Complete Active Space Self-consistent Field Level Research Articles

QTAIM Study on the Degenerate Cope Rearrangements of 1,5-Hexadiene and Semibullvalene

Using the homotropylium cation (1) as an archetypal example of a homoaromatic molecule, we carried out a quantum theory of atoms-in-molecules (QTAIM) computational study--at DFT (density functional theory), CCSD (coupled cluster with singles and doubles), and CASSCF (complete active space self-consistent field) levels--on 1 and the degenerate Cope rearrangements of 1,5-hexadiene (2) and semibullvalene (3) including the evaluation of delocalization indexes and a visualization of atomic basins. This study yielded new insights into the factors determining the reaction barriers and the bonding of the ground and transitions states of 2 and 3. Contrary to conclusions reached in earlier studies, we found that the transition state for the degenerate rearrangement of 2 is not aromatic and that the driving force for the very facile Cope rearrangement of semibullvalene is caused by the stabilization of individual atoms as well as electronic delocalization, not by the release of strain in the three-membered ring.

Accurate ab initio density fitting for multiconfigurational self-consistent field methods

Using Cholesky decomposition and density fitting to approximate the electron repulsion integrals, an implementation of the complete active space self-consistent field (CASSCF) method suitable for large-scale applications is presented. Sample calculations on benzene, diaquo-tetra-mu-acetato-dicopper(II), and diuraniumendofullerene demonstrate that the Cholesky and density fitting approximations allow larger basis sets and larger systems to be treated at the CASSCF level of theory with controllable accuracy. While strict error control is an inherent property of the Cholesky approximation, errors arising from the density fitting approach are managed by using a recently proposed class of auxiliary basis sets constructed from Cholesky decomposition of the atomic electron repulsion integrals.

Theoretical study of low-lying electronic states of Mn 2 using a newly developed relativistic model core potential

We investigated the electronic structure of low-lying electronic states of Mn 2 using a newly developed relativistic model core potential (spdsMCP). Calculations were performed at complete active space self-consistent field (CASSCF) and second-order multiconfiguration quasidegenerate perturbation theory (MCQDPT2) levels. The MCQDPT2 calculations reveal that the 1Σg + state is the ground state. Calculated spectroscopic constants are very similar to the results of recent all-electron calculations and experimental values, indicating that the spdsMCP works well for Mn 2, which requires a highly correlated calculation. The wave functions of low-lying states are also analyzed at the CASSCF level.

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.

Excited electronic state decomposition of furazan based energetic materials: 3,3′-diamino-4,4′-azoxyfurazan and its model systems, diaminofurazan and furazan

We report the first experimental and theoretical study of gas phase excited electronic state decomposition of a furazan based, high nitrogen content energetic material, 3,3'-diamino-4,4'-azoxyfurazan (DAAF), and its model systems, diaminofurazan (DAF) and furazan (C2H2N2O). DAAF has received major attention as an insensitive high energy explosive; however, the mechanism and dynamics of the decomposition of this material are not clear yet. In order to understand the initial decomposition mechanism of DAAF and those of its model systems, nanosecond energy resolved and femtosecond time resolved spectroscopies and complete active space self-consistent field (CASSCF) calculations have been employed to investigate the excited electronic state decomposition of these materials. The NO molecule is observed as an initial decomposition product from DAAF and its model systems at three UV excitation wavelengths (226, 236, and 248 nm) with a pulse duration of 8 ns. Energies of the three excitation wavelengths coincide with the (0-0), (0-1), and (0-2) vibronic bands of the NO A 2Sigma+<--X 2Pi electronic transition, respectively. A unique excitation wavelength independent dissociation channel is observed for DAAF, which generates the NO product with a rotationally cold (20 K) and a vibrationally hot (1265 K) distribution. On the contrary, excitation wavelength dependent dissociation channels are observed for the model systems, which generate the NO product with both rotationally cold and hot distributions depending on the excitation wavelengths. Potential energy surface calculations at the CASSCF level of theory illustrates that two conical intersections between the excited and ground electronic states are involved in two different excitation wavelength dependent dissociation channels for the model systems. Femtosecond pump-probe experiments at 226 nm reveal that the NO molecule is still the main observed decomposition product from the materials of interest and that the formation dynamics of the NO product is faster than 180 fs. Two additional fragments are observed from furazan with mass of 40 amu (C2H2N) and 28 amu (CH2N) employing femtosecond laser ionization. This observation suggests a five-membered heterocyclic furazan ring opening mechanism with rupture of a CN and a NO bond, yielding NO as a major decomposition product. NH2 is not observed as a secondary decomposition product of DAAF and DAF.

