The use of multidimensional Franck-Condon simulations to assess model chemistries: a case study on phenol

Multidimensional Franck-Condon simulations of the dispersed fluorescence spectra of phenol generated with geometries obtained from the highly correlated post-Hartree-Fock methods CASSCF, MRCI, and SACCI are presented. While the simulations based on CASSCF and MRCI optimized geometries are very similar to each other and fail to reproduce the experimentally measured intensities faithfully, the simulations obtained from SACCI optimized geometries are very close to the experimental spectra. The code developed for the multidimensional Franck-Condon simulations is described. It is shown that the integral storage problem common to the evaluation of multidimensional Franck-Condon integrals can be overcome by saving all quantities needed to disk. This strategy allows the code to run on computers with limited resources and is very well suited for application to molecules with a very large number of vibrational modes.     

Franck-Condon simulations of clusters: phenol-nitrogen

Multidimensional Franck-Condon simulations of the resonance enhanced multiphoton ionization (REMPI) and mass-analyzed threshold ionization (MATI) spectra of phenol-nitrogen are obtained from CASSCF, MRCI, and SACCI optimized geometries. In the REMPI simulations, the results are unsatisfactory, as the transitions associated with intermolecular modes are widely underestimated and much less intense than those associated with intramolecular modes. Conversely, the simulations of the MATI spectra show a good similarity to experiment. The best simulations are obtained in both instances from the SACCI optimized geometries. Furthermore, the simulations suggest that the two most prominent Franck-Condon envelopes present in the MATI spectra are due to the sigma and sigma + ngamma' combination bands in accord with the assignments of the MATI spectra of the analogous phenol-carbon monoxide cluster.     

Photoreaction in BLUF receptors: proton-coupled electron transfer in the flavin-Gln-Tyr system

Photoinduced electron transfer from tyrosine to the flavin chromophore is involved in activation of BLUF (sensor of blue light using FAD) photoreceptors. We studied the electron transfer (ET) coupled with proton-transfer (PT) reactions, by means of XMCQDPT2//CASSCF calculations on a molecular cluster model. By defining a minimum active space in the CASSCF calculations, we could compute the entire photoreaction pathway. We find that the crossing of the locally excited and ET states is located along the flavin bond-stretching coordinate. The ET state is stabilized by a proton transfer from the electron donor to the electron acceptor. We mapped two different PT pathways from tyrosine to flavin via the conserved glutamine. These reactions generate a tautomeric form of glutamine. Along the PT coordinates, we find geometries where the ET and the electronic ground states degenerate. At the state crossing structures, either formation of the ground state biradical intermediate or a relaxation back to the Franck-Condon minimum takes places. The computed relaxation pathways reveal that the hydrogen bonds involving glutamine in the chromophore-binding pocket control BLUF photoefficiency.     

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.     

反式和顺式HOOOH的电子光谱的理论研究

用密度泛函方法(DFT)和全活化空间自洽场方法(CASSCF)以及耦合簇理论(CCSD)优化了反式和顺式HOOOH的平衡几何构型, 用DFT计算了HOOOH顺反异构化反应的势能曲线和谐振动频率. 用含时密度泛函理论(TD-DFT)和二阶全活化空间微扰理论(CASPT2)计算了反式和顺式HOOOH垂直激发能. 计算结果表明: (1)反式异构体比顺式异构体稳定; (2)两种稳定构型的异构化反应有两种路径; (3)对于垂直跃迁能最低的单态和叁态, 反式的垂直跃迁能比顺式的低; (4)在单激发态中, CASPT2方法预测的顺式HOOOH寿命最长的激发态为21A′′, 其跃迁能是167.43 nm, 寿命为 1.44×10−5 s; 反式HOOOH寿命最长的激发态为21A, 其跃迁能是165.52 nm, 寿命为 2.07×10−5 s.     

