Extensive ab initio study of the electronic states of SCl including spin-orbit coupling

The effect of different basis sets for calculation of the spectroscopic constants of the ground state of sulfur monochloride (SCl) was analyzed using scalar relativistic multireference configuration interaction with single and double excitations plus Davidson correction. Then the generally contracted all-electronic correlation-consistent polarized valence quintuple zeta basis sets were selected to compute the electronic states of SCl including 12 valence and 9 Rydberg lambda-S states. The spin-orbit coupling effect was calculated via the state interaction approach with the full Breit-Pauli Hamiltonian. This effect splits these lambda-S states into 42 omega states. Potential-energy curves of all these states are plotted with the help of the avoided crossing rule between the electronic states of the same symmetry. The structural properties of these states are analyzed. Spectroscopic constants of bound excited states that have never been observed in experiment are obtained. The transition dipole moments and the Franck-Condon factors of several transitions from low-lying bound excited states to the ground state were also calculated.     

Extensive theoretical study on the low-lying electronic states of silicon monofluoride cation including spin-orbit coupling

Ab initio calculations on the low-lying electronic states of SiF+ are performed using the internally contracted multireference configuration interaction method with the Davidson correction and entirely uncontracted aug-cc-pV5Z basis set. The effects of spin-orbit coupling are accounted for by the state interaction approach with the full Breit-Pauli Hamiltonian. The entire 23 Omega states generated from the 12 valence Lambda-S states, which correlate with the first dissociation channel are studied for the first time. Good agreement is found between the calculated results and the available experimental data. The spin-orbit coupling effects on the potential energy curves and spectroscopic properties are studied. Various curve crossings are revealed, which could lead to the predissociation of the a3Pi, A1Pi, and (2)3Sigma+ states and the predissociation pathways are analyzed based upon the calculated spin-orbit matrix elements. The calculated ionization potentials of the ground-state SiF to a few states of SiF+ are in good agreement with the available experimental measurements. Moreover, the transition dipole moments of the dipole-allowed transitions and the transition properties for the A3Pi0+ -X1Sigma+ 0+ and B3Pi1-X1Sigma+ 0+ transitions are predicted, including the Franck-Condon factors and the radiative lifetimes.     

Extensive theoretical study on electronically excited states and predissociation mechanisms of sulfur monoxide including spin-orbit coupling

The potential energy curves of the 69 Ω states generated from the 24 Λ-S states of sulfur monoxide are calculated for the first time using the internally contracted multireference configuration interaction method with the Davidson correction and the entirely uncontracted aug-cc-pV5Z basis set. Spin-orbit coupling is taken into account by the state interaction approach with the full Breit-Pauli Hamiltonian. Very good agreement is achieved between our computed spectroscopic properties and the available experimental data. The transition properties of the B(3)Σ(-) -X(3)Σ(-) and (4)1-X0(+) transitions are predicted, and our computed Franck-Condon factors and radiative lifetimes match the experimental results very well. The predissociation mechanisms are investigated, and various new predissociation channels are located. We present a new interpretation on the breaking-off of the rotational levels of the B(3)Σ(-) lower vibrational states observed in experiment, and propose that the predissociation is induced by the Coriolis coupling between the B(3)Σ(-) rovibrational levels and the A(3)Π state. Our calculations indicate that, at ν' = 9, the B(3)Σ(-) state predissociates via the C(3)Π state; around ν' = 14, three spin-orbit-induced predissociation pathways via (1)(5)Σ(+) , (2)(5)Π, and e(1)Π would be open; around ν' = 17, the pathways via (2)(1)Σ(+) , (2)(3)Σ(+) and (2)(5)Σ(+) would contribute. These satisfactorily explain the experimental results about the diffuseness of the B(3)Σ(-) bands. Furthermore, various predissociation pathways of the C'(3)Π state are predicted, through which the C'(3)Π state could predissociate rapidly.     

