Analytic evaluation of nonadiabatic coupling terms at the MR-CI level. I. Formalism

An efficient and general method for the analytic computation of the nonandiabatic coupling vector at the multireference configuration interaction (MR-CI) level is presented. This method is based on a previously developed formalism for analytic MR-CI gradients adapted to the use for the computation of nonadiabatic coupling terms. As was the case for the analytic energy gradients, very general, separate choices of invariant orbital subspaces at the multiconfiguration self-consistent field and MR-CI levels are possible, allowing flexible selections of MR-CI wave functions. The computational cost for the calculation of the nonadiabatic coupling vector at the MR-CI level is far below the cost for the energy calculation. In this paper the formalism of the method is presented and in the following paper [Dallos et al., J. Chem. Phys. 120, 7330 (2004)] applications concerning the optimization of minima on the crossing seam are described.     

Extensive ab initio study of the valence and low-lying Rydberg states of BBr including spin-orbit coupling

The electronic states of the BBr molecule, including 12 valence states and 12 low-lying Rydberg states, have been studied at the theoretical level of MR-CISD+Q with all-electron aug-cc-pVQZ basis sets and Douglas-Kroll [Ann. Phys. (N.Y.) 82, 89 (1974)] scalar relativistic correction. The spin-orbit coupling effect in the valence states was calculated by the state interaction approach with the full Breit-Pauli Hamiltonian. This is the first multireference ab initio study of the excited electronic states of BBr. Potential energy curves of all states were plotted with the help of the avoided crossing rule between electronic states of the same symmetry. The structural properties of these states were analyzed. Computational results reproduced most experimental data well. The transition properties of the a (3)Pi(0(+) ), a (3)Pi(1), and A (1)Pi(1) states to the ground state X (1)Sigma(0(+) ) (+) transitions were obtained, including the transition dipole moments, the Franck-Condon factors, and the radiative lifetimes. The evaluated radiative lifetime of the a (3)Pi(0(+) ), and a (3)Pi(1) states are near 1 ms, much longer than that of the A (1)Pi(1) state.     

The photodynamics of ethylene: a surface-hopping study on structural aspects

Simulations of the photodynamics of ethylene were carried out by employing the semiempirical direct trajectory with surface hopping method in order to assess quantitatively the importance of different regions of the S(2)S(1) and S(1)S(0) crossing seams. The results show that during the first 50 fs after a vertical photoexcitation to the pipi(*) state, the nonadiabatic coupling between the S(1) and the S(2) states produces a recurrence pattern of oscillation of the populations in these states. Within the first 100 fs, the S(1) state population spans a limited region of the configuration space between the initial geometries and the twisted-pyramidalized minimum on the crossing seam (MXS). Depending on the way of counting, about 50% of the S(1)-->S(0) transitions occur in the pyramidalized region of the crossing seam, but not necessarily close to the MXS. The remaining 50% occurs in the H-migration and ethylidene regions. Our analysis shows that the ethylidene region becomes more important in later stages of the dynamics when the flux of trajectories that was not effectively converted to the ground state in the pyramidalized region starts to reach this part of the configuration space. The excited-state nonadiabatic dynamics could be employed to generate suitable initial phase space distributions for the hot-ethylene ground-state kinetic studies.     

Striving to understand the photophysics and photochemistry of thiophosgene: a combined CASSCF and MR-CI study

The potential energy surfaces for Cl(2)CS dissociation into ClCS + Cl in the five lowest electronic states have been determined with the combined complete active space self-consistent field (CASSCF) and MR-CI method. The wavelength-dependent photodissociation dynamics of Cl(2)CS have been characterized through computed potential energy surfaces, surface crossing points, and CASSCF molecular dynamics calculations. Irradiation of the Cl(2)CS molecules at 360-450 nm does not provide sufficient internal energy to overcome the barrier on S(1) dissociation, and the S(1)/T(2) intersection region is energetically inaccessible at this wavelength region; therefore, S(1) --> T(1) intersystem crossing is the dominant process, which is the main reason S(1)-S(0) fluorescence breaks off at excess energies of 3484-9284 cm(-1). Also, the S(1) --> T(2) intersystem crossing process can take place via the S(1)-T(2) vibronic interaction in this range of excess energies, which is mainly responsible for the quantum beats observed in the S(1) emission. Both S(2) direct dissociation and S(2) --> S(3) internal conversion are responsible for the abrupt breakoff of S(2)-S(0) fluorescence at higher excess energies. S(2) direct dissociation leads to the formation of the fragments of Cl(X(2)P) + ClCS(A(2)A' ') in excited electronic states, while S(2) --> S(3) internal conversion followed by direct internal conversion to the ground electronic state results in the fragments produced in the ground state.     

