Electric properties of the water molecule in 1A1, 1B1, and 3B1 electronic states: Refined CASSCF and CASPT2 calculations

Summary The dipole moments and dipole polarizabilities of the ¹A₁, ¹B₁, and ³B₁ electronic states of the water molecule have been calculated by using the CASSCF approach followed by the evaluation of the dynamic electron correlation contribution by the second-order perturbation scheme CASPT2. All calculations have been carried out in a specifically extended ANO basis set which accounts for the Rydberg character of the two excited states. In order to estimate the correctness and accuracy of the present data a scan over a variety of different active spaces for the CASSCF wave function has been made. The present results are superior to earlier CASSCF calculations, although their qualitative features remain essentially the same. The dipole moments in ¹B₁ and ³B₁ states are predicted to be about 0.49 a.u. and 0.33 a.u., respectively, and have the opposite orientation with respect to the ground state dipole moment. The dipole polarizability tensors of the excited states are characterized by high anisotropy and are dominated by the in-plane component perpendicular to the symmetry axis. All their components are found to be about an order of magnitude larger than those of the ground state polarizability tensor. The excitation energy dependence on the choice of the active orbital space in the CASSCF reference function is also considered and the analysis of the present data concludes in the concept of what is called the mutually compatible active spaces for the two states involved in excitation. All CASPT2 results are in good agreement with the results of recent calculations carried out in the framework of the open-shell coupled cluster formalism. This agreement confirms the high efficiency of the CASSCF/CASPT2 approach to the treatment of the electron correlation effects.     

Full configuration interaction benchmark calculations for transition moments

Full configuration-interaction (FCI) calculations have been performed for the ã ¹A₁–b¹B₁and ã ¹A₁–(2)¹A₁transitions in CH₂ and for selected dipole and quadrupole transitions in BeO. The FCI transition moments are compared to those obtained from correlation treatments that truncate the n-particle expansion. The state-averaged MCSCF/SOCI and FCI results agree well, even for BeO, where the CASSCF level nonorthogonal transition moment differs from the state-averaged CASSCF transition moment.     

Excited electronic states, transition probabilities, and radiative lifetimes of CAs: a theoretical contribution and challenge to experimentalists

High-level CASSCF/MRCI calculations with a quintuple-ζ quality basis set are reported by characterizing for the first time a manifold of electronic states of the CAs radical yet to be investigated experimentally. Along with the potential energy curves and the associated spectroscopic constants, the dipole moment functions for selected electronic states as well as the transition dipole moment functions for the most relevant electronic transitions are also presented. Estimates of radiative transition probabilities and lifetimes complement this investigation, which also assesses the effect of spin-orbit interaction on the A (2)Π state. Whenever pertinent, comparisons of similarities and differences with the isovalent CN and CP radicals are made.     

Potential energy curves for the X1∑ g, B1△g and B''''1∑ g states of C2 using MRCI and approximate CI methods

The potential energy curves for the X1∑ g, B1△g and B′1∑ g states of C2 have been studied by using MRCI and approximate CI methods, and are benchmarked against the calculations of full configuration interaction (FCI). The results obtained by MRCI method agree with the FCI very well, and even are accurate enough to compare other approximate methods as benchmark, when the calculations of FCI are not feasible. The approximate CI methods mentioned in this paper are reliable for treating chemical problems.     

Application of the iterative difference-dedicated configuration interaction method to the determination of excitation energies in some benchmark systems: Be, CH+, BH and CH2

The iterative difference-dedicated CI method (IDDCI) has been applied to determine excitation energies in small systems for which benchmark FCI and other high-level calculations exist. Transitions to excited singlet and triplet states in Be and vertical transitions in CH⁺, BH and CH₂ are reported. The deviations from FCI results are lower than 0.1 eV and compare advantageously with SDCI including size-consistency corrections, (SC)²SDCI, and with coupled cluster calculations including the effect of triples, especially for the states which have a predominant double excitation character. The IDDCI procedure has been speeded up by using smaller subspaces for optimizing the molecular orbitals. Received: 17 January 1997 / Accepted: 31 July 1997     

Theory of the photodissociation of ozone in the Hartley continuum: potential energy surfaces, conical intersections, and photodissociation dynamics