Theoretical characterization of the SiC3H- anion

Highly correlated ab initio methods are used to predict the equilibrium structures and spectroscopic parameters of the SiC(3)H(-) anion. The total energies and physical properties are reported using CASSCF/MRCI, RCCSD(T), and RCCSD(T)-F12 approaches and extended basis sets. The search of stable geometries leads to a total of 12 isomers (4 linear and 8 cyclic), for which electronic ground states have close-shell configurations. The stability of the linear form, l-SiC(3)H(-), is prominent. For the most stable linear isomer, the B(e) equilibrium rotational constant has been calculated with RCCSD(T) and a complete basis set. Core-correlation and vibrational effects have been taken into account to predict a B(0) of 2621.68 MHz for l-SiC(3)H(-) and 2460.48 MHz for l-SiC(3)D(-). The dipole moment of l-SiC(3)H(-) was found to be 2.9707 D with CASSCF/aug-cc-pV5Z and the electron affinity to be 2.7 eV with RCCSD(T)-F12A/aug-cc-pVTZ. Anharmonic spectroscopic parameters are derived from a quadratic, cubic, and quartic RCCSD(T)-F12A force field and second order perturbation theory. CASSCF/MRCI vertical excitations supply three metastable electronic states, (1)Σ(+) (3)Σ(+) and (3)Δ. Electron affinities calculated for a series of chains type SiC(n)H and SiC(n) (n=1-5) allow us to discuss the anion formation probabilities.     

Ab initio study of the ground and excited states of HCP and its isomer HPC

The potential energy surface of HCP converting to HPC in its ground electronic state has been investigated with ab initio methods at levels up to MP2/6-311G**//MP4/6-311G** as well as TZV + + ** CASSCF. All geometries are fully optimized and compare favorably to previous theoretical and experimental values. The HCP molecule is predicted to be 85.4 kcal/mol lower in energy than its linear isomer at the-MP2/6-31G*//MP2/6-31G* level. The energy barrier for hydrogen rearrangement is found to be merely 2.3 kcal from the HPC end. CASSCF studies were initiated to clarify the low barrier and lent support to a flat surface as HPC converts to stable, linear HCP at the TZV + + ** level. CASSCF also predicts that HPC is unstable with respect to bending. Harmonic vibrational frequencies for HCP results in 5% accuracy or better. A bent triplet is found to be the lowest excited state using the CASSCF method. © 1993 John Wiley & Sons, Inc.     

The electronic structure of oxo-Mn(salen): single-reference and multireference approaches

Using single- and multireference approaches we have examined many of the low-lying electronic states of oxo-Mn(salen), several of which have not been explored previously. Large complete-active-space self-consistent-field (CASSCF) computations have been performed in pursuit of an accurate ordering for the lowest several electronic states. Basis set and relativistic effects have also been considered. For the geometry considered, our best results indicate the ground spin state to be a closed-shell singlet, followed by a pair of low-lying triplet states, with additional singlet states and the lowest quintet state lying significantly higher in energy. Hartree-Fock and density functional theory (DFT) results are obtained and are compared to the more robust CASSCF results. The Hartree-Fock results are qualitatively incorrect for the relative energies of the states considered. Popular density functionals such as BP86 and B3LYP are superior to Hartree-Fock for this problem, but they give inconsistent answers regarding the ordering of the lowest singlet and triplet states and they greatly underestimate the singlet-quintet gap. We obtained multiple Hartree-Fock and DFT solutions within a given spin multiplicity, and these solutions have been subjected to wave function stability analysis.     

Ab initio calculations of triplet excited states and potential-energy surfaces of vinyl chloride: insights into spectroscopy and photodissociation dynamics

The equilibrium geometries and harmonic vibrational frequencies of three low-lying triplet excited states of vinyl chloride have been calculated using the state-averaged complete active space self-consistent field (CASSCF) method with the 6-311++G(d,p) basis set and an active space of four electrons distributed in 13 orbitals. Both adiabatic and vertical excitation energies have been obtained using the state-averaged CASSCF and the multireference configuration-interaction methods. The potential-energy surfaces of six low-lying singlet states have also been calculated. While the 3(pi, pi*) state has a nonplanar equilibrium structure, the 3(pi, 3s) and 3(pi, sigma*) states are planar. The calculated vertical excitation energy of the 3(pi, pi*) state is in agreement with the experiment. The singlet excited states are found to be multiconfigurational, in particular, the first excited state is of (pi, 3s) character at the planar equilibrium structure, of (pi, sigma*) as the C-Cl bond elongates, and of (pi, pi*) for highly twisted geometries. Avoided crossings are observed between the potential-energy surfaces of the first three singlet excited states. The absorption spectra of vinyl chloride at 5.5-6.5 eV can be unambiguously assigned to the transitions from the ground state to the first singlet excited state. The dissociation of Cl atoms following 193-nm excitation is concluded to take place via two pathways: one is through (pi, sigma*) at planar or nearly planar structures leading to fast Cl atoms and the other through (pi, pi*) at twisted geometries from which internal conversion to the ground state and subsequent dissociation produces slow Cl atoms.     