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

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

An ab initio study of the excited States, isomerization energy profiles and conical intersections of a chiral cyclohexylidene derivative

The excited valence and Rydberg states of the chiral (4-methylcyclohexylidene) fluoromethane (4MCF) have been investigated using multiconfigurational CASSCF and CASPT2, and coupled-cluster methods (RI-CC2). A 3s Rydberg state is predicted below the valence (1)pipi* state. To gain insight into the photophysics of the cis-trans isomerization of this olefin, potential energy profiles for the valence (10pipi* state along the twisting and pyramidalization reaction coordinates have been computed using variational methods (CASSCF and multireference configuration interaction with singles and doubles (MR-CISD)). Starting from geometries with energies close to degeneracy in the valence and ground-state curves, three minima on the crossing seam that can be correlated with the conical intersections known for fluoroethylene, have been found. On the basis of these features, the photochemistry of 4MCF is discussed.     

Ground and valence excited states of BI: a MR-CISD+Q study

Ab initio calculations on the valence electronic states of the BI molecule have been performed by using the entirely uncontracted all-electronic aug-cc-pVQZ (for the B atom) and Sadlej-pVTZ (for the I atom) basis sets and the internally contracted multireference singles and doubles configuration interaction method with Davidson size-extensively correction and Douglas-Kroll scalar relativistic correction. The potential energy curves of all valence states and the spectroscopic constants of bound states are fitted. It is the first time that the 12 Lambda-S states of BI molecule and all of the 23 Omega states generated from the former are studied in a theoretical way. Calculation results reproduce well most of the experimental data. The effects of the spin-orbit coupling and the avoided crossing rule between Omega states of the same symmetry are analyzed. The transition properties of the A3Pi0+, B3Pi1, and C1Pi1 states to the ground-state transitions are predicted, including the transition dipole moments, the Franck-Condon factors, and the radiative lifetimes. The radiative lifetime of the C1Pi1 state of BI molecule is less than 1 micros, while that of the A3Pi0+ and B3Pi1 states are the order of 1 ms.     

Ab initio study of the VUV-induced multistate photodynamics of formaldehyde

Although formaldehyde, H?CO, has been extensively studied there are still several issues not-well understood, specially regarding its dynamics in the VUV energy range, mainly due to the amount of nonadiabatic effects governing its dynamics. Most of the theoretical work on this molecule has focused on vertical excitation energies of Rydberg and valence states. In contrast to photodissociation processes involving the lowest-lying electronic states below 4.0 eV, there is little known about the photodynamics of the high-lying electronic states of formaldehyde (7-10 eV). One question of particular interest is why the (π, π*) electronic state is invisible experimentally even though it corresponds to a strongly dipole-allowed transition. In this work we present a coupled multisurface 2D photodynamics study of formaldehyde along the CO stretching and the symmetric HCH bending motion, using a quantum time-dependent approach. Potential energy curves along all the vibrational normal modes of formaldehyde have been computed using equation-of-motion coupled cluster including single and double excitations with a quadruply augmented basis set. In the case of the CO stretching coordinate, state-averaged complete active space self-consistent field followed by multireference configuration interaction was used for large values of this coordinate. 2D (for the CO stretching coordinate and the HCH angle) and 3D (including the out-of-plane distortion) potential energy surfaces have been computed for several Rydberg and valence states. Several conical intersections (crossings between potential energy surfaces of the same multiplicity) have been characterized and analyzed and a 2D 5 × 5 diabatic model Hamiltonian has been constructed. Based on this Hamiltonian, electronic absorption spectra, adiabatic and diabatic electronic populations and vibrational densities have been obtained and analyzed. The experimental VUV absorption spectrum in the 7-10 eV energy range is well reproduced, including the vibrational structure and the high irregularity in the regime of strong interaction between the (π, π*) electronic state and neighboring Rydberg states.     

