Complete Active Space SCF Method Research Articles

Can Anisotropic Exchange Be Reliably Calculated Using Density Functional Methods? A Case Study on Trinuclear MnIII‐MIII‐MnIII (M=Fe, Ru, and Os) Cyanometalate Single‐Molecule Magnets

Density functional studies have been performed on a set of trinuclear single-molecule magnets (SMMs) of general formula [{Mn2(5-Br salen)2(MeOH)2}M(CN)6](NEt4) (M=Fe(III) (1), Ru(III) (2) and Os(III) (3); 5-Brsalen=N,N'-ethylenebis(5-bromosalicylidene)iminato anion). We have computed the orbital-dependent exchange interaction for all three complexes for the first time using DFT and complete active space self-consistent field (CASSCF) methods. DFT calculations yield the anisotropic exchange as J(ξξ)=3.5 cm(-1) for 1; J(ξξ)=12.1 cm(-1), J(ζζ)=-6.9 cm(-1) and J(ηη)=-14 cm(-1) for 2; and J(ξξ)=23.7 cm(-1) and J(ζζ) =-11.1 cm(-1) for 3. The computed values are in agreement with the experimental report, and this suggests that the established methodology can be used to compute the anisotropic exchange in larger clusters. Our calculations reiterate the fact that the exchange is described by a three-axis anisotropic exchange for complexes 2 and 3 as evidenced by the experiments. A stronger exchange coupling as we move down the periodic table from 3d to 5d is reproduced by our calculations, and the origin of this enhancement in the exchange interaction has been probed by using molecular orbital analysis. The electronic origin of different types of exchange observed in this series is found to be related to the energy difference between possible degenerate pairs and the nature of orbital interactions. By computing the exchange interaction, the single-ion anisotropy of Mn(III) and zero-field splitting of the S=9/2 ground state of complexes 1-3 using CASSCF and/or DFT methods, we have attempted to shed light on the issue of anisotropic exchange and the barrier height for the magnetisation reversal in SMMs. Comprehensive magneto-structural correlations have been developed to offer clues on how to further enhance the barrier height in this class of SMMs.

Geometries and Vertical Excitation Energies in Retinal Analogues Resolved at the CASPT2 Level of Theory: Critical Assessment of the Performance of CASSCF, CC2, and DFT Methods.

A systematic investigation of structural properties and vertical excitation energies of a series of structurally modified 11-cis-retinal chromophores in vacuo was performed by means of multiconfigurational second-order perturbation theory (CASPT2). CASPT2-based geometries agree reasonably well with Møller-Plesset second-order perturbation theory (MP2), local second-order approximate coupled cluster singles and doubles (LCC2), and density functional theory (DFT) geometries, while the complete active space self-consistent field (CASSCF) method exaggerates dramatically the bond length pattern in the polyene chain. The quality of the resulting vertical excitation energies obtained by employing CASSCF, second-order approximate coupled cluster singles and doubles (CC2), LCC2, and time-dependent density functional theory (TD-DFT) approaches is assessed with respect to the CASPT2 data. We show that the commonly used CASSCF/CASPT2 approach works reasonably well in the case of vertical excitation energies of planar structures, but lack of dynamic correlation leads to large errors in energetics for strongly strained structures. For example, the highly twisted conformers of 9,10-dimethyl and 9,10,13-trimethyl species are found as global minima at the CASSCF level, whereas they turn almost planar at the CASPT2, MP2, LCC2, and DFT levels of theory. The CC2 method has shown a remarkable performance, manifested by a maximum deviation of 0.05 eV from the reference CASPT2 results, whereas the local version of CC2 seems to fail to describe the charge-transfer character of the S0 → S1 transitions correctly. We believe that our CASPT2 benchmark set will provide a reference that can be utilized for validation and development studies on 11-cis-retinal protonated Schiff base chromophore analogues.

