F-loss and H-loss dissociations in low-lying electronic states of the CH3F+ ion studied using multiconfiguration second-order perturbation theory

Complete active space self-consistent field (CASSCF) and multiconfiguration second-order perturbation theory (CASPT2) calculations with an atomic natural orbital basis were performed for the 1(2)A', 1(2)A', 2(2)A', 2(2)A', and 3(2)A' (X2E, A2A1, and B2E) states of the CH3F+ ion. The 1(2)A' state is predicted to be the ground state, and the C(s)-state energy levels are different from those of the CH3Cl+ ion. The 2(2)A' (A2A1) state is predicted to be repulsive, and the calculated adiabatic excitation energies for 2(2)A' and 3(2)A' are very close to the experimental value for the B state. The CASPT2//CASSCF potential energy curves (PECs) were calculated for F-loss dissociation from the five C(s) states and H-loss dissociation from the 1(2)A', 1(2)A', and 2(2)A' states. The electronic states of the CH3+ and CH2F+ ions as the dissociation products were carefully determined by checking the energies and geometries of the asymptote products, and appearance potentials for the two ions in different states are predicted. The F-loss PEC calculations for CH3F+ indicate that F-loss dissociation occurs from the 1(2)A', 1(2)A', and 2(2)A' states [all correlating with CH3+(X1A1')], which supports the experimental observations of direct dissociation from the X and A states, and that direct F-loss dissociation can occur from the two Jahn-Teller component states of B2E, 2(2)A' and 3(2)A' [correlating with CH3+(1(3)A') and CH3+(1(3)A'), respectively]. Some aspects of the 3(2)A' Cl-loss PEC of the CH3Cl+ ion are inferred on the basis of the calculation results for CH3F+. The H-loss PEC calculations for CH3F+ indicate that H-loss dissociation occurs from the 1(2)A', 1(2)A', and 2(2)A' states [correlating with CH2F+(1(3)A'), CH2F+(X1A1), and CH2F+(1(1)A'), respectively], which supports the observations of direct dissociation from the X and B states. As the 2(2)A' H-loss PEC of CH3Cl+, the 2(2)A' H-loss PEC of CH3F+ does not lead to H + CH2X+, but the PECs of the two ions represent different types of reactions.     

Bromine-loss and hydrogen-loss dissociations in low-lying electronic states of the CH3Br+ ion studied using multiconfiguration second-order perturbation theory

Complete active space self-consistent field (CASSCF) and multiconfiguration second-order perturbation theory (CASPT2) calculations with an ANO-RCC basis were performed for the 1(2)A', 1(2)A", 2(2)A', and 2(2)A" states of the CH3Br+ ion. The 1(2)A' state is predicted to be the ground state. The 2(2)A' state is predicted to be a bound state. The adiabatic and vertical excitation energies and the relative energies at the molecular geometry were calculated, and the energetic results for 2(2)A' and 2(2)A" are in reasonable agreement with the experimental data. Potential energy curves (PECs) for Br-loss and H-loss dissociations from the four C(s) states were calculated at the CASPT2//CASSCF level and the electronic states of the CH3(+) and CH2Br(+) ions as the dissociation products were determined by checking the relative energies and geometries of the asymptote products along the PECs. In the Br-loss dissociation, the 1(2)A', 1(2)A", and 2(2)A' states correlate with CH3(+) (X1A1') and the 2(2)A" state correlates with CH3(+) (1(3)A"). The energy increases monotonically with the R(C-Br) value along the four Br-loss PECs. In the H-loss dissociation the 1(2)A', 1(2)A", 2(2)A', and 2(2)A" states correlate with the X(1)A(1), 1(3)A", 1(3)A', and 1(1)A" states (1(3)A' lying above 1(1)A") of CH2Br(+), respectively. Along the 2(2)A" H-loss PEC there is an energy barrier and the CASSCF wave functions at large R(C-H) values have shake-up ionization character. Along the 2(2)A' H-loss PEC there are an energy barrier and a minimum. At the end of the present paper we present a comprehensive review on the electronic states and the X-loss and H-loss dissociations of the CH(3)X(+) (X = F, Cl, and Br) ions on the basis of our previous studies and the present study.     