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

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

Rydberg-valence interactions of CO, and spectroscopic evidence characterizing the C' 1Sigma+ valence state

Rotationally cold absorption and two-photon ionization spectra of CO in the 90-100 nm region have been recorded at a resolution of 0.3-1.0 cm(-1). The analyses of up to four isotopomers seek to clarify the observations in regions where the Rydberg levels built on the ground state X (2)Sigma(+) of the ion interact with valence states of (1)Sigma(+) and (1)Pi symmetry. Previous observations of the 3ssigma, B (1)Sigma(+) Rydberg state, reviewed by Tchang-Brillet et al. [J. Chem. Phys. 96, 6735 (1992)], have been extended to energies above its avoided crossing with the repulsive part of the D(') (1)Sigma(+) valence state where resonances of varying intensities and widths have been attributed to the fully coupled 3ssigma or 4ssigma and D(') potentials, and where the B state approaches a second avoided crossing with the C(') (1)Sigma(+) valence state [Cooper and Kirby, J. Chem. Phys. 87, 424 (1987); 90, 4895 (1989); Chem. Phys. Lett. 152, 393 (1988)]. Fragments of a progression of weak and mostly diffuse bands, observed for all four isotopomers, have been assigned to the C(')<--X transition. The least-squares modeling of the 4p and 5p complexes reveals the 3ppi, E (1)Pi Rydberg state to be one of the perturbers, violating the Deltav=0 selection rule for Rydberg-Rydberg interactions on account of its rapid transition with increasing v from Rydberg to valence state. A second (1)Pi perturber, very loosely bound and clearly of valence type, contributes to the confusion in the published literature surrounding the 5p, v=0 complex.     

Ground and valence-excited states of SF: a multireference configuration interaction with single and double excitations+Q study

Ab initio calculations on the ground and valence-excited states of the sulfur monofluoride radical have been performed using entirely uncontracted all-electron augmented correlation consistent polarized valence quintuple zeta basis sets and the internally contracted multireference configuration interaction with single and double excitations method and Davidson correction (+Q). Potential-energy curves of all valence electronic states and the spectroscopic constants of several bound states are fitted. It is the first time that the entire 27-omega states generated from the 12 valence lambda-S states which come from the S(3P(g)) and F(2P(u)) atomic states of SF radical have been studied theoretically. The effects of spin-orbit coupling and the avoided crossing rule between omega states of the same symmetry are analyzed. The calculated results reproduce well the available experimental values and predict the properties of several bound excited states that have never been observed in experiment. The transition properties of the dipole-allowed transitions from bound excited states to the ground state are predicted for the first time, including the transition dipole moments, the Franck-Condon factors, and the radiative lifetimes.     

A comparative multi-reference configuration interaction study of the low-lying states of two thione isomers of thiophenol

Multi-reference configuration interaction, MR-CI (including extensivity corrections, named +Q), calculations were performed on the S₀–S₃ states of cyclohexa-2,4-diene-1-thione (thione 24 ) and cyclohexa-2,5-diene-1-thione (thione 25 ), which are thione isomers of thiophenol. Several types of uncontracted MR-CIS and MR-CISD wavefunctions were employed, comprising MR-CI expansions as large as ~365 × 10⁶ configuration state functions. The nature of the studied excited states was characterized. Vertical excitation energies (ΔE) and oscillator strengths (f) were computed. The most intense transitions (S₀ → S₂ for 24 and S₀ → S₃ for 25 ) did not change with the wavefunction, although a variation as large as ~1 eV was obtained for the S₃ state of 24 , at the highest (MR-CI+Q) level. On the other hand, ΔE changed at most by ~0.56 eV for 25 as the wavefunction changes, at the same level. The S₁ state of both thiones was found to have nπ* character and is in the visible region. For 24 , S₂ and S₃ are ππ* and nπ* states, respectively, while for 25 the reverse order is obtained. S₂ and S₃ are in the range ~3.5 to 5.2 eV, again at the highest level. It is the first time that the excited states of the title molecules are studied. The computed results agree with the experimental onset of photoreactions of thiones 24 and 25 found by Reva et al (Phys. Chem. Chem. Phys., 2015 , 17, 4888).     