Role of non-Condon vibronic coupling and conformation change on two-photon absorption spectra of green fluorescent protein

Two-photon absorption spectra of green fluorescent proteins (GFPs) often show a blue-shift band compared to their conventional one-photon absorption spectra, which is an intriguing feature that has not been well understood. We present here a systematic study on one- and two-photon spectra of GFP chromophore by means of the density functional response theory and complete active space self-consistent field (CASSCF) methods. It shows that the popular density functional fails to provide correct vibrational progression for the spectra. The non-Condon vibronic coupling, through the localised intrinsic vibrational modes of the chromophore, is responsible for the blue-shift in the TPA spectra. The cis to trans isomerisation can be identified in high-resolution TPA spectra. Our calculations demonstrate that the high level ab initio multiconfigurational CASSCF method, rather than the conventional density functional theory is required for investigating the essential excited-state properties of the GFP chromophore.

Performance of PNOF5 Natural Orbital Functional for Radical Formation Reactions: Hydrogen Atom Abstraction and C-C and O-O Homolytic Bond Cleavage in Selected Molecules.

Radical formation through hydrogen abstraction and C-C and O-O homolytic bond cleavage from selected molecules is investigated by use of natural orbital functional theory in its PNOF5 natural orbital functional implementation, and the results are compared to high-level ab initio complete active space self-consistent field (CASSCF) and complete active space with second-order perturbation theory (CASPT2) methods and experimental data. It is observed that PNOF5 is able to treat the strong electron correlation effects along the homolysis of X-H (X = C, N, O) and X-X (X = C, O) bonds, leading, in general, to the correct trends in the corresponding bond strengths and a good description of the resultant electronic structure for these radicals. In general, PNOF5 bond energies are lower than the experimental ones, because of partial lack of dynamical electron correlation. However, the part of dynamical electron correlation recovered by PNOF5 allows it to give more accurate results than CASSCF methods with a minimum window required to treat near-degeneracy effects. In addition, inspection of the natural orbital occupancies with respect to the CASSCF ones shows an outstanding performance of PNOF5 in treating degenerate and quasidegenerate states, giving a correct description of diradicals and diradicaloids formed upon C-C cleavage in cyclopropane and derivatives.

Theoretical Studies for Excited-State Tautomerization in the 7-Azaindole–(CH3OH)n (n = 1 and 2) Complexes in the Gas Phase

The excited-state tautomerization of 7-azaindole (7AI) complexes bonded with either one or two methanol molecule(s) was studied by systematic quantum mechanical calculations in the gas phases. Electronic structures and energies for the reactant, transition state (TS), and product were computed at the complete active space self-consistent field (CASSCF) levels with the second-order multireference perturbation theory (MRPT2) to consider the dynamic electron correlation. The time-dependent density functional theory (TDDFT) was also used for comparison. The excited-state double proton transfer (ESDPT) in 7AI-CH(3)OH occurs in a concerted but asynchronous mechanism. Similarly, such paths are also found in the two transition states during the excited-state triple proton transfer (ESTPT) of the 7AI-(CH(3)OH)(2) complex. In the first TS, the pyrrole ring proton first migrated to methanol, while in the second the methanol proton moved first to the pyridine ring. The CASSCF level with the MRPT2 correction showed that the former path was much preferable to the latter, and the ESDPT is much slower than the ESTPT. Additionally, the vibrational-mode enhanced tautomerization in the 7AI-(CH(3)OH)(2) complex was also studied. We found that the excitation of the low-frequency mode shortens the reaction path to increase the tautomerization rate. Overall, most TDDFT methods used in this study predicted different TS structures and barriers from the CASSCF methods with MRPT2 corrections.