Ab initio potential energy and transition dipole moment surfaces are presented for the five lowest singlet even symmetry electronic states of ozone. The surfaces are calculated using the complete active space self consistent field method followed by contracted multireference configuration interaction (MRCI) calculations. A slightly reduced augmented correlation consistent valence triple-zeta orbital basis set is used. The ground and excited state energies of the molecule have been computed at 9282 separate nuclear geometries. Cuts through the potential energy surfaces, which pass through the geometry of the minimum of the ground electronic state, show several closely avoided crossings. Close examination, and higher level calculations, very strongly suggests that some of these seemingly avoided crossings are in fact associated with non-symmetry related conical intersections. Diabatic potential energy and transition dipole moment surfaces are created from the computed ab initio adiabatic MRCI energies and transition dipole moments. The transition dipole moment connecting the ground electronic state to the diabatic B state surface is by far the strongest. Vibrational-rotational wavefunctions and energies are computed using the ground electronic state. The energy level separations compare well with experimentally determined values. The ground vibrational state wavefunction is then used, together with the diabatic B<--X transition dipole moment surface, to form an initial wavepacket. The analysis of the time-dependent quantum dynamics of this wavepacket provides the total and partial photodissociation cross sections for the system. Both the total absorption cross section and the predicted product quantum state distributions compare well with experimental observations. A discussion is also given as to how the observed alternation in product diatom rotational state populations might be explained.     

Conical intersections involving the dissociative 1pisigma* state in 9H-adenine: a quantum chemical ab initio study

The conical intersections of the dissociative 1pisigma* excited state with the lowest 1pipi* excited state and the electronic ground state of 9H-adenine have been investigated with multireference electronic structure calculations. Adiabatic and quasidiabatic potential energy surfaces and coupling elements were calculated as a function of the NH stretch coordinate of the azine group and the out-of-plane angle of the hydrogen atom, employing MultiReference Configuration-Interaction (MRCI) as well as Complete-Active-Space Self-Consistent-Field (CASSCF) methods. Characteristic properties of the 1pipi*-1pisigma* and 1pisigma*-S0 conical intersections, such as the diabatic-to-adiabatic mixing angle, the geometric phase of the adiabatic electronic wavefunctions, the derivative coupling, as well as adiabatic and diabatic transition dipole moment surfaces were investigated in detail. These data are a prerequisite for future quantum wavepacket simulations of the photodissociation and internal-conversion dynamics of adenine.     

Energetics, transition states, and intrinsic reaction coordinates for reactions associated with O(3P) processing of hydrocarbon materials

Electronic structure calculations based on multiconfiguration wave functions are used to investigate a set of archetypal reactions relevant to O(3P) processing of hydrocarbon molecules and surfaces. These include O(3P) reactions with methane and ethane to give OH plus methyl or ethyl radicals, O(3P) + ethane to give CH3O + CH3, and secondary reactions of the OH product radical with ethane and the ethyl radical. Geometry optimization is carried out with CASSCF/cc-pVTZ for all reactions, and with CASPT2/cc-pVTZ for O(3P) + methane/ethane. Single-point energy corrections are applied with CASPT2, CASPT3, and MRCI + Q with the cc-pVTZ and cc-pVQZ basis sets, and the energies extrapolated to the complete basis set limit (CBL). Where comparison of computed barriers and energies of reaction with experiment is possible, the agreement is good to excellent. The best agreement (within experimental error) is found for MRCI + Q/CBL applied to O(3P) + methane. For the other reactions, CASPT2/CBL and MRCI + Q/CBL predictions differ from experiment by 1-5 kcal/mol for 0 K enthalpies of reaction, and are within 1 kcal/mol of the best-estimate experimental range of 0 K barriers for O(3P) + ethane and OH + ethane. The accuracy of MRCI + Q/CBL is limited mainly by the quality of the active space. CASPT2/CBL barriers are consistently lower than MRCI + Q/CBL barriers with identical reference spaces.     

Photostability via a sloped conical intersection: a CASSCF and RASSCF study of pyracylene

An extensive ab initio study of the ground- and excited-state potential energy surfaces of pyracylene is presented in this work. CASSCF calculations show that there is an accessible sloped S0/S1 conical intersection, which leads to ultrafast internal conversion and explains the observed photostability. RASSCF calculations (using a well-defined subset of the CASSCF configurations) are shown to be able to reproduce CASSCF results satisfactorily and will therefore be useful for larger systems where CASSCF is currently too expensive. MRCI and MRPT2 energy corrections are computed to assess the ionic character of the excited states. Finally, MMVB calculations are also benchmarked against CASSCF, to assess the reliability of this parametrized method for excited states of large conjugated polycyclic aromatic hydrocarbons.     

Oscillator strengths of the Mulliken, Swan, Ballik-Ramsay, Phillips, and d3Pi g<--c 3Sigma u+ systems of C2 calculated by MRCI methods utilizing a biorthogonal transformation of CASSCF orbitals

Ab initio oscillator strengths and lifetimes for the D (1)Sigma(u) (+)<--X (1)Sigma(g) (+) Mulliken system of C(2) are reported. The calculations were carried out at the MRCI level of theory with Davidson's correction using aug-cc-pV6Z basis sets and include core and core-valence correlation as well as relativistic corrections, computed with aug-cc-pCVQZ and cc-pVQZ bases, respectively. The MRCI calculations of transition moments utilize a biorthogonal transformation of the CASSCF orbitals. This approach was also employed to recompute the transition moments of the Swan, Ballik-Ramsay, Phillips, and d (3)Pi(g)<--c (3)Sigma(u) (+) systems of C(2), which were the subject of our previous study [D. L. Kokkin et al., J. Chem. Phys. 126, 084302 (2007)], resulting in an improved set of oscillator strengths for the latter systems as well. The oscillator strength of the Mulliken origin band, f(00) (DA), was calculated to be 0.0535, in excellent agreement with the accepted astronomical value of 0.054.     