Mass Analyzed Threshold Ionization Spectroscopy of o-, m-, and p-Dichlorobenzenes. Influence of the Chlorine Position on Vibrational Spectra and Ionization Energy

For the first time, vibrational spectra of the 35Cl2 and 35Cl37Cl isotopomers of o-, m-, and p-dichlorobenzene cations in the electronic ground state have been measured via S1 intermediate states by mass analyzed threshold ionization (MATI) spectroscopy. Additionally, ab initio calculations at DFT (density functional theory), CIS (configuration interaction singles), and CASSCF (complete active space self-consistent field) levels of theory have been conducted to compare experimental findings with theory. From the MATI spectra, adiabatic ionization energies of the ortho, meta, and para isomers have been determined to be the same for each pair of investigated isotopomers to 73,237 +/- 6, 72,191 +/- 6, and 73,776 +/- 6 cm(-1), respectively. Several vibrational modes, including fundamentals, combinations, and progressions have been assigned by comparing the experimental and theoretical results. The appearance of overtone progressions involving the 7a mode could be explained by a geometry change of all three isomers during ionization in the direction of this mode by retraining the symmetry of the molecules. Although the general spectral features of the investigated isotopomers are similar, frequencies of some vibrations are slightly different up to a few wavenumbers depending on the involvement of the chlorine atoms in the molecular motion.

Dissociation of ground and nσ* states of CF3Cl using multireference configuration interaction with singles and doubles and with multireference average quadratic coupled cluster extensivity corrections

Extended complete active space self-consistent field (CASSCF), multireference configuration interaction with singles and doubles (MR-CISD), and multireference average quadratic coupled cluster (MR-AQCC) calculations have been performed on the ground (S(0)) and first excited (nsigma(*),S(1)) states of the CF(3)Cl molecule. Full geometry optimizations have been carried out for S(0) as well as "relaxed" potential energy calculations for both states, along the C-Cl bond distance. Vertical excitation energies (DeltaE(vertical)), dissociation energies (DeltaE(diss)), dissociation enthalpies (DeltaH(diss)), and the oscillator strength (f) have also been computed. Basis set effects, basis set superposition error (BSSE), and spin-orbit and size-extensivity corrections have also been considered. The general agreement between theoretical and available experimental results is very good. The best results for the equilibrium geometrical parameters of S(0) (at MR-AQCCaug-cc-pVTZ+d level) are 1.762 and 1.323 A, for the C-Cl and C-F bond distances, respectively, while the corresponding experimental values are 1.751 and 1.328 A. The [angle](ClCF) and [angle](FCF) bond angles are in excellent agreement with the corresponding experimental values (110.3 degrees and 108.6 degrees ). The best calculated values for DeltaE(vertical), DeltaH(diss), and f are 7.63 eV [at the MR-AQCCaug-cc-pV(T+d)Z level], 3.59 eV[MR-AQCCaug-cc-pV(T+d)Z level+spin-orbit and BSSE corrections], and 2.74x10(-3) (MR-CISD/cc-pVTZ), in comparison with the corresponding experimental values of 7.7+/-0.1 eV, 3.68 eV, and 3.12 x 10(-3)+/-2.50 x 10(-4). The results concerning the potential energy curves for S(0) and S(1) show a tendency toward the nonoccurrence of crossing between these two states (in the intermediate region along the C-Cl coordinate), as the basis set size increases. Such tendency is accompanied by a decreasing well depth for the S(1) state. Dynamic electronic correlation (especially at the MR-AQCC level) is also an important factor toward an absence of crossing along the C-Cl coordinate. Further investigations of a possible crossing using gradient driven techniques (at CASSCF and MR-CISD levels) seem to confirm its absence.