Cl-loss and H-loss dissociations in low-lying electronic states of the CH3Cl+ ion studied using multiconfiguration second-order perturbation theory

To examine the experimentally suggested scheme of the pathways for Cl- and H-loss dissociations of the CH(3)Cl(+) ion in the X(2)E (1(2)A', 1(2)A' '), A(2)A(1) (2(2)A'), and B(2)E (3(2)A', 2(2)A") states, the complete active space-self-consistent field (CASSCF) and multiconfiguration second-order perturbation theory (CASPT2) calculations with an atomic natural orbital (ANO) basis were performed for the 1(2)A' (X(2)A'), 1(2)A", 2(2)A', and 2(2)A'" states. The potential energy curves describing dissociation from the four C(s) states were obtained on the basis of the CASSCF partial geometry optimization calculations at fixed C-Cl or C-H distance values, followed by the CASPT2 energy calculations. The electronic states of the CH3(+) and CH(2)Cl(+) ions produced by Cl-loss and H-loss dissociation, respectively, were carefully determined. Our calculations confirm the following experimental facts: Cl-loss dissociation occurs from the 1(2)A' (X(2)A'), 1(2)A", and 2(2)A' states (all leading to CH3(+) (X(1)A(1)') + Cl), and H-loss dissociation does not occur from 2(2)A'. The calculations indicate that H-loss dissociation occurs from the 1(2)A' and 1(2)A' ' states (leading to CH(2)Cl(+) (X(1)A(1)) + H and CH(2)Cl(+) (1(3)A") + H, respectively). The calculations also indicate that H-loss dissociation occurs (with a barrier) from the 2(2)A" state (leading to CH(2)Cl(+) (1(1)A") + H), supporting the observation of direct dissociation from the B state to CH(2)Cl(+) and that Cl-loss dissociation occurs from the 2(2)A" state (leading to CH3(+) (1(3)A") + Cl), not supporting the previously proposed Cl-loss dissociation of the B state via internal conversion of B to A. The predicted appearance potential values for CH3(+) (X(1)A(1)') and CH(2)Cl(+) (X(1)A(1)) are in good agreement with the experimental values.     

Low-lying electronic states and Cl-loss photodissociation of the C2H3Cl+ ion studied using multiconfiguration second-order perturbation theory

We studied the 1(2)A' '(X2A' '), 1(2)A' (A2A'), 2(2)A' ' (B2A' '), and 2(2)A' (C2A') states of the C2H3Cl+ ion using the complete active space self-consistent field (CASSCF) and multiconfiguration second-order perturbation theory (CASPT2) methods. For the four ionic states, we calculated the equilibrium geometries, adiabatic (T0) and vertical (Tv) excitation energies, and relative energies (Tv') at the geometry of the molecule at the CASPT2 level and the Cl-loss dissociation potential energy curves (PECs) at the CASPT2//CASSCF level. The computed oscillator strength f value for the X2A' ' <-- A2A' transition is very small, which is in line with the experimental fact that the A state has a long lifetime. The CASPT2 geometry and T0 value for the A2A' state are in good agreement with experiment. The CASPT2 Tv' values for the A2A', B2A' ', and C2A' states are in good agreement with experiment. The Cl-loss PEC calculations predict that the X2A' ', A2A', and C2A' states correlate to C2H3+ (XA1) and the BA' ' state to C2H3+ (1A' ') (the B2A' ' and C2A' PECs cross at R(C-Cl) approximately 2.24 A). Our calculations indicate that at 357 nm the X2A' ' state can undergo a transition to B2A' ' followed by a predissociation of B2A' ' by the repulsive C2A' state (via the B/C crossing), leading to C2H3+ (X1A1), and therefore confirm the experimentally proposed pathway for the photodissociation of X2A' ' at 357 nm. Our CASPT2 D0 calculations support the experimental fact that the X state does not undergo dissociation in the visible spectral region and imply that a direct dissociation of the A state to C2H3+ (X1A1) is energetically feasible.     

O‐loss photodissociation of the OCS+ ion in the low‐lying electronic states studied using multiconfiguration second‐order perturbation theory