An ab initio study of the low-lying electronic states of S3

Accurate calculations of the low-lying singlet and triplet electronic states of thiozone, S(3), have been carried out using large multireference configuration interaction wave functions. Cuts of the full potential energy surfaces along the stretching and bending coordinates have been presented, together with the vertical excitation spectra. The strong experimentally observed absorption around 395 nm is assigned to the 1 (1)B(2) state, which correlates to ground state products. Absorption at wavelengths shorter than 260 nm is predicted to lead to singlet excited state products, S(2) (a (1)Delta(g))+S((1)D). The spectroscopic properties of the X (3)Sigma(g) (-), a (1)Delta(g), and b (1)Sigma(g) (+) electronic states of the S(2) radical have also been accurately characterized in this work. The investigations of the low-lying electronic states were accompanied by accurate ground state coupled cluster calculations of the thermochemistry of both S(2) and S(3) using large correlation consistent basis sets with corrections for core-valence correlation, scalar relativity, and atomic spin-orbit effects. Resulting values for D(0)(S(2)+S) and SigmaD(0) for S(3) are predicted to be 61.3 and 162.7 kcal/mol, respectively, with conservative uncertainties of +/-1 kcal/mol. Analogous calculations predict the C(2v)-D(3h) (open-cyclic) isomerization energy of S(3) to be 4.4+/-0.5 kcal/mol.     

An ab initio study of the ground and valence excited states of GaF

Ab initio calculations on the ground and valence excited states of the GaF molecule have been performed by using the internally contracted multireference electronic correlation methods (MR-CISD, MR-CISD + Q, and MR-AQCC) with entirely uncontracted all-electronic basis sets and Douglas-Kroll scalar relativistic correction. The potential energy curves of all valence states and the spectroscopic constants of bound states are fitted. It is the first time that the 12 valence Lambda-S states of GaF molecule and all of the 23 Omega states generated from the former are studied in a theoretical way. Calculation results well reproduce most of the experimental data. The effects of the size-extensivity correction and the avoided crossing rule between Omega states of the same symmetry are analyzed. The transition properties of the A 3Pi0+, B 3Pi1, C 1Pi1, and 3Sigma1+ states are predicted, including the transition dipole moments, the Franck-Condon factors and the radiative lifetimes. The radiative lifetime of the C 1Pi1 state of GaF molecule is of the order of nanosecond, implying that it is a rather short-live state. The lifetimes of the B 3Pi1 and 3Sigma1+ states are of the order of microsecond, while the lifetime of the A 3Pi0+ state are the order of millisecond.     

An ab initio study of the ground and low-lying excited states of the permanganate ion

The results of ab-initio self-consistent field calculations for the ground state and configuration interaction calculations for the excited states of the permanganate ion are presented and discussed. The calculations were performed using two large basis sets of contracted gaussian functions, and singly excited configurations were used in the calculations of the excited states. Fair agreement is obtained between these results and the experimental absorption spectra.     

An ab initio study on the ground and low-lying doublet electronic states of SbO2

Geometry optimization and harmonic vibrational frequency calculations have been carried out on the low-lying doublet electronic states of antimony dioxide (SbO(2)) employing a variety of ab initio methods, including the complete active space self-consistent field/multireference configuration interaction and the RCCSD(T) methods. Both large and small core relativistic effective core potentials were used for Sb in these calculations, together with valence basis sets of up to aug-cc-pV5Z quality. Contributions from outer core correlation and off-diagonal spin-orbit interaction to relative electronic energies have been calculated. The ground electronic state of SbO(2) is determined to be the X (2)A(1) state, as is the case for dioxides of other lighter group 15 p-block (or group VA) elements. However, the A (2)B(2) and B (2)A(2) states are estimated to be only 4.1 and 10.7 kcalmole above the X (2)A(1) state, respectively, at the complete basis set limit. Reliable vertical excitation energies from the X (2)A(1) state to low-lying excited states of SbO(2) have been computed with a view to assist future spectral assignments of the absorption and/or laser-induced fluorescence spectra of SbO(2), when they become available.     