Ab initio study of the BiSe and BiTe electronic spectra: what happens with X2-X1 emission in the heavier Bi chalcogenides?

A series of spin-orbit configuration interaction calculations has been carried out for the BiSe and BiTe molecules and analyzed in comparison with data obtained earlier for the isovalent BiO and BiS systems. An avoided crossing caused by the spin-orbit interaction between the X2Pi and A4Pi electronic states is shown to have a decisive effect on the lower-energy spectrum in each case. Irregularities in the X2 3/2 state vibrational manifold occur as a consequence of this nonadiabatic interaction, and the v vibrational number for the onset of these perturbations is found to gradually decrease in going from BiO to BiSe, in agreement with experiment. In BiTe the shape of the X2 potential curve is so altered by the avoided crossing that its minimum becomes shifted to a significantly larger distance than for the X1 state, unlike the case for BiSe or the lighter Bi chalcogenides. This characteristic appears to be the root cause for the fact that the X2 state has not yet been found experimentally in the BiTe spectrum, despite careful searches in the expected energy range. Radiative lifetimes have also been calculated for the low-lying states of both the BiSe and BiTe molecules, and these results are found to be consistent with experimental observations.     

Ab initio n-electron valence state perturbation theory study of the adiabatic transitions in carbonyl molecules: formaldehyde, acetaldehyde, and acetone

The application of the recently developed second-order n-electron valence state perturbation theory (NEVPT2) to small carbonyl molecules (formaldehyde, acetaldehyde, and acetone) is presented. The adiabatic transition energies are computed for the singlet and triplet n-->pi(*), pi-->pi(*), and sigma-->pi(*) states performing a full geometry optimization of the relevant states at the single state CASSCF level and taking into account the zero point energy correction in the harmonic approximation. The agreement with the known experimental values and with previously published high level calculations confirms that NEVPT2 is an efficient tool to be used for the interpretation of molecular electronic spectra. Moreover, different insight into the nature of the excited states has been obtained. Some of the transitions presented here have never been theoretically computed previously [(3)(pi-->pi(*)) and (3)(sigma-->pi(*)) adiabatic transitions in acetaldehyde and acetone] or have been studied only using moderate level (single reference based) ab initio methods (all adiabatic transitions in acetaldehyde). In the present work a consistent disagreement between NEVPT2 and experiment has been found for the (3)(pi-->pi(*)) adiabatic transition in all molecules: this result is attributed to the low intensity of the transition to the first vibrational levels of the excited state. The n-->pi(*) singlet and triplet vertical transition energies are also reported for all the molecules.     

Electronically excited-state properties and predissociation mechanisms of phosphorus monofluoride: a theoretical study including spin-orbit coupling

The 51 Ω states generated from the 22 Λ - S states of phosphors monofluoride have been investigated using the valence internally contracted multireference configuration interaction method with the Davidson correction and the entirely uncontracted aug-cc-pV5Z basis set. The spin-orbit coupling is computed using the state interaction approach with the Breit-Pauli Hamiltonian. Based on the calculated potential energy curves, the spectroscopic constants of the bound and quasibound Λ - S and Ω states are obtained, and very good agreement with experiment is achieved. Several quasibound states caused by avoided crossings are found. Various curve crossings and avoided crossings are revealed, and with the help of our computed spin-orbit coupling matrix elements, the predissociation mechanisms of the a(1)Δ, b(1)Σ(+), e(3)Π, g(1)Π, and (3)(3)Π states are analyzed. The intricate couplings among different electronic states are investigated. We propose that the avoided crossing between the A(3)Π(0 +) and b(1)Σ(0+) (+) states may be responsible for the fact that the A(3)Π ν' ≥ 12 vibrational levels can not be observed in experiment. The transition properties of the A(3)Π - X(3)Σ(-) transition are studied, and our computed Franck-Condon factors and radiative lifetimes match the experimental results very well.     