Effects on spectroscopic properties for several low-lying electronic states of CS molecule by core–valence correlation and relativistic corrections

The PECs of a 3 Π, a ′ 3 Σ + , d 3 Δ, e 3 Σ − and A 1 Π of CS molecule have been studied using the CASSCF method followed by the MRCI approach with large correlation-consistent basis sets of Dunning and co-workers. Effects on the PECs by the core–valence correlation and relativistic corrections have been taken into account at the level of cc-pV5Z basis set. The way to consider the relativistic corrections is to use the second-order Douglas–Kroll Hamiltonian approximation. Using the CCSD(T), MRCI and MRCI with the Davidson modification, the PECs of electronic states involved are extrapolated to the CBS limit. With these PECs, the spectroscopic parameters and molecular constants of the electronic states involved are determined, which are in excellent agreement with the experimental data. Comparison with the measurements shows that the two-point total-energy extrapolation scheme can obviously improve the quality of spectroscopic parameters and molecular constants. ► Effect on the PECs by the core–valence correlation and relativistic corrections is considered. ► The PECs obtained by the CCSD(T), MRCI and MRCI + Q are extrapolated to the CBS limit. ► The energy extrapolation scheme obviously improves the quality of spectroscopic parameters. ► The spectroscopic parameters and molecular constants obtained achieve much high accuracy. The potential energy curves (PECs) of six low-lying electronic states (X 1 Σ + , a 3 Π, a ′ 3 Σ + , d 3 Δ, e 3 Σ − and A 1 Π) of CS molecule have been investigated using the full valence complete active space self-consistent field (CASSCF) method followed by the highly accurate valence internally contracted multireference configuration interaction (MRCI) approach with large correlation-consistent basis sets. Effects on the PECs by the core–valence correlation and relativistic corrections have been taken into account. And the two corrections are performed at the level of cc-pV5Z basis set. The way to consider the relativistic corrections is to use the second-order Douglas–Kroll Hamiltonian approximation. Using the CCSD(T), MRCI and MRCI with the Davidson modification (MRCI + Q), the PECs of electronic states involved are extrapolated to the complete basis set (CBS) limit. With the PECs, the spectroscopic parameters ( T e , R e , ω e , ω e x e , ω e y e , α e , β e , γ e and B e ) of the six low-lying electronic states are determined. These parameters are in excellent agreement with the experimental data. The complete vibrational states are computed for the six low-lying electronic states when the rotational quantum number J equals zero, and the inertial rotation constants of the first 23 vibrational states are reported, which agree favorably with the RKR data. Comparison with the measurements shows that the two-point total-energy extrapolation scheme can obviously improve the quality of spectroscopic parameters and molecular constants.

The study of actinide chemistry with multiconfigurational quantum chemical methods

AbstractThe major contributions of Björn Roos to actinide chemistry, both in terms of quantum chemical method development and applications, will be reviewed. The extension of the complete active space SCF method followed by second order perturbation theory (CASSCF/CASPT2) method to a relativistic regime will be discussed, together with some of the most significant applications, like the study of U2 and UO2. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem 111:3302–3306, 2011

Prediction of electronic structure of organic radicaloid anions using efficient, economical multireference gradient approach

The improved virtual orbital-complete active space configuration interaction (IVO-CASCI) method enables an economical and reasonably accurate treatment of static correlation in systems with significant multireference character, even when using a moderate basis set. This IVO-CASCI method supplants the computationally more demanding complete active space self-consistent field (CASSCF) method by producing comparable accuracy with diminished computational effort because the IVO-CASCI approach does not require additional iterations beyond an initial SCF calculation, nor does it encounter convergence difficulties or multiple solutions that may be found in CASSCF calculations. Our IVO-CASCI analytical gradient approach is applied to compute the equilibrium geometry for the ground and lowest excited state(s) of the theoretically very challenging 2,6-pyridyne, 1,2,3-tridehydrobenzene and 1,3,5-tridehydrobenzene anionic systems for which experiments are lacking, accurate quantum calculations are almost completely absent, and commonly used calculations based on single reference configurations fail to provide reasonable results. Hence, the computational complexity provides an excellent test for the efficacy of multireference methods. The present work clearly illustrates that the IVO-CASCI analytical gradient method provides a good description of the complicated electronic quasi-degeneracies during the geometry optimization process for the radicaloid anions. The IVO-CASCI treatment produces almost identical geometries as the CASSCF calculations (performed for this study) at a fraction of the computational labor. Adiabatic energy gaps to low lying excited states likewise emerge from the IVO-CASCI and CASSCF methods as very similar. We also provide harmonic vibrational frequencies to demonstrate the stability of the computed geometries.