Accurate evaluation of valence and low-lying Rydberg states with standard time-dependent density functional theory

Using a standard exchange-correlation functional, namely, PBE0, the basis set dependence of time-dependent density functional theory (TD-DFT) calculations has been explored using 33 different bases and five organic molecules as test cases. The results obtained show that this functional can provide accurate (i.e., at convergence) results for both valence and low-lying Rydberg excitations if at least one diffuse function for the heavy atoms is included in the basis set. Furthermore, these results are in fairly good agreement with the experimental data and with those delivered by other functionals specifically designed to yield correct asymptotic/long-range behavior. More generally, the PBE0 calculations show that a greater accuracy can be obtained for both Rydberg and valence excitations if they occur at energies below the epsilonHOMO + 1 eV threshold. This latter value is proposed as a thumb rule to verify the accuracy of TD-DFT/PBE0 applications.     

CASSCF and multireference CI with singles and doubles study of low-lying valence and Rydberg states of 2H-tetrazole

Complete active space self-consistent field (CASSCF) and multireference CI with singles and doubles (MR-CISD) calculations [including extensivity corrections, at MR-CISD+Q and multireference averaged quadratic coupled cluster (MR-AQCC) levels] have been performed to characterize the low-lying valence and the Rydberg states of 2H-tetrazole. The highest level results (MR-AQCC/d'-aug'-cc-pVDZ) indicate the following ordering of the valence singlet excited states: S(1) (n-pi*), 6.06 eV; S(2) (n-pi*), 6.55 eV; S(3) (pi-pi*), 6.55 eV. The MR-CISD+Q/d'-aug'-cc-pVDZ results indicate the same ordering, but at slight higher energies: 6.16, 6.68, and 6.69 eV, respectively. According to our MR-CISD+Q/d'-aug'-cc-pVDZ results, the next two states are Rydberg states, at 7.69 eV (pi-3s) and 7.89 eV (n-3s). The calculated energies of these two states, as well as their proximity, are consistent with the conclusion reached by Palmer and Beveridge (Chem Phys 1987, 111, 249) that the first band of the photoelectron spectrum of 2H-tetrazole is likely to be associated to the first two ionizations processes (of pi and N lone pair electrons), at energies close to 11.3 eV.     

The low-lying electronic states of H2CN+: a preliminary ab initio study

Ab initio molecular-orbital calculations have been carried out on the low-lying triplet and singlet electronic states of the H₂CN⁺ cation, at the SCF and Møller-Plesset levels of theory. Both triplet ³A₂ and ³B₂ electronic states have similar energies. The barriers to isomerization to the ³A″ and ³A' electronic states of HCNH⁺ are estimated. It appears that ³A₂ and ³B₂ states are stable towards both isomerization and dissociation. The results of mass spectroscopic experiments involving H₂CN⁺ are discussed.     

Wheland intermediates: an ab initio valence bond study

The traditional resonance model for electrophilic attacks on substituted aromatic rings is revisited using high level valence bond (VB) calculations. A large π-donation is found in the X = NH(2) case and a weaker one for the X = Cl case, not only for ortho and para isomers but also for the meta case, which can be explained by considering five (not three) fundamental VB structures. No substantial π-effect is found in the X = NO(2) case, generally viewed as π-attractive.     

The electronic spectrum of AgCl2: ab initio benchmark versus density-functional theory calculations on the lowest ligand-field states including spin-orbit effects