The CASPT2 potential energy curves (PECs) for O‐loss dissociation from the X²Π, A²Π, B²Σ⁺, C²Σ⁺, 1⁴Σ^?, 1²Σ^?, and 1⁴Π states of the OCS⁺ ion were calculated. The PEC calculations indicate that X²Π, 1⁴Σ^?, 1²Σ^?, and 1⁴Π correlate with CS⁺(X²Σ⁺) + O(³P_g); A²Π and B²Σ⁺ correlate with CS⁺(A²Π) + O(³P_g); and C²Σ⁺ probably correlates with CS⁺(X²Σ⁺) + O(¹D_g). The CASSCF minimum energy crossing point (MECP) calculations were performed for the C²Σ⁺/1⁴Σ^?, C²Σ⁺/1⁴Π, A²Π/1⁴Σ^?, A²Π/1²Σ^?, A²Π/1⁴Π, and B²Σ⁺/1²Σ^? state pairs and the spin‐obit couplings were calculated at the located MECPs. A conical intersection point between the B²Σ⁺ and C²Σ⁺ potential energy surfaces was found at the CASSCF level. Based on our calculations, seven O‐loss predissociation processes of the C²Σ⁺ state are suggested and an appearance potential value of 7.13 eV for the CS⁺ + O product group is predicted. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

MRSDCI studies of low-lying electronic states of the CF 2 + ion

Summary The equilibrium geometries, excitation energies, force constants and vibrational frequencies for four low-lying electronic statesX ² A ₁,² B ₁,² B ₂ and² A ₂ of the CF ₂ ⁺ ion have been calculated at the MRSDCI level with a double zeta plus polarization basis set. Our calculated excitation energies for these states and vibrational frequencies for the ground state are in good agreement with experimental data via photoelectron spectroscopy of the CF₂ radical (carbene). The electronic transition dipole moments, oscillator strengths for the² B ₁ X ² A ₁ and² B ₂ X ² A ₁ transitions, radiative lifetimes for the² B ₁ and² B ₂ states and the spin properties for theX ² A ₁ state are calculated based on the MRSDCI wavefunctions.     

Spin component scaling in multiconfiguration perturbation theory

We investigate a term-by-term scaling of the second-order energy correction obtained by perturbation theory (PT) starting from a multiconfiguration wave function. The total second-order correction is decomposed into several terms, based on the level and the spin pattern of the excitations. To define individual terms, we extend the same spin/different spin categorization of spin component scaling in various ways. When needed, identification of the excitation level is facilitated by the pivot determinant underlying the multiconfiguration PT framework. Scaling factors are determined from the stationary condition of the total energy calculated up to order 3. The decomposition schemes are tested numerically on the example of bond dissociation profiles and energy differences. We conclude that Grimme's parameters determined for single-reference M?ller-Plesset theory may give a modest error reduction along the entire potential surface, if adopting a multireference based PT formulation. Scaling factors obtained from the stationary condition show relatively large variation with molecular geometry, at the same time they are more efficient in reducing the error when following a bond dissociation process.     

Theoretical study on HBO+ and HOB+ cations using multiconfiguration second‐order perturbation theory

The HBO⁺ and HOB⁺ cations have been reinvestigated using the CASSCF and CASPT2 methods in conjunction with the contracted atomic natural orbital (ANO) basis sets. The geometries of all stationary points in the potential energy surfaces were optimized at the CASSCF/ANO and CASPT2/ANO levels. The ground and the first excited states of HBO⁺ are predicted to be X²Π and A²Σ⁺ states, respectively. It was predicted that the ground state of HOB⁺ is X²Σ⁺ state. The A²Π state of HOB⁺ has unique imaginary frequency. A bending local minimum M1 was found for the first time along the 1²A′′ potential energy surface and the A²Π state of HOB⁺ should be the transition state of the isomerization reactions for M1? M1. The CASPT2/ANO potential energy curves (PECs) of isomerization reactions were calculated as functions of the HBO bond angle. Many of the CASSCF and CASPT2 calculated results were different from the previously published QCISD(T) results. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Theoretical prediction on HAlS+ and HSAl+ cations using multiconfiguration second‐order perturbation theory

Some low‐lying states of the HAlS⁺ and HSAl⁺ cations have been studied for the first time by large‐scale theoretical calculations using three methods: complete active space self‐consistent field (CASSCF), complete active second‐order perturbation theory (CASPT2), and density functional theory Becke's three‐parameter hybrid function with the nonlocal correlation of Lee–Yang–Parr (B3LYP) with the contracted atomic natural orbital (ANO‐L) and cc‐pVTZ basis sets. The geometries of all stationary points along the potential energy surfaces (PESs) were optimized at the CASSCF/ANO‐L and B3LYP/cc‐pVTZ levels. The ground and the first excited states of linear HAlS⁺ are predicted to be X²Π and A²Σ⁺ states, respectively. For the linear HSAl⁺ structure, the first excited state is A²Σ⁺. The X²Π state of linear HSAl⁺ is a second‐order saddle point, because it has two imaginary frequencies. Two bent global minima M1 and M2 were found along the 1²A′ and 1²A″ PESs, respectively. The CASPT2/ANO‐L potential energy curves of isomerization reactions were calculated as a function of HAlS bond angle. According to our calculations, the ground‐state HAlS⁺ is linear, whereas the ground‐state HSAl⁺ is bent. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