Theoretical Study of the Energetics of the Reactions of Triplet Dioxygen with Hydroquinone, Semiquinone, and Their Protonated Forms: Relation to the Mechanism of Superoxide Generation in the Respiratory Chain

One-electron reduction of the dioxygen molecule by the reduced form of mitochondrial ubiquinones (Q) of the NADH dehydrogenase (complex I) and mitochondrial cytochrome bc1 (complex III) is believed to be the main source of the superoxide anion radical O2*- and the hydroperoxide radical OOH*. In this work, we modeled the energetics of four possible reactions of the triplet ((3)Sigma(g)) dioxygen-molecule reduction by fully reduced and protonated ubiquinone (QH2; reaction 1), its deprotonated form (QH-; reaction 2), the semiquinone radical (QH*; reaction 3), and the semiquinone anion radical (Q*-; reaction 4), by means of ab initio calculations with the 6-31G(d) and 6-31+G(d) basis set in the restricted open-shell Hartree-Fock (ROHF), unrestricted Hartree-Fock (UHF), and complete active space self-consistent field (CASSCF) with dynamic correlation [at the second-order Møller-Plesset (MP2) or multiple reference Møller-Plesset (MRMP), respectively] schemes and the basis set superposition error (BSSE) correction included, as well as semiempirical AM1 and PM3 calculations in the UHF and ROHF schemes. 2-Butene-1,4-dione and p-benzoquinone were selected as model compounds. For the reduced forms of both compounds, reaction 1 turned out to be energetically unfavorable at all levels of theory, this agreeing with the experimentally observed diminished reductive properties of hydroquinone derivatives at low pH. For 2-butene-1,4-dione treated at the most advanced MRMP/CASSCF/6-31+G(d) level, the energies of reactions 1-4 are 4.7, -34.3, -15.0, and -4.1 kcal/mol, respectively. This finding suggests that reactions 2 and 3 are the most likely mechanisms of electron transfer to molecular oxygen in aprotic environments and that proton transfer is involved in this process. Nearly the same energies of reactions 2 and 3 were calculated at the MRMP/CASSCF/6-31+G(d) level for reduced forms of p-benzoquinone. Inclusion of diffuse functions in the basis set and dynamic correlation at the CASSCF level appears essential. Because deprotonated ubiquinol is unlikely to exist in physiological environments, reaction 3 appears to be the most likely mechanism of one-electron reduction of oxygen; however, if oxygen can penetrate cytochrome bc1 as far as the Q(o) center where ubiquinol can be deprotonated, reaction 2 can also come into play. The energies of reactions 2 and 3 calculated at the MRMP/CASSCF/6-31+G(d) level are most closely reproduced in the ab initio and semiempirical UHF PM3 calculations. Additional semiempirical calculations on more realistic models of ubiquinone, 2,3-dimethoxy-6-methyl-p-benzoquinone and 2,3-dimethoxy-5-isoprenyl-6-methyl-p-benzoquinone, gave qualitatively the same relations between the energies of reactions 2 and 3 as those carried out for p-benzoquinone species, thereby suggesting that this method could be used in studying electron-transfer reactions from reduced quinone derivatives to molecular oxygen in more complex systems, such as a model of the Q(o) site of cytochrome bc1, where applying ab initio methods is unfeasible.