The X 2pi(g), 2sigma(g)+, and 2delta(g) states of AgCl2 have been studied through benchmark ab initio complete active space self-consistent field plus second-order complete active space multireference Moller-Plesset algorithm (CASSCF+CASPT2) and complete active space self-consistent field plus averaged coupled pair functional (CASSCF+ACPF) and density-functional theory (DFT) calculations using especially developed basis sets to study the transition energies, geometries, vibrational frequencies, Mulliken charges, and spin densities. The spin-orbit (SO) effects were included through the effective Hamiltonian formalism using the LambdaSSigma ACPF energies as diagonal elements. At the ACPF level, the ground state is 2pi(g) in contradiction with ligand-field theory, SCF, and large CASSCF; the adiabatic excitation energies for the 2sigma(g)+ and 2delta(g) states are 1640 and 18,230 cm(-1), respectively. The inclusion of the SO effects leads to a pure omega = 32(2pi(g)) ground state, a omega = 12 (66%2pi(g) and 34%2sigma(g)+) A state, a omega = 12 (34%2pi(g) and 66%2sigma(g)+) B state, a omega = 52(2delta(g))C state, and a omega = 32(99%2delta(g))D state. The X-A, X-B, X-C, and X-D transition energies are 485, 3715, 17 246, and 20 110 cm(-1), respectively. The B97-2, B3LYP, and PBE0 functionals overestimate by approximately 100% the X 2pi(g)-2sigma(g)+T(e) but provide a qualitative energetic ordering in good agreement with ACPF results. B3LYP with variable exchange leads to a 42% optimal Hartree-Fock exchange for transition energies but all equilibrium geometries get worsened. Asymptotic corrections to B3LYP do not provide improved values. The nature of the bonding in the X 2pi(g) state is very different from that of CuCl2 since the Mulliken charge on the metal is 1.1 while the spin density is only 0.35. DFT strongly delocalizes the spin density providing even smaller values of around 0.18 on Ag not only for the ground state, but also for the 2sigma(g)+ state.     

Electronic structures of low-lying Bu excited states in trans-oligoenes: Pariser-Parr-Pople and ab initio calculations

Two lowest-lying excited singlets with B(u) symmetry of all-trans-oligoenes, the well-known ionic 1(1)B(u)(+) state as well as the "hidden" ionic-covalent-mixed 1(1)B(u)(-) state, are calculated within both the Pariser-Parr-Pople (PPP) model at full configuration interaction (FCI) level and ab initio methods. The vertical excitation energies as well as wavefunctions from PPP-FCI calculations are found to be in good agreement with those from high-level multi-reference methods, such as multi-reference complete active space self-consistent field (CASSCF) with second order perturbative corrections (CASPT2), multi-reference M?ller-Plesset perturbation theory (MRMP), and complete active space valence bond theory (CASVB). The oscillator strengths from PPP calculation are in good agreement with spectroscopy experiments. The relatively small oscillator strength of 1(1)B(u)(-) is due to the approximate electron-hole symmetry of this state. In addition, the bond lengths in both states are found to show remarkable relativity with the bond orders calculated with ground state geometries, which suggests a possible strategy for initial guess in geometry optimization of excited states.     

Ab initio study of low-lying triplet states of the lithium dimer

Observation of Bose-Einstein condensation in Li27 initiated the interest in the scattering length of two ground state lithium atoms when they approach each other as a radical pair triplet aSigmau+3 state. But some properties of this state are still unknown. In present work, a number of low-lying triplet states of lithium molecule are calculated by multi-configuration self-consistent field (MCSCF) and response techniques with account of spin-orbit coupling, spin-spin coupling and some other magnetic perturbations. The singlet-triplet transition probabilities to the ground state are also presented. Most results are connected with the weakly bound lowest triplet a3Sigmau+ state, whose radiative lifetime and spin-splitting are unknown so far in spite of its great importance in Bose-Einstein condensation. Calculations indicate that this state has a very small spin-splitting, lambdass=-0.01 cm-1, which is negligible in comparison with the line-width in experimental Fourier transform spectra published so far. Similar splitting is obtained for the upper state of the 1(3)Sigmag+--a3Sigmau+ transition. This is in agreement with experimental rovibronic analysis of the 1(3)Sigmag+--a3Sigmau+ band system in which the triplet structure was not resolved. The radiative lifetime of the a3Sigmau+ state is predicted to exceed 10 h.     