The 1 (2)A(1), 1 (2)B(2), and 1 (2)A(2) states of the SO(2) (+) ion studied using multiconfiguration second-order perturbation theory

The 1 (2)A(1), 1 (2)B(2), and 1 (2)A(2) electronic states of the SO(2) (+) ion have been studied using multiconfiguration second-order perturbation theory (CASPT2) and two contracted atomic natural orbital basis sets, S[6s4p3d1f]/O[5s3p2d1f] (ANO-L) and S[4s3p2d]/O[3s2p1d] (ANO-S), and the three states were considered to correspond to the observed X, B, and A states, respectively, in the previous experimental and theoretical studies. Based on the CASPT2/ANO-L adiabatic excitation energy calculations, the X, A, and B states of SO(2) (+) are assigned to 1 (2)A(1), 1 (2)B(2), and 1 (2)A(2), respectively, and our assignments of the A and B states are contrary to the previous assignments (A to (2)A(2) and B to (2)B(2)). The CASPT2/ANO-L energetic calculations also indicate that the 1 (2)A(1), 1 (2)B(2), and 1 (2)A(2) states are, respectively, the ground, first excited, and second excited states at the ground-state (1 (2)A(1)) geometry of the ion and at the geometry of the ground-state SO(2) molecule. Based on the CASPT2/ANO-L results for the geometries, we realize that the experimental geometries (determined by assuming the bond lengths to be the same as the neutral ground state of SO(2)) were not accurate. The CASPT2/ANO-S calculations for the potential energy curves as functions of the OSO angle confirm that the 1 (2)B(2) and 1 (2)A(2) states are the results of the Renner-Teller effect in the degenerate (2)Pi(g) state at the linear geometry, and it is clearly shown that the 1 (2)B(2) curve, as the lower component of the Renner splitting, lies below the 1 (2)A(2) curve. The UB3LYP/cc-pVTZ adiabatic excitation energy calculations support the assignments (A to (2)B(2) and B to (2)A(2)) based on the CASPT2/ANO-L calculations.     

Analytic techniques for the coupled multiconfiguration SCF perturbation theory

The perturbation theory based on the paired excitation multiconfiguration self-consistent field approach of Clementi and Veillard is considered. The coupled first-order perturbed orbital equations are analysed and an appropriate computational scheme for their solution is discussed. The proposed computational scheme is analogous to the technique employed for the solution of the coupled Hartree–Fock equations in the one-configuration approximation. However, because of the presence ofnondiagonal Lagrangian multipliers and the use of different one-electron operators for different orbitals, the present scheme raises some new computational problems. In this context a new technique for the solution of the unperturbed multiconfiguration self-consistent field equations is proposed. A simple illustration of the superiority of the multiconfiguration perturbation approach with respect to the ordinary coupled Hartree–Fock scheme is given. Also the validity of the variation formulation of the presented scheme and its relation to the finite-field approach are discussed.     

On the low-lying electronic states of BiF

Relativistic CI calculations on the low-lying states of BiF(0⁺, 1, 2, 0⁺(II)) arising from the σ²π² configuration are carried out. Comparison calculations of the λ-s states without spin-orbit interaction (³Σ⁻, ¹Σ⁺ and ¹Δ) are also presented. These calculations enable the assignment of three experimentally observed low-lying states. In addition, the properties of a new state (2) are calculated (yet to be observed). The calculated dissociation energy of the ground state is 2.63 eV. The potential energy surfaces of the low-lying electronic states of BiF reveal interesting avoided crossings. Our calculations clarify the earlier assignment of the electronic transitions of BiF.     

Ab initio study of low-lying electronic states of SnCl2+

Complete active space self-consistent field (CASSCF), multireference configuration interaction (MRCI), and restricted-spin coupled-cluster singles-doubles with perturbative triples [RCCSD(T)] calculations have been carried out on low-lying doublet and quartet states of SnCl2+, employing basis sets of up to aug-cc-pV5Z quality. Effects of core correlation and off-diagonal spin-orbit interaction on computed vertical ionization energies were investigated. The best theoretical estimate of the adiabatic ionization energy (including zero-point vibrational energy correction) to the X2A1 state of SnCl2+ is 10.093+/-0.010 eV. The first photoelectron band of SnCl2 has also been simulated by employing RCCSD(T)/aug-cc-pV5Z potential energy functions and including Duschinsky rotation and anharmonicity.     