A first principles approach to optimal control

This article shows that by using ab initio or first principle calculations it is possible to obtain reliable ingredients needed to simulate pump-probe and optimal control experiments. Our experimental challenge is to elucidate the reaction mechanism behind an optimal pulse tailored to maximize ionization in the system CpMn(CO)₃, while avoiding CO dissociation. Starting from MRCI/CASSCF potential energy curves calculated along the relevant CO fragmentation channel, we use the resulting MRCI wave function to estimate non-adiabatic couplings, as well as neutral-to-neutral and neutral-to-ionic dipole couplings. The state-of-the-art potentials and couplings serve to perform wave packet propagations which simulate the femtosecond pump-probe spectra that explain the features shown in the experimental optimal pulse.     

Theoretical study with vibration–rotation and dipole moment calculations of quartet states of the CrCl molecule

The potential energy curves have been investigated for the 10 lowest quartet electronic states in the ^2s+1Λ^± representation below 30,000 cm^?1 of the molecule CrCl via CASSCF and MRCI (singly and doubly excitation with Davidson correction) calculations. The harmonic frequency ω_e, the internuclear distance r_e, the rotational constant B_e, the electronic energy with respect to the ground state T_e, and the permanent dipole moment μ have been calculated. By using the canonical functions approach, the eigenvalues E_v, the rotational constant B_v, and the abscissas of the turning points r_min and r_max have been calculated for the considered electronic states up to the vibrational level v = 19. Seven electronic states have been studied here theoretically for the first time. The comparison of these values to the theoretical results available in the literature shows a good agreement. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

TiO2基态和激发态的几何结构、激发能和偶极矩

采用二阶微扰理论MP2、密度泛函B3LYP方法和含时密度泛函TD-B3LYP方法分别优化了TiO₂分子的基态¹A₁和六个激发态¹B₂、³B₂、¹B₁、³B₁、¹A₂和³A₂的几何结构. ¹A₁、¹B₂、³B₂、¹B₁和³B₁具有弯曲几何结构, ¹A₂和³A₂具有线性对称结构. 我们发现激发态¹B₂、³B₂、¹B₁和³B₁键偶极矩的数值大小顺序和相应的键角大小顺序完全一致. 另外, 采用完全活化空间自洽场(CASSCF)CASSCF(6,6)、CASSCF(8,8)、多参考组态相互作用(MRCI)和含时密度泛函TD-B3LYP 计算了TiO₂ 分子各激发态的垂直激发能和绝热激发能. 对¹B₂、³B₂和¹B₁三个态, MRCI/CASSCF(6,6) 计算的垂直激发能和绝热激发能与已有的实验值最接近. 对其他三个激发态³B₁、¹A₂和³A₂, 计算的激发能和文献报道的激发能计算值基本一致. 最后, 还计算了TiO₂分子的基态和激发态的偶极矩. 对¹A₁和¹B₂态, 偶极矩的计算值与已有的实验值相吻合. 采用原子偶极矩校正的Hirshfeld 布居方法计算了TiO₂分子在¹A₁、¹B₂、³B₂、¹B₁和³B₁态时各原子的电荷, 发现从基态到激发态偶极矩的变化与电荷从氧原子向钛原子的转移有关. 整个计算中还考察了基函数cc-pVDZ、cc-pVTZ和cc-pVQZ对计算结果的影响.     

Comparing electronic structure predictions for the ground state dissociation of vinoxy radicals

This paper reports a series of electronic structure calculations performed on the dissociation pathways of the vinoxy radical (CH(2)CHO). We use coupled-cluster with single, double, and perturbative triple excitations (CCSD(T)), complete active space self-consistent field (CASSCF), multireference configuration interaction (MRCI), and MRCI with the Davidson correction (MRCI+Q) to calculate the barrier heights of the two unimolecular dissociation pathways of this radical. The effect of state averaging on the barrier heights is investigated at the CASSCF, MRCI, and MRCI+Q levels. The change in mixing angle along the reaction path is calculated as a measure of derivative coupling and found to be insufficient to suggest nonadiabatic recrossing. We also present a new analysis of previous experimental data on the unimolecular dissociation of ground state vinoxy. In particular, an error in the internal energy distribution of vinoxy radicals reported in a previous paper is corrected and a new analysis of the experimental sensitivity to the onset energy (barrier height) for the isomerization reaction is given. Combining these studies, a final "worst case" analysis of the product branching ratio is given and a statistical model using each of the calculated transition states is found to be unable to correctly reproduce the experimental data.     