Electronic structure of [(CpCr)[(CO)3M]]mu-Cot (M = Cr, Fe): a theoretical study

The electronic structure of two cyclooctatetraene-bridged dinuclear first-row transition metal complexes of the type [(CpM)[(CO)3M']]mu-Cot (M = Cr; M' = Fe (1), Cr (2)) was investigated by complete active space self-consistent field (CASSCF) calculations. In this context the differences in the binding capabilities of the complex fragments CpM and (CO)3M are discussed on the basis of extended Huckel molecular orbital (MO) calculations. The geometries used for the CASSCF calculations for complex 1 were obtained from the crystal structure. For 2 a model structure was established by geometry optimization using density functional methods. The CASSCF results agree well with the experimental findings and provide insight into the binding situation of the two compounds. Complex 1 can be regarded as being composed of a chromocene-like subunit CpCr(eta5-C5H5) and the fragment (CO)3Fe(eta3-C3H3). A direct metal-metal bond is found, involving one initially singly occupied orbital of each fragment, leading to a doublet ground state for 1 with the remaining unpaired electron localized at the chromium center. For 2 no such direct metal-metal bond can be recognized. A very weak direct metal-metal interaction is induced by electron donation from the Cot2- ligand into a formally unoccupied metal-metal binding orbital combination. In the quartet ground state all three unpaired electrons are localized at the chromium center of the formally doubly positive charged CpCr unit, on which complex fragment [(CO)3Cr(eta5-Cot)]2- acts like a cyclopentadienyl ligand. The coordination sphere of the chromium center of the CpCr unit resembles that of a metallocene metal center and its metal 3d occupation scheme corresponds to that of vanadocene.     

A theoretical study of the lowest-energy singlet and triplet electronic states p-iminophosphaalkyne and nitrilimine

The equilibrium geometries and fundamental vibrational frequencies of the two energetically lowest-lying electronic states of p-iminophosphaalkyne (HCPNH) and nitrilimine (HCNNH) were determined using a split-valence basis set with polarization functions on the heavy atoms. The most extensively correlated functions used in the geometry optimizations were of the Complete Active Space Self-Consistent Field (CASSCF) variety and included eight electrons distributed among seven active orbitals for HCPNH and six active orbitals for HCNNH. The effects on predicted geometry of the size of the CASSCF active space were investigated for HCPNH and are reported. Multi-Reference Configuration Interaction with Single and Double excitations calculations have been performed at the equilibrium geometries using larger basis sets to determine more accurately the relative energetics of the electronic states. It was found that nitrilimine has the expected singlet ground state, with the triplet lying 38.5 kcal mol⁻¹ higher in energy; however, p-iminophosphaalkyne has a triplet ground state, lying 9.7 kcal mol⁻¹ below the singlet.     

On the stability of Be3: a benchmark complete active space self-consistent field + averaged quadratic coupled cluster study

The optimized geometries and binding energies for the linear and triangular isomers of the beryllium trimer have been obtained through benchmark multireference averaged quadratic coupled cluster (AQCC) calculations using very large complete active space SCF (CASSCF) references (12 active electrons in 13 and 14 orbitals). Geometries were optimized with the cc-pV5Z basis, while the binding energies (including counterpoise correction) were obtained with the significantly larger aug-cc-pV5Z basis set. The binding energies (27.3 and 16.3 kcal/mol for the equilateral and linear isomers, respectively) are larger than the previous full CI benchmark values, while the corresponding Be-Be equilibrium distances of 4.101 and 4.088 a.u. are smaller. In view of the near-size consistency character of the CASSCF + AQCC method, the fact that all 12 electrons are fully correlated, the active reference space includes 14 orbitals, and the very large basis set used here, we propose to consider these results as reference data for Be(3). Using the electron pair localization function obtained at the CASSCF(12,15) level, it is clearly illustrated that the 2p orbitals lying in the molecular plane play a dominant role in the bonding pattern for the equilateral isomer.     