Systematic Theoretical Study of the Zero-Field Splitting in Coordination Complexes of Mn(III). Density Functional Theory versus Multireference Wave Function Approaches

This paper presents a detailed evaluation of the performance of density functional theory (DFT) as well as complete active space self-consistent field (CASSCF)-based methods (CASSCF and second-order N-electron valence state perturbation theory, NEVPT2) to predict the zero-field splitting (zfs) parameters for a series of coordination complexes containing the Mn(III) ion. The physical origin of the experimentally determined zfs's was investigated by studying the different contributions to these parameters. To this end, a series of mononuclear Mn(III) complexes was chosen for which the structures have been resolved by X-ray diffraction and the zfs parameters have been accurately determined by high-field EPR spectroscopy. In a second step, small models have been constructed to allow for a systematic assessment of the factors that dominate the variations in the observed zfs parameters and to establish magnetostructural correlations. Among the tested functionals, the best predictions have been obtained with B3LYP, followed by the nonhybrid BP86 functional, which in turn is more successful than the meta-hybrid GGA functional TPSSh. For the estimation of the spin-orbit coupling (SOC) part of the zfs, it was found that the coupled perturbed SOC approach CP is more successful than the Pederson-Khanna method. Concerning the spin-spin interaction (SS), the restricted open-shell Kohn-Sham (ROKS) approach led to a slightly better agreement with the experiment than the unrestricted KS (UKS) approach. The ab initio state-averaged CASSCF (SA-CASSCF) method with a minimal active space and the most recent implementation that treats the SOC and SS contributions on an equal footing provides the best predictions for the zfs. The analysis demonstrates that the major contribution to the axial zfs parameter (D) originates from the SOC interaction but that the SS part is far from being negligible (between 10 and 20% of D). Importantly, the various excited triplet ligand field states account for roughly half of the value of D, contrary to popular ligand field models. Despite covering dynamic correlation contributions to the transition energies, NEVPT2 does not lead to large improvements in the results as the excitation energies of the Mn(III) d-d transitions are already fairly accurate at the SA-CASSCF level. For a given type of coordination sphere (e.g., elongated or compressed octahedron), the magnetic anisotropy of the Mn(III) ion, D, does not appear to be highly sensitive to the nature of the ligands, while the E/D ratio is notably affected by all octahedral distortions. Furthermore, the introduction of different halides into the coordination sphere of Mn(III) only leads to small effects on D. Nevertheless, it appears that oxygen-based ligands afford larger D values than nitrogen-based ligands.

The reaction mechanism of ozone with the NO and NO 2 oxides

Ab initio calculations using Hartree Fock (HF), density functional theory (DFT), complete active space self-consistent field (CASSCF), second order Moller–Plesset perturbation theory (MP2) and coupled cluster with singles and doubles substitutions (CCSD) quantum chemistry models have been made on all of the four reactions in which the mono-nitrogen oxides react with ozone to generate higher oxidation states culminating in N 2O 5. The relative reaction energies were determined and all reactions were found to be exothermic. Potential energy surfaces of the O 3–NO and O 3–NO 2 reactions were modeled using the HF, MP2, DFT and CASSCF methods and the presence of a transition state was indicated in the HF, MP2 and CASSCF calculations but not in the DFT models. The MP2 level of theory was further applied with three different basis function sets and finer potential energy scan resolution and the activation energies, E a, determined. For the O 3–NO reaction there was reasonably good correlation with the experimental Arrhenius activation energy of 1.2 kcal/mol. However, for the O 3–NO 2 reaction the calculated activation energy was a factor of 4 higher than the experimental Arrhenius activation energy of 2.2 kcal/mol.