X, A, B, C, and D states of the C6H5F+ ion studied using multiconfiguration wave functions

Electronic states of the C6H5F+ ion have been studied within C2v symmetry by using the complete active space self-consistent field (CASSCF) and multiconfiguration second-order perturbation theory (CASPT2) methods in conjunction with an atomic natural orbital basis. Vertical excitation energies (Tv) and relative energies (Tv') at the ground-state geometry of the C6H5F molecule were calculated for 12 states. For the five lowest-lying states, 1(2)B1, 1(2)A2, 2(2)B1, 1(2)B2, and 1(2)A1, geometries and vibrational frequencies were calculated at the CASSCF level, and adiabatic excitation energies (T0) and potential energy curves (PEC) for F-loss dissociations were calculated at the CASPT2//CASSCF level. On the basis of the CASPT2 T0 calculations, we assign the X, A, B, C, and D states of the ion to 1(2)B1, 1(2)A2, 2(2)B1, 1(2)B2, and 1(2)A1, respectively, which supports the suggested assignment of the B state to (2)(2)B1 by Anand et al. based on their experiments. Our CASPT2 Tv and Tv' calculations and our MRCI T0, Tv, and Tv' calculations all indicate that the 2(2)B1 state of C6H5F+ lies below 1(2)B2. By checking the relative energies of the asymptote products and checking the fragmental geometries and the charge and spin density populations in the asymptote products along the CASPT2//CASSCF PECs, we conclude that the 1(2)B1, 1(2)B2, and 1(2)A1 states of C6H5F+ correlate with C6H5+ (1(1)A1) + F (2P) (the first dissociation limit). The energy increases monotonically along the 1(2)B1 PEC, and there are barriers and minima along the 1(2)B2 and 1(2)A1 PECs. The predicted appearance potential value for C6H5+ (1(1)A1) is very close to the average of the experimental values. Our CASPT2//CASSCF PEC calculations have led to the conclusion that the 1(2)A2 state of C6H5F+ correlates with the third dissociation limit of C6H5+ (1(1)A2) + F (2P), and a preliminary discussion is presented.     

The low-lying electronic states of alloxan

A series of low-lying (n,π*) states of alloxan have been investigated through semiempirical calculations and absorption and emission studies. The energy of the lowest (n,π*) triplet state as calculated by UHF methodology agrees very well with that of the observed phosphorescent state.     

The low-lying electronic states of YCu

The spectroscopic constants for the singlet and tripletstates of YCu below about 15 000 cm⁻¹ are determined using an internally contracted multireference configuration-interaction approach. These calculations are calibrated by studies of fewer states using higher levels of correlation treatment and/or basis sets. The computed T_c values and radiative lifetimes are in reasonable agreement with experiment. The calculations confirm the previous experimental assignment for all but one state, where theory helps resolve between two possible assignments.     

Theoretical investigations of the low-lying electronic states of the HeC2+ dication

Extended MC SCF computations of the CAS SCF type have been performed on four energetically low-lying electronic states of HeC²⁺ dications. The X ¹Σ⁺ ground state is predicted to be thermodynamically stable by 0.72 eV, while the a ³Π and A ¹Π excited states represent metastable species with barrier heights of 2.19 and 0.20 eV, respectively. The b ³Σ⁺ state exhibits merely a very shallow potential dip with a well depth of only 0.06 eV. The HeC²⁺ dication is therefore predicted to be experimentally observable in the gas phase. Bonding in these unusual dications is discussed and compared to the isoelectronic CH⁺ cation.     

Solvent effects on electronic spectra studied by multiconfigurational perturbation theory

The complete active space (CAS) self-consistent field (SCF) method combined with multiconfigurational second-order perturbation theory (CASPT2) and a self-consistent reaction field (SCRF) model is used to study the effect of solvation on excited states of different molecules such as acetone, pyrimidine, some aminobenzene derivatives, indole, and imidazole. The present SCRF model, in which the solute molecule is placed into a spherical cavity surrounded by a dielectric continuum, also includes a repulsive potential representing the solute–solvent exchange repulsion and considers the time dependence of the absorption process. In general, we find that our calculations do reproduce the trends observed in experiment but underestimate the solvatochromic shifts. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 65 : 167–181, 1997