A theoretical treatment of the intersystem crossing in the spin–forbidden reaction [formula omitted

The mechanism of the spin–forbidden reaction N ( S 4 ) + CS 2 ( X ∑ g + 1 ) → NS ( X ∏ 2 ) + CS ( X 1 ∑ + ) on both doublet and quartet potential energy surfaces has been investigated at B3LYP, CCSD(T) and CASSCF levels of theory. The minimum energy point (MEX-1) on the doublet–quartet crossing surface is determined using the complete-active-space-self-consistent field (CASSCF) calculations with (3,4), (5,5), (7,6), and (7,7) active spaces with a weighting of 50%/50% to the doublet and quartet states. The minimum energy point (MEX-1) has a Cs structure resembling the intermediate structure 2M-1. The intersystem crossing at the MEX-1 crossing point is taking place, and it is attributed to the stronger spin–orbit coupling (SOC)(50.2–75.5 cm −1) and the barrier (65.01–72.10 kJ/mol) with respect to the ground state reactants N ( S 4 ) + CS 2 ( X ∑ g + 1 ) . This is in close agreement with the experimental observation reporting large rate coefficients.

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.

Computational studies on the ground and excited states of BrOOBr

In this work, theoretical computations for the ground and excited states of BrOOBr have been performed at high-level ab initio molecular orbital theories. The ground-state geometries of BrOOBr in different forms (trans, cis, and twist form) have been optimized at the couple-cluster CCSD(T) level of theory with cc-pVTZ and aug-cc-pVTZ basis sets, which indicates that at CCSD(T)/cc-pVTZ level of theory, the twist form is 4.96 kcal/mol more stable than the trans form and 10.67 kcal/mol more stable than the cis form; at the CCSD(T)/aug-cc-pVTZ basis set the twist form is 4.33 kcal/mol more stable than the trans form and 9.54 kcal/mol more stable than the cis form. The vertical excitation energies and potential-energy curves for the singlet and triplet low-lying excited states of BrOOBr were calculated at both the complete active space self-consistent-field (CASSCF) level of theory and the multireference internally contracted configuration interaction (MRCI) level of theory. The differences of potential-energy curves at CASSCF and MRCI levels of theory are found for the BrOOBr excited states. At CASSCF level of theory, none of the BrOOBr excited states are bound. However, at MRCI level of theory, all the BrOOBr states studied in this work are bound or slightly bound at the Frank-Condon region. In addition, the scalar relativistic effect and the spin-orbital coupling effect on the vertical excitation energies of the electronic states of BrOOBr were estimated.

Theoretical study of the formation and isomerization of Al2H2

The lowest singlet and triplet potential energy surfaces of Al2H2 have been characterized using a full-valence complete active space self-consistent field (CASSCF) wavefunction. The CASSCF geometries of minima on the singlet potential energy surface are compared to those previously reported using density functional theory (DFT) and coupled cluster (CCSD(T)) methods. Energies at the CASSCF geometries are corrected for dynamic correlation effects using multi-reference second-order perturbation theory (MRMP2) and CCSD(T). Relative energies calculated at the MRMP2//CASSCF level are comparable to those evaluated at CCSD(T) optimized geometries. This approach to characterizing stationary points and calculating relative energies is utilized to describe isomerization pathways between minima on the lowest singlet and triplet surfaces and to characterize pathways leading to formation of bound Al2H2 species from various fragments (e.g., AlH, AlH2, Al2, and H2). The results presented here confirm that the global minimum is the singlet dibridged isomer, with other singlet isomers lying slightly higher in energy. Though not previously analysed, most triplet structures were found to be less than 20 kcal mol−1 higher in energy than their singlet counterparts. A purely attractive singlet reaction channel, involving the insertion of H2 directly into the Al–Al bond of an excited Al2 species, was located and found to be exothermic by about 40 kcal mol−1. Based on energy and frequency analyses of the singlet and triplet surfaces, previous conclusions that only the singlet dibridged and monobridged isomers have been observed in matrix isolation experiments are analysed further.

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.