Ab initio study of the electronic states of BS including spin–orbit coupling

The entire 30 Ω states generated from the 12 valence and two Rydberg Λ–S states of the BS radical have been studied at the MR-CISD + Q level of theory for the first time. The effects of spin–orbit coupling and the avoided crossing rule between electronic states of the same symmetry were analyzed. Spectroscopic constants of several excited states that have never been observed in experiment were obtained. The transition properties of several low-lying bound excited states to ground state transitions, including the transition dipole moments and the Franck–Condon factors, were also calculated, from which the corresponding single-channel radiative lifetimes were derived.     

Ab initio study including spin-orbit effects on the B-X transition of AgI

The lowest Omega = 0-,0+,1,2 fine-structure potential energy curves arising from the two lowest-lying singlet (X 1Sigma+ and 2 1Sigma+) and the first 3Pi electronic states of AgI were obtained through an effective Hamiltonian; the purely electronic LambdaSSigma energies were used as diagonal elements, which were calculated through extensive complete active space self-consistent field + averaged coupled pair functional calculations, with relativistic effective core potentials and optimized Gaussian basis sets for both atoms. The spin-orbit interactions were included using the Stuttgart effective spin-orbit potentials. For the excited Omega = 0+ states, very strong mixtures were found of the 2 1Sigma+ and 3Pi parents that lead to the fine-structure (0+) single B state (dominated by the 2 1Sigma+ parent at long distance), that explains the B <-- X transitions. The present results also explain the presence of a second long-distance minimum for the B0+ state, experimentally Rydberg-Klein-Rees fitted. These calculations produced, as a byproduct, a new lower-lying Omega = 0+ yet unobserved fine-structure state predicted to exist around 22,000 cm(-1). Our theoretical results are compared and discussed in the light of the experimental data for the B-X transitions in silver halides [J. Chem. Phys. 109, 9831 (1998)].     

An ab initio valence bond study on cyclopenta-fused naphthalenes and fluoranthenes

To probe the effect of external cyclopenta-fusion on a naphthalene core, ab initio valence bond (VB) calculations have been performed, using strictly atomic benzene p-orbitals and p-orbitals that are allowed to delocalize, on naphthalene (1), acenaphthylene (2), pyracylene (3), cyclopenta[b,c]acenaphthylene (4), fluoranthene (5), and cyclopenta[c,d]fluoranthene (6). For the related compounds 1-4 and 5,6 the total resonance energies (according to Pauling's definition) are similar. Partitioning of the total resonance energy in contributions from the possible 4n + 2 and 4n pi-electron conjugated circuits shows that only the 6pi-electron conjugated circuits (benzene-like) contribute to the resonance energy. The results show that cyclopenta-fusion does not extend the pi system in the ground state; the five-membered rings act as peri-substituents. As a consequence, the differences in (total) resonance energy do not coincide with the differences in thermodynamic stability. Notwithstanding, the relative energies of the Kekule structures can be estimated using Randic's conjugated circuits model.     

An ab initio multireference doubles excitation configuration interaction study of low-lying electronic states of Cd2 using Slater-type orbitals

Potential-energy curves for the ground state and lower excited states of the Cd₂ dimer have been calculated. They are obtained using a multireference doubles excitation configuration interaction procedure and employing Slater basis sets, previously optimized at the self-consistent-field level for excited states of the Cd atom. The spectroscopic constants and excitation energies for the bound states of Cd₂ have been compared with experimental as well as other theoretical results. The ground state of Cd₂ is essentially repulsive and presents a shallow van der Waals minimum. The computed adiabatic electronic transitions are in good agreement with the experimental ones. Received: 16 September 1999 / Accepted: 3 February 2000 / Published online: 2 May 2000     

Ab initio calculation of the potential surfaces for low-lying valence electronic states of the C2H radical

The results of an extensive CI treatment for the three lowest-lying electronic states 1² A′, 2² A′ and 1² A″ of C₂H are reported. Two-dimensional C-C stretching/bending potential surfaces for these species are calculated. Electronic dipole and transition moments are computed as a function of the bond angle and the C-C bond length. The results serve as a starting point in a theoretical analysis of the rovibronic structure of the long-wavelength spectra of C₂H.