Theoretical study of the dipole moment of oxygen monofluoride (OF)

Theoretical X²II potentials and dipole moment functions for OF are presented at the CASSCF, externally contracted Cl, and MRCI(SD) levels using DZP and extended gaussian basis sets. The best theoretical results (with experiment in parentheses) are μ_ν =0 = ?0.0089 (?0.0043) and μ_ν=1 = ?0.0318 (?0.0267) D, where the minus sign implies O⁺F^?.     

Geometrical derivatives of dipole moments and polarizabilities

Molecular dipole moments and polarizabilities, as well as their geometrical derivatives, are given analytical expressions for multiconfiguration self-consistent-field and configuration interaction wavefunctions. By considering the response of the electronic wavefunction induced by electric field and geometrical displacement terms in the Hamiltonian, the response of the total electronic energy to these terms is analyzed. The dipole moment and polarizability are then identified through the factors in the energy which are linear and quadratic in the electric field, respectively. Derivatives with respect to molecular deformation are obtained by identifying factors in these moments which are linear, quadratic, etc., in the distortion parameter. The analytical derivative expressions obtained here are compared to those which arise through finite-difference calculations, and it is shown how previous configuration-interaction-based finite difference dipole moment and polarizability derivatives are wrong. The proper means of treating such derivatives are detailed.     

Theoretical study with rovibrational and dipole moment calculation of sextet states of the CrCl molecule

The potential energy curves have been investigated for the 13 lowest sextet electronic states in the representation below 53,000 cm^?1 of the molecule CrCl via CASSCF and MRCI (single and double excitation with Davidson correction) calculations. The harmonic frequency ω_e, the internuclear distance r_e, the rotational constant B_e, the electronic energy with respect to the ground state T_e, and the permanent dipole moment μ have been calculated. By using the canonical functions approach, the eigenvalues E_v, the rotational constant B_v, and the abscissas of the turning points r_min and r_max have been calculated for the considered electronic states up to the vibrational level v = 16. Nine electronic states have been studied theoretically here for the first time. The comparison of these values with the theoretical and experimental results available in the literature shows a good agreement. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Asymptotic multipolar expansion of collision-induced properties

The collision-induced (CI) dipole moment, CI polarizability, and CI hyperpolarizability are considered for three H(2)-rare gas (Rg) pairs (Rg = He, Ne, Ar). In this study, the symmetry-adapted (SA) components, the projection of the CI dipole, polarizability, and hyperpolarizability on an appropriately tailored set of spherical harmonics are calculated. A set of equations for the respective SA components is derived. The Cartesian components of the CI properties calculated by quantum chemistry methods for three intermolecular geometries are used in our calculations as input data. The analytical, multipolar long-range behavior of the CI properties studied is considered within a multipole-induced multipole model. Taking the SA components at large distances, the ab initio SA numerical results and the model semianalytical data were compared. In general, a good agreement has been found. The results of our study are expected to be of value in spectral line shape analysis and in modeling of processes in the Earth's and planetary atmospheres.     

Comparison of valence-only model potential and all-electron ab initio LCAO SCF MO studies of Li2 and LiH

A previously developed gaussian-based model potential theory for a single valence electron outside a core has been extended to the simple two-valence electron systems Li₂ and LiH within the LCAO SCF MO formulation, using an extended valence basis set. Comparisons of the results with corresponding ab initio calculations show excellent agreement of the total valence energy and the orbital energy in both systems, and for the dipole moment in LiH.     

Relative stability of the 3A2, 1A2, and 1A1 states of phenylnitrene: A difference-dedicated configuration interaction calculation

The relative stability of the ³A₂, ¹A₂, and ¹A₁ states of phenylnitrene is evaluated by means of ab initio calculations followed by difference-dedicated configuration interaction (DDCI). This approach is based on effective Hamiltonian theory at a low order of perturbation to select rationally the determinants which contribute to the energy difference. The CI space built on this criterion is then treated variationally. The method allows a considerable reduction of the CI space compared with a complete CAS*SDCI calculation (where CAS stands for complete active space). Depending on the concerned energy difference, different model spaces may be chosen, as illustrated in the ³A₂ → ¹A₂ and the ³A₂ → ¹A₁ transitions in phenylnitrene. Since the CI space may reach considerable dimensions, a direct CI algorithm for selected CI spaces, the SCIEL algorithm, has been used to perform the calculations. The results are in excellent agreement with previous calculations and with available experimental data. © 1996 by John Wiley & Sons, Inc.