Vibrational spectra and electron–vibration interactions of the naphthalene radical anion — Experimental and theoretical study

Vibrational analysis is carried out for the radical anions of naphthalene-h8 and -d8. Their infrared (IR) spectra are observed in tetrahydrofuran by using a cell designed for IR measurements of unstable species. The vibrational force field and the IR intensities are calculated by the ab initio molecular orbital and density functional methods at various theoretical levels. As found in the cases of the radical cations of many polycyclic aromatic hydrocarbons (PAHs), a few strong IR bands with intensities of the order of 102 km mol–1 are observed in the 1700–900 cm–1 region. These observed spectral features are well reproduced by the calculations at the CASSCF (complete active space self-consistent field) and B3LYP (Becke's three-parameter hybrid method using the Lee–Yang–Parr correlation functional) levels. The calculation at the B3LYP level gives a better fit between the observed and calculated absolute IR intensities. Normal modes and the origin of the strong IR intensities characteristic of the radical anions are discussed in terms of molecular symmetry coordinates and the dipole derivatives based on these coordinates. It is found that the IR intensities of the b2u modes below 2000 cm–1 are dominated by the contribution from one molecular symmetry coordinate, in which the C—C bonds in one ring stretch while those in the other ring shrink. The mechanism that gives rise to the strong IR intensity for this vibration is discussed by examining the changes in the electronic structure induced by this vibration.Key words: vibrational spectra, electron–vibration interaction, naphthalene, radical anion.

The reaction of F with N 3 studied using multiconfiguration wave functions

CASSCF (complete active space self-consistent field) and CASPT2 (multiconfiguration second-order perturbation theory) calculations with the cc-pVTZ and cc-pVQZ basis sets were carried out for exploring the mechanisms of the N 3 + F → NF( 1 Δ ) + N 2 (i) and N 3 + F → NF( 3 Σ − ) + N 2 (ii) reactions. The CASSCF and CASPT2 calculations indicate that channel (i) occurs in the 1 A ′ potential energy surface (PES) and along the reaction path there exists an intermediate [IM ( 1 A ′ )] followed by a transition state and that channel (i) is energetically feasible. The CASSCF calculations indicate that channel (ii) occurs in the 3 A″ PES and it has a single step with a transition state [TS( 3 A″ )], but the CASPT2 single-point calculations imply that TS( 3 A″ ) may not exist. The 1 A ′ and 3 A″ PES crossing was explored by performing conical intersection and spin–orbit coupling calculations at the CASSCF level and the calculations imply that the crossing may not cause predissociation of IM( 1 A ′ ) into the triplet ground state product.

Structure and bonding of the (C6H6)+ 2 radical

To elucidate the relative stability of various structures of the benzene dimer cation radical, (C6H6)+ 2 in its ground and low-lying excited states, ab initio complete active space self-consistent field (CASSCF), multi-reference singly and doubly excited configuration interaction (MRSDCI), and multi-reference coupled pair approximation (MRCPA) calculations were performed. Full optimization was performed at the CASSCF level for various structures of the dimer cation, followed by MRSDCI and MRCPA calculations. It was found that the global minimum of the cation is at a slipped C2h sandwich structure but there are some other sandwich structures with almost the same stability, being within about kcal mol−1. T-shape structures are less stable than the sandwich structures, by more than 5 kcal mol−1 by MRCPA calculations. Low lying electronic excited states in various structures are also discussed.

A theoretical study of the 21Ag ← 11Ag two-photon transition and its vibronic band in trans-stilbene

The two-photon spectrum of the 21Ag ← 11Ag transition in trans-stilbene has been calculated at the complete active space self-consistent field (CASSCF) level of theory. Energies were obtained at the complete active space second-order perturbation (CASPT2) level of theory, while the geometries of both the initial and final states were optimized at the CASSCF level. The energy and the geometry optimizations were performed using an active space of 14 electrons in 14 active π orbitals. The vibrational frequencies of both states and the two-photon transition (TPT) cross-section were calculated with a smaller active space where the two lowest π orbitals were kept inactive. A newly implemented algorithm, in the quantum chemical package Molcas was used to determine the two-photon transition intensity. This method requires only the linear response of the CASSCF wavefunction. Furthermore, the vibronic structure of this TPT was studied. The Franck-Condon factors were obtained by calculating the overlap between the vibrational states involved, which were determined from the force fields of both the initial and final states, at the CASSCF level of theory. The results are in agreement with experiment.

Ab initio study on the photochemical behavior of 4-dimethylamino,4 ′-cyanostilbene

Ab initio complete active space self-consistent field (CASSCF) and the second order perturbation (MRMP2) calculations have been performed to examine the photochemical behavior of 4-dimethylamino,4 ′-cyanostilbene (DCS) in the low-lying excited states. The potential energy curves with respect to four torsional angles at the CASSCF level is possible to give a reasonable interpretation on the experimental findings and the MRMP2 calculation well reproduces the experimental observable such as the excitation energy. The S 1 state in the Franck–Condon region is the internal charge transfer (ICT) state where the electron is partially transferred from the 4-dimethylanilino into the 4-cyanostyryl groups. Only the potential energy curve in S 1 with respect to the torsional motion of the ethylenic double bond has a small barrier to the perpendicularly twisted conformation leading to the cis–trans photoisomerization, though the others becomes energetically much unstable. DCS in S 1 in polar solvent is, on the other hand, stabilized by the torsional motion of the 4-dimethylanilino group.

Theoretical study on the photoisomerization of azobenzene

Ab initio calculations are performed to elucidate the mechanism of the photoisomerization of azobenzene. We obtain the excitation energies of the S1(n→π*), S2(π→π*), and S3(n2→π*2) states by complete active space self-consistent field (CASSCF) and multireference single double configuration interaction (MRSDCI) calculations. Two-dimensional potential surfaces of the ground- and excited states are obtained at the CASSCF level in order to investigate the isomerization pathways. A conical intersection between the ground state and the S1 state is found near the midpoint of the rotation pathway, and causes a radiationless transition. On the other hand, the S2 state has local minima at the cis and trans structures, so that the isomerization proceeds at the S2 surface following the deexcitation.

Theoretical study of spin-orbit coupling constants for O2+ (A 2Π3/2,1/2u, v+=0–17 and a 4Π5/2,3/2,1/2,−1/2u, v+=0–25)

The spin-orbit coupling constants (Av+) for O2+(A 2Πu,v+=0–17) and O2+(a 4Πu,v+=0–25) were computed based on the Pauli–Breit Hamiltonian with one and two electron terms for comparison with experimental measurements. In the present theoretical study, the vibrational wave functions are obtained using the potential energy curve calculated at the multireference configuration interaction (MRCI) level of theory, with single and double excitations from the complete active space self-consistent field (CASSCF) reference wave function. The electronic wave functions and spin-orbit coupling constants are obtained at the CASSCF and restricted MRCI levels. The effect on Av+ for O2+(A 2Πu,v+) and O2+(a 4Πu,v+) due to interactions of the O2+(A 2Πu,v+), O2+(a 4Πu,v+), and O2+(2Σu+) states is examined. The theoretical Av+ predictions for O2+(A 2Πu,v+) are found to be consistent with the experimental finding that O2+(A 2Πu) is an inverted spin-orbit state at low v+ levels and becomes a regular spin-orbit state at higher v+ levels. Good accord between theoretical predictions and experimental results for O2+(A 2Πu,v+=0–12) is observed with discrepancies in the range of 2–10 cm−1. In the case of O2+(a 4Πu,v+), excellent agreement between theoretical ab initio and experimental results is found with a discrepancy of 2–5 cm−1. Our effort to theoretically reproduce experimental fine structure in the Av+ curve for O2+(a 4Πu,v+) based on interstate vibrational interactions has met with limited success.