Spin–orbit ab initio investigation of the UV photoinduced bond cleavage in iodotrimethylstannane

The photoinduced homolytic cleavage of the Sn–I bond in iodotrimethylstannane (CH3)3SnI, observed after UV irradiation, is investigated by means of spin–orbit ab initio calculations based on CASSCF (complete active space self-consistent field) and MS-CASPT2 (multi-state complete active space 2nd order perturbation theory) methods. The absorption electronic spectrum is characterized by ten low-lying 1,3A′ and 1,3A″ spin eigenstates corresponding to py(I),px(I) → σ*SnI; σSnI → σ*SnI and py(Sn), px(Sn) → σ*SnI, where σSnI and σ*SnI are the bonding and anti-bonding orbitals of the Sn–I bond along the pz axis. From the 1A′ electronic ground state and these ten spin eigenstates, 21 spin–orbit states are generated leading to various deactivation channels of (CH3)3SnI, corresponding to the formation of radicals (CH3)3Sn• and •I and to the ionic species (CH3)3Sn+ and I–. Irradiation into the upper band at 175 nm should lead to the heterolytic cleavage of the Sn–I bond to form the ionic primary products exclusively, whereas absorption into the shoulder at 250 nm induces the homolytic breaking with formation of the radical products.

The complete active space SCF method in a fock-matrix-based super-CI formulation

A simplified super-CI technique is presented, which is used to solve the orbital optimization problem in the Complete Active Space SCF method (CASSCF). All super-CI matrix elements are expressed in terms of an average Fock operator, where the major parts can be obtained directly from the AO integrals. Only a relatively small number of transformed two-electron integrals are needed, thus reducing the transformation bottleneck in MCSCF to an absolute minimum. Since all matrix elements are given in terms of first-and second-order reduced density matrix elements with indices restricted to a small active subspace of the orbital space, the super-CI calculation becomes independent of the length of the CI expansion. This is an important aspect, since the complete active space CI expansion can include many terms. The method is demonstrated in a calculation of potential curves for the three lowest states of the N2 molecules, and some equilibrium properties of the water molecules. The following results were obtained for N2 for the states 1Σ+g, 3Σ+u and 3Πg; De: 9.04 (9.90), 2.71 (3.68), and 3.86 (4.89) eV;re: 1.109 (1.098), 1.309 (1.287), and (1.213) A; (experimental values in parenthesis). For H2O it was demonstrated that a balanced calculation around the equilibrium geometry must use eight active valence orbitals. The results are re: 0.964 (0.957) A; θe: 104°.8 (1.4°.5); dipole moment: 1.98 (1.86) debye; quadrupole moment: 2.64, −2.51, −0.13 (2.63, −2.50, −0.13) × 10−26 esu cm2.

Multireference determinant CI calculations and CASSCF calculations on the CH3-NO2 decomposition pathway of nitromethane

The multideterminant character of CH3NO2. at its ground-state equilibrium geometry, involving the ground SCF state plus a doubly excited (π*-like) [2] configuration out-of-plane with respect to the plane of the NO2 group, has been studied by MRD-CI (multireference determinant configuration interaction) and CASSCF (complete active space SCF) methods to elucidate the configurations required for an accurate description of the system along the decomposition pathway of the C-N bond. In the MRD-CI work, the ground and three lowest electronically excited states were investigated at a number of values of r(C-N); at each point about 850,000 configurations were generated by single and double excitations, of which ˜4500 were included explicitly in the larger MRD-CI wave function by selection criteria. Perturbation extrapolation procedures then provided the correction for the omitted configurations, and this was augmented/supplemented by a Davidson-type correction for the higher than double excitations. The CASSCF investigation included seven active orbitals. Both the MRD-CI results and the CASSCF results verified our earlier findings of the two-determinant character of CH3NO2 even in its ground electronic state at equilibrium geometry. Further, both these results indicate that a number of additional determinants become important along the C-N decomposition pathway.