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.     

Structure and stability of the [TCNE](2)(2-) dimers in dichloromethane solution: a computational study

The solution behavior of [TCNE](.-), which forms long-living pi-[TCNE]22- dimers, is computationally studied by B3LYP and MCQDPT/CASSCF(2,2) calculations (a multiconfigurational quasi-degenerate perturbative calculation using a CASSCF(2,2) wavefunction, which properly accounts for the dispersion interaction). B3LYP calculations indicate minimum-energy [TCNE](2)(2-)(dichloromethane)(4) aggregates, a solvent where pi-[TCNE](2)(2-) dimers are spectroscopically observed. Their existence is attributed to [TCNE](.-)...solvent interactions that exceed the [TCNE](.-)...[TCNE](.-) repulsion. The lowest energy minimum at the B3LYP level corresponds to an open-shell singlet electronic structure, a metastable minimum where the shortest interanion C...C distance is 5.23 A. A slightly less stable minimum is also found for the closed-shell singlet when double-occupancy of the orbitals is imposed, but it converts into the open-shell singlet minimum when the double occupancy is relaxed. At the MCQDPT/CASSCF(2,2) level, the only minimum is for the closed-shell singlet (24.0 kcal/mol (101 kJ/mol) more stable than the dissociation products), consistent with experimental enthalpy of dimerization of [TCNE](.-) in dichloromethane solutions. It has an interanion C...C distance of 2.75 A and is in accord with the UV-vis experimental properties of the [TCNE](.-) solutions.     

Can large active-space CASSCF calculation make sense to the reaction analysis of iron complex? A benchmark study of methane oxidation reaction by FeO+

A methane oxidation reaction by FeO⁺ cation was theoretically investigated based on the density functional theory (DFT) and the complete active-space self-consistent field (CASSCF) method as well as the coupled-cluster singles, doubles, and perturbative triples (CCSD(T)) to explore the active-space dependency to computational analyses in such strongly correlated reaction systems. A small active-space CASSCF(5e in 5o) calculation, which only includes five 3d orbitals of the Fe atom in the active-space, showed remarkable difference both in energy and geometry compared to those computed by the DFT and CCSD(T) methods. Interestingly, a large active-space CASSCF(17e in 17o) calculation, which includes almost all the valence orbitals gives a qualitative agreement with either the DFT or the CCSD(T) results in the first half part of the reaction, although it varies from them in the latter half part. Therefore, it is indicated that the active-space dependency is serious in some part of the reaction and the small active-space CASSCF might lead a wrong discussion. We further investigated the optimized geometry of the intermediate complex with the small and the large active-space CASSCF methods as well as the CCSD(T) method, and found that the CASSCF(5e in 5o)-optimized geometry is considerably different from the others. In consequence, a small active-space CASSCF/CASPT2 calculation does not really work for such a strongly correlated reaction system even qualitatively, and a sophisticated assessment using the large active-space CASSCF/CASPT2 method will be indispensable. © 2018 Wiley Periodicals, Inc.     

HO2自由基电子激发态的理论研究

采用CASPT2/CASSCF方法对HO2自由基进行统计算, 优化了三个电子态的稳定点几何构型, 得到详细的频率数据. 利用垂直激发计算确定了3个里德堡态、11个价电子态的电子结构以及在三种理论水平上(CASSCF, SS-CASPT2和MS-CASPT2)的能量信息. 计算中使用了ANO-L和ANO-L+基组, 验证了已知实验数据的同时, 通过与其它理论计算结果的对比, 揭示了应用弥散轨道系数对于该体系激发态研究的重要性.     

A Complete Active Space Self‐Consistent Field (CASSCF) Study of the Reaction Mechanism of the α‐Alkynone Rearrangement

The pyrolytic rearrangement of α‐alkynones has been discovered by Karpf and Dreiding [1] in 1979. The mechanism of this reaction, which involves an acetylene‐vinylidene rearrangement followed by cyclization of the intermediate vinylidene carbene by insertion into a β‐C−H bond, has been debated in a couple of theoretical investigations. Restricted Hartