FE correspond to three pairs of mirror-symmetrical conformers. Based on the potential energy surfaces calculated for the FE molecule in the T₁ and S₁ states, the one-dimensional problems on the torsion and inversion nuclear motions as well as the two-dimensional torsion-inversion problems were solved.     

All-valence-electron CI study of the ground and lowest excited states of the hydroperoxyl radical

Ab initio calculations using a double-zeta plus polarization AO basis are used to study the lowest-lying (²A′ ← ²A″) transition of the HO₂ radical. A large-scale CI treatment is found to result in a transition energy for this system which agrees to within less than 0.1 eV with its experimental value. The life-time of the process is predicted to be in the order of 3 × 10^?3 s using the dipole length formula for this quantity, while the generally less reliable dipole velocity result is found to be several orders of magnitude larger.     

Correlation of substituent effects and energy levels of the two lowest excited states of the azulenic chromophore

[structure: see text] Experimental and calculated data show that the relative energy levels of the two lowest excited states of azulene are sensitive to the nature and position of substituents on the nonalternant hydrocarbon. Extending such investigations led to a rational explanation for some of the baffling data on azulenic bacteriorhodopsin analogues in the literature.     

Energies of the lowest singlet S and triplet S states of helium by the local energy method

The least squares local energy method is applied to the helium atom in greater detail in a formulation which can easily be extended to more complicated atoms. The energies of the 1 ¹ S and 2³ S states are calculated to be – 2.9025 H and – 2.1753 H respectively. These values are in excellent agreement with the non-relativistic values of – 2.9037 H and – 2.1752 H calculated by Pekeris.

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Zusammenfassung Die Methode, die Varianz der lokalen Energie zu minimisieren, wird in einer leicht auf kompliziertere Atome zu erweiternden Form ausführlicher auf das Heliumatom angewandt. Die Energien des 1 ¹ S – und des 2 ³ S–Zustandes werden zu – 2,9025 bzw. – 2,1753 at. E. berechnet. Diese Werte stimmen ausgezeichnet mit den von Pekeris berechneten nichtrelativistischen Werten von – 2,9037 bzw. – 2,1752 at. E. überein.

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Résumé Le calcul de l'énergie locale par la méthode des moindres carrés est appliqué plus en détail à l'atome d'hélium, dans une forme qui s'étend aisément à des atomes plus compliqués. Les énergies des états 1 ¹ S et 2 ³ S se calculent à – 2,9025 et – 2,1753 u. a., respectivement. Ces valeurs sont en excellent accord avec les valeurs de – 2,9037 et – 2,1752 u. a. (sans relativité) calculées par Pekeris.

     

Ab initio adiabatic and quasidiabatic potential energy surfaces of lowest four electronic states of the H+ + O2 system

Ab initio global adiabatic and quasidiabatic potential energy surfaces of lowest four electronic (1-4 (3)A(")) states of the H(+)+O(2) system have been computed in the Jacobi coordinates (R,r,γ) using Dunning's cc-pVTZ basis set at the internally contracted multireference (single and double) configuration interaction level of accuracy, which are relevant to the dynamics studies of inelastic vibrational and charge transfer processes observed in the scattering experiments. The computed equilibrium geometry parameters of the bound [HO(2)](+) ion in the ground electronic state and other parameters for the transition state for the isomerization process, HOO(+)?OOH(+) are in good quantitative agreement with those available from the high level ab initio calculations, thus lending credence to the accuracy of the potential energy surfaces. The nonadiabatic couplings between the electronic states have been analyzed in both the adiabatic and quasidiabatic frameworks by computing the nonadiabatic coupling matrix elements and the coupling potentials, respectively. It is inferred that the dynamics of energy transfer processes in the scattering experiments carried out in the range of 9.5-23 eV would involve all the four electronic states.     

Fully relativistic calculations on the potential energy surfaces of the lowest 23 states of molecular chlorine

The electronic structure and spectroscopic properties (R(e), omega(e), omega(e)x(e), beta(e), and T(e)) of the ground state and the 22 lowest excited states of chlorine molecule were studied within a four-component relativistic framework using the MOLFDIR program package. The potential energy curves of all possible 23 covalent states were calculated using relativistic complete open shell configuration interaction approach. In addition, four component multireference configuration interaction with single and double excitation calculations were performed in order to infer the effects due to dynamical correlation in vertical excitations. The calculated properties are in good agreement with the available experimental data.     

Radiative lifetimes of the lowest 3P1 metastable states of Ca and Sr

The lifetimes of the lowest ³P₁ states of Ca and Sr have been measured in atomic beam experiments. These measurements have been made by observing the exponential decay of the fluorescence emitted from excited states populated either by a discharge or a dye-laser pumping. In both cases, the velocity distributions of the radiating atoms were also measured by a time-of-flight technique. Our results show that the lifetime measurements using the discharge excitation are hampered by a systematic error introduced probably by cascade transitions that repopulate the upper energy levels of the transitions of interest. The radiative lifetimes of the 4s4p ³P₁ state of Ca and 5s5p ³P₁ state of Sr are determined to be 0.34 ± 0.02 ms and 21.3 ± 0.5 μs, respectively.     