Nature of the Fe−O2 Bonding in Oxy-Myoglobin: Effect of the Protein

The nature of the Fe-O2 bonding in oxy-myoglobin was probed by theoretical calculations: (a) QM/MM (hybrid quantum mechanical/molecular mechanical) calculations using DFT/MM and CASSCF/MM methods and (b) gas-phase calculations using DFT (density functional theory) and CASSCF (complete active space self-consistent field) methods. Within the protein, the O2 is hydrogen bonded by His64 and the complex feels the bulk polarity of the protein. Removal of the protein causes major changes in the complex. Thus, while CASSCF/MM and DFT/MM are similar in terms of state constitution, degree of O2 charge, and nature of the lowest triplet state, the gas-phase CASSCF(g) species is very different. Valence bond (VB) analysis of the CASSCF/MM wave function unequivocally supports the Weiss bonding mechanism. This bonding arises by electron transfer from heme-Fe(II) to O2 and the so formed species coupled then to a singlet state Fe(III)-O2(-) that possesses a dative sigma(Fe-O) bond and a weakly coupled pi(Fe-O2) bond pair. The bonding mechanism in the gas phase is similar, but now the sigma(Fe-O) bond involves higher back-donation from O2(-) to Fe(III), while the constituents of pi(Fe-O2) bond pair have greater delocalization tails. The protein thus strengthens the Fe(III)-O2(-) character of the complex and thereby affects its bonding features and the oxygen binding affinity of Mb. The VB model is generalized, showing how the protein or the axial ligand of the oxyheme complex can determine the nature of its bonding in terms of the blend of the three bonding models: Weiss, Pauling, and McClure-Goddard.

Active-space two-electron reduced-density-matrix method: Complete active-space calculations without diagonalization of the N-electron Hamiltonian

Molecular systems in chemistry often have wave functions with substantial contributions from two-or-more electronic configurations. Because traditional complete-active-space self-consistent-field (CASSCF) methods scale exponentially with the number N of active electrons, their applicability is limited to small active spaces. In this paper we develop an active-space variational two-electron reduced-density-matrix (2-RDM) method in which the expensive diagonalization is replaced by a variational 2-RDM calculation where the 2-RDM is constrained by approximate N-representability conditions. Optimization of the constrained 2-RDM is accomplished by large-scale semidefinite programming [Mazziotti, Phys. Rev. Lett. 93, 213001 (2004)]. Because the computational cost of the active-space 2-RDM method scales polynomially as r(a)(6) where r(a) is the number of active orbitals, the method can be applied to treat active spaces that are too large for conventional CASSCF. The active-space 2-RDM method performs two steps: (i) variational calculation of the 2-RDM in the active space and (ii) optimization of the active orbitals by Jacobi rotations. For large basis sets this two-step 2-RDM method is more efficient than the one-step, low-rank variational 2-RDM method [Gidofalvi and Mazziotti, J. Chem. Phys. 127, 244105 (2007)]. Applications are made to HF, H(2)O, and N(2) as well as n-acene chains for n=2-8. When n>4, the acenes cannot be treated by conventional CASSCF methods; for example, when n=8, CASSCF requires optimization over approximately 1.47x10(17) configuration state functions. The natural occupation numbers of the n-acenes show the emergence of bi- and polyradical character with increasing chain length.

Ab Initio and Coupled-Perturbed Density Functional Theory Estimation of Zero-Field Splittings in MnII Transition Metal Complexes

The paper presents a method comparison for the prediction of zero-field splitting (ZFS) parameters in a series of Mn (II) coordination complexes. The test set consists of Mn (II) complexes that are experimentally well-characterized by X-ray diffraction and high-field electron paramagnetic resonance. Their ZFS parameters have been calculated using density functional theory (DFT) as well as complete active space self-consistent field (CASSCF) methods. It is shown that the recently introduced coupled-perturbed spin-orbit coupling (CP-SOC) approach [ Neese, F. J. Chem. Phys. 2007, 127, 164112 ] together with hybrid-DFT functionals leads to a slope of the correlation line (plot of experimental vs calculated D values) that is essentially unity provided that the direct spin-spin interaction is properly included in the treatment. This is different from our previous DFT study on the same series of complexes where a severe overestimation of the D parameter has been found [ Zein, S. ; Duboc, C. ; Lubitz, W. ; Neese, F. Inorg. Chem. 2008, 47, 134 ]. CASSCF methods have been used to evaluate the ZFS in an "ab initio ligand-field" type treatment. The study demonstrates that a substantial part of the relevant physics is lost in such a treatment since only excitations within the manganese d-manifold are accounted for. Thus, a severe underestimation of the D parameter has been found. Because the CASSCF calculations in combination with quasidegenerate perturbation theory treats the SOC to all orders, we have nevertheless verified that second-order perturbation theory is an adequate approximation in the case of the high-spin d (5) configuration.

Low-lying quartet electronic states of nitrogen dioxide

The environmentally active molecule nitrogen dioxide (NO2) has been systematically studied using high level theoretical methods. The electronic ground state and the low-lying quartet states of NO2 have been investigated. Single reference restricted open-shell self-consistent field (SCF), complete active space SCF (CASSCF), spin-restricted (R) and spin-unrestricted (U) configuration interaction with single and double excitations (CISD), coupled cluster with single and double excitations (CCSD), CCSD with perturbative triple excitations [CCSD(T)], and internally contracted multireference configuration interaction (ICMRCI) methods along with Dunning's correlation consistent polarized valence cc-pVXZ and augmented cc-pVXZ (where X=T,Q,5) basis sets were used in this research. At the aug-cc-pV5Z/UCCSD(T) level the classical adiabatic excitation energies (Te values) of the three lowest-lying quartet excited states were predicted to be 83.3 kcalmol (3.61 eV, 29 200 cm(-1)) for the ã 4A2 state, 93.3 kcalmol (4.05 eV, 32 600 cm(-1)) for the b 4B2 state, and 100.8 kcalmol (4.37 eV, 35 300 cm(-1)) for the c 4A1 state. The quantum mechanical excitation energies (T 0 values) were determined to be 81.6 kcalmol (3.54 eV, 28 500 cm(-1)) for the a 4A2 state and 90.7 kcalmol (3.93 eV, 31 700 cm(-1)) for the b 4B2 state. The lowest quartet linear Renner-Teller 4Pi state gives rise to the a 4A2 state with 112.8 degrees and the b 4B2 state with 124.4 degrees <(ONO) bond angles upon bending. The b state shows some peculiar behavior. Although CASSCF, RCISD, UCISD, RCCSD, UCCSD, and RCCSD(T) methods predicted the presence of a Cs equilibrium geometry (a double minimum 4A' state), SCF, UCCSD(T), and ICMRCI wave functions predicted the C2v structure for the b 4B2 state. The importance of both dynamical and nondynamical correlation treatments for the energy difference between C2v and Cs structures of b state is highlighted in this context. The c 4A1 state is predicted to have a very small bond angle of 85.8 degrees . Potential energy diagrams with respect to the bond angles of the ground state and four quartet states are presented.

Computational Investigation of the Conrotatory and Disrotatory Isomerization Channels of Bicyclo[1.1.0]butane to Buta-1,3-diene: A Completely Renormalized Coupled-Cluster Study