Photodissociation dynamics of the NO dimer. I. Theoretical overview of the ultraviolet singlet excited states

Molecular orbital theory and calculations are used to describe the ultraviolet singlet excited states of NO dimer. Qualitatively, we derive and catalog the dimer states by correlating them with monomer states, and provide illustrative complete active space self-consistent field calculations. Quantitatively, we provide computational estimates of vertical transition energies and absorption intensities with multireference configuration interaction and equations-of-motion coupled-cluster methods, and examine an important avoided crossing between a Rydberg and a valence state along the intermonomer and intramonomer stretching coordinates. The calculations are challenging, due to the high density of electronic states of various types (valence and Rydberg, excimer and charge transfer) in the 6-8 eV region, and the multiconfigurational nature of the ground state. We have identified a bright charge-transfer (charge-resonance) state as responsible for the broadband seen in UV absorption experiments. We also use our results to facilitate the interpretation of UV photodissociation experiments, including the time-resolved 6 eV photodissociation experiments to be presented in the next two papers of this series.     

Excited states of the water molecule: analysis of the valence and Rydberg character

The excited states of the water molecule have been analyzed by using the extended quantum-chemical multistate CASPT2 method, namely, MS-CASPT2, in conjunction with large one-electron basis sets of atomic natural orbital type. The study includes 13 singlet and triplet excited states, both valence and 3s-, 3p-, and 3d-members of the Rydberg series converging to the lowest ionization potential and the 3s- and 3p-Rydberg members converging to the second low-lying state of the cation, 1 (2)A(1). The research has been focused on the analysis of the valence or Rydberg character of the low-lying states. The computation of the 1 (1)B(1) state of water at different geometries indicates that it has a predominant 3s-Rydberg character at the equilibrium geometry of the molecule but it becomes progressively a valence state described mainly by the one-electron 1b(1)-->4a(1) promotion, as expected from a textbook of general chemistry, upon elongation of the O-H bonds. The described valence-Rydberg mixing is established to be originated by a molecular orbital (MO) Rydbergization process, as suggested earlier by R. S. Mulliken [Acc. Chem. Res. 9, 7 (1976)]. The same phenomenon occurs also for the 1 (1)A(2) state whereas a more complex behavior has been determined for the 2 (1)A(1) state, where both MO Rydbergization and configurational mixing take place. Similar conclusions have been obtained for the triplet states of the molecule.     

Determination of energy minima and saddle points using multireference configuration interaction methods in combination with reduced gradient following: the S(0) surface of H(2)CO and the T(1) and T(2) surfaces of acetylene

The implementation of the reduced gradient following (RGF) method into the COLUMBUS quantum-chemical program system is reported using the newly developed analytic MR-CISD/AQCC gradient feature. By this combination a very useful tool has been developed for general searches of stationary points on ground- and excited-state energy surfaces. This procedure is applied to the S(0) surface of H(2)CO and the T(1) and T(2) surfaces of acetylene. For H(2)CO we investigated three minima (formaldehyde, s-trans, and s-cis hydroxycarbene) and five saddle points. For the T(1) and T(2) states of acetylene the cis- and trans-minima and the planar and nonplanar saddle points were computed.     

The change of the LMM auger spectra in 3d-metals due to oxidation and its correlation with the change of the atomic magnetic moment.

The surfaces of crystalline samples of 3d-metals (Mn, Fe, Co, Ni, and Cu) and their stoichiometric oxides have been studied by Auger spectroscopy. A correlation between the change in the LVV (L-inner level-valence-valence electron transition) Auger intensities and the change of the squares of the corresponding atomic-magnetic moments has been observed. This is because of the complicated nature of the Auger process. That is, the Auger electron emission is a result of the inner atomic level excitation by electron impact and Auger annihilation of the inner-level hole. Therefore, the Auger process has been considered a second-order process, and spin polarization of the valence states has been taken into account for the LMM (L-inner level-M-inner level-M-inner level electron transition) Auger spectra of 3d-metals.