Predissociation mechanism for the lowest 1 Pi u states of N2

Separate coupled-channel Schr?dinger-equation (CSE) models of the interacting (1)Pi(u) (b,c,o) and (3)Pi(u) (C,C(')) states of N(2) are combined, through the inclusion of spin-orbit interactions, to produce a five-channel CSE model of the N(2) predissociation. Comparison of the model calculations with an experimental database, consisting principally of detailed new measurements of the vibrational and isotopic dependence of the (1)Pi(u) linewidths and lifetimes, provides convincing evidence that the predissociation of the lowest (1)Pi(u) levels in N(2) is primarily an indirect process, involving spin-orbit coupling between the b (1)Pi(u)- and C (3)Pi(u)-state levels, the latter levels themselves heavily predissociated electrostatically by the C(') (3)Pi(u) continuum. The well-known large width of the b(v=3) level in (14)N(2) is caused by an accidental degeneracy with C(v=9). This CSE model provides the first quantitative explanation of the predissociation mechanism for the dipole-accessible (1)Pi(u) states of N(2), and is thus likely to prove useful in the construction of realistic radiative-transfer and photochemical models for nitrogen-rich planetary atmospheres.     

Density functional theory calculations of the lowest energy quintet and triplet states of model hemes: role of functional, basis set, and zero-point energy corrections

We investigated the effect of several computational variables, including the choice of the basis set, application of symmetry constraints, and zero-point energy (ZPE) corrections, on the structural parameters and predicted ground electronic state of model 5-coordinate hemes (iron(II) porphines axially coordinated by a single imidazole or 2-methylimidazole). We studied the performance of B3LYP and B3PW91 with eight Pople-style basis sets (up to 6-311+G*) and B97-1, OLYP, and TPSS functionals with 6-31G and 6-31G* basis sets. Only hybrid functionals B3LYP, B3PW91, and B97-1 reproduced the quintet ground state of the model hemes. With a given functional, the choice of the basis set caused up to 2.7 kcal/mol variation of the quintet-triplet electronic energy gap (DeltaEel), in several cases, resulting in the inversion of the sign of DeltaEel. Single-point energy calculations with triple-zeta basis sets of the Pople (up to 6-311G++(2d,2p)), Ahlrichs (TZVP and TZVPP), and Dunning (cc-pVTZ) families showed the same trend. The zero-point energy of the quintet state was approximately 1 kcal/mol lower than that of the triplet, and accounting for ZPE corrections was crucial for establishing the ground state if the electronic energy of the triplet state was approximately 1 kcal/mol less than that of the quintet. Within a given model chemistry, effects of symmetry constraints and of a "tense" structure of the iron porphine fragment coordinated to 2-methylimidazole on DeltaEel were limited to 0.3 kcal/mol. For both model hemes the best agreement with crystallographic structural data was achieved with small 6-31G and 6-31G* basis sets. Deviation of the computed frequency of the Fe-Im stretching mode from the experimental value with the basis set decreased in the order: nonaugmented basis sets, basis sets with polarization functions, and basis sets with polarization and diffuse functions. Contraction of Pople-style basis sets (double-zeta or triple-zeta) affected the results insignificantly for iron(II) porphyrin coordinated with imidazole. Poor performance of a "locally dense" basis set with a large number of basis functions on the Fe center was observed in calculation of quintet-triplet gaps. Our results lead to a series of suggestions for density functional theory calculations of quintet-triplet energy gaps in ferrohemes with a single axial imidazole; these suggestions are potentially applicable for other transition-metal complexes.     

Structure, bonding, and lowest energy transitions in unsymmetrical squaraines: a computational study

Natural resonance theory (NRT) and natural bond orbital (NBO) analysis have been carried out on a simple symmetrical and an unsymmetrical substituted squaraine with a view of understanding the structure of the latter type of squaraines. It is found that there are some fundamental differences in the structure and bonding between these two types of squaraines particularly in the resonance weights and delocalization energies. These differences are expected to reflect in the low energy transitions and charge transfer in these squaraines. To investigate this, the nature of the lowest energy transitions occurring on excitation in unsymmetrical squaraines has been studied using high-level symmetry adapted cluster-configuration interaction method (SAC/SAC-CI) and compared with reported experimental observations. In general the agreement with the experimental data is very good. The transition dipole moment always lies on the pi-backbone and is quite large in magnitude. The ground state dipole moment in some cases does not change in the excited state upon excitation while in some other cases there is a large reduction/enhancement in the magnitude indicative of some charge rearrangement in this direction. Inclusion of the solvent using the IEFPCM model, a slightly better agreement with the experiment is found in some cases. Studies are carried out with a different basis set and it is found that the change in basis set has very little effect on the transition energies. In the case of weak side donor groups attached to the central ring the larger charge transfer to the central acceptor ring in general takes place from the O- atoms of the squarylium moiety while in the case of strong donors the charge transfer from the O- atoms to the central rings drop down. We have not observed any correlation between the charge transfer in the excited state to the central ring from the side donor groups and the lowest energy excitation in the molecules. Reduction of the HOMO-LUMO gap (an indication of increase of the diradicaloid character) always leads to a bathochromic shift.