The conrotatory and disrotatory mechanisms of the isomerization of bicyclo[1.1.0]butane to trans-buta-1,3-diene have been computationally investigated with the CASSCF, MCQDPT2, (U)B3LYP, CCSD(T), CR-CCSD(T), and CR-CC(2,3) approaches. The coupled-cluster (CC) methods, including the CC approach with singles, doubles, and noniterative triples (CCSD(T)), and its completely renormalized (CR) extensions called CR-CCSD(T) and CR-CC(2,3), and the density functional theory B3LYP approach do an excellent job of correctly predicting the activation barrier for the conrotatory pathway, which corresponds to a weakly biradical transition state (TS), producing values within experimental error bars. In particular, the recently developed CR-CC(2,3) method gives 40.8 or 41.1 kcal/mol, in perfect agreement with the experimental value of 40.6 +/- 2.5 kcal/mol. The complete-active-space self-consistent-field (CASSCF) approach and the second-order multireference perturbation theory (MCQDPT2) are less accurate in describing the conrotatory barrier than CR-CC(2,3). The higher energy disrotatory pathway, which has not been characterized experimentally and which involves a strongly biradical TS, poses a great challenge for many methods. CCSD(T) fails, predicting the activation barrier for the disrotatory pathway significantly below the conrotatory barrier, contradicting the experimental result that the conrotatory pathway describes the mechanism. The strongly biradical character of the disrotatory TS, spin contamination, and the proximity of singlet and triplet potential energy surfaces cause difficulties for B3LYP, which does not link this TS with gauche-buta-1,3-diene. No such difficulties occur in the CASSCF calculations, which offer a proper description of the structure of the disrotatory TS that links it with the reactant and product molecules. The CR-CC(2,3) approach, which accurately balances dynamical and nondynamical correlations in systems containing closed-shell and biradical structures, predicts the activation enthalpy for the disrotatory mechanism of approximately 66 kcal/mol. CR-CCSD(T) gives approximately 69 kcal/mol. In agreement with experiment and earlier multireference configuration interaction calculations of Nguyen and Gordon, CR-CCSD(T) and CR-CC(2,3) favor the conrotatory mechanism. The CASSCF, MCQDPT2, and B3LYP methods correctly place the disrotatory barrier above the conrotatory one, but, on the basis of a comparison with the accurate CR-CC(2,3) results, they underestimate the activation energy for the disrotatory pathway. All CC approaches employed in this study produce very good estimates of the enthalpy of isomerization of bicyclo[1.1.0]butane into buta-1,3-diene, the experimental value of which is -25.9 +/- 0.4 kcal/mol, giving about -28 kcal/mol, when trans-buta-1,3-diene is used as a product, and -25 kcal/mol, when the nearly isoenergetic gauche-buta-1,3-diene rotamer is used as a product. The CC reaction enthalpies are more accurate than those obtained with CASSCF, MCQDPT2, and B3LYP.

Conical Intersections in Thymine

The mechanisms which are responsible for the radiationless deactivation of the npi* and pipi* excited singlet states of thymine have been investigated with multireference ab initio methods (the complete-active-space self-consistent-field (CASSCF) method and second-order perturbation theory with respect to the CASSCF reference (CASPT2)) as well as with the CC2 (approximated singles and doubles coupled-cluster) method. The vertical excitation energies, the equilibrium geometries of the 1npi*and 1pipi* states, as well as their adiabatic excitation energies have been determined. Three conical intersections of the S1 and S0 energy surfaces have been located. The energy profiles of the excited states and the ground state have been calculated with the CASSCF method along straight-line reaction paths leading from the ground-state equilibrium geometry to the conical intersections. All three conical intersections are characterized by strongly out-of-plane distorted geometries. The lowest-energy conical intersection (CI1) arises from a crossing of the lowest 1pipi* state with the electronic ground state. It is found to be accessible in a barrierless manner from the minimum of the 1pipi* state, providing a direct and fast pathway for the quenching of the population of the lowest optically allowed excited states of thymine. This result explains the complete diffuseness of the absorption spectrum of thymine in supersonic jets. The lowest vibronic levels of the optically nearly dark 1npi* state are predicted to lie below CI1, explaining the experimental observation of a long-lived population of dark excited states in gas-phase thymine.

Theoretical Studies on the Low-Lying Electronic States of the HSO Neutral Radical and Its Cation

Using the complete active space self-consistent field (CASSCF) method with large atomic natural orbital (ANO-L) basis set, four electronic states of the HSO neutral radical are optimized. The vertical transitions of the HSO neutral radical are investigated by using the same method under the basis set of ANO-L functions augmented with a series of adapted 1s1p1d Rydberg functions, through which eight valence states and eight Rydberg states are probed. Ionic states of the HSO neutral radical are extensively studied in both cases of the adiabatic and vertical ionization, from which the relatively complete understanding of ionization energies is given. To include further correlation effects, the second-order perturbation method (CASPT2) is implemented, and the comparison between CASSCF and CASPT2 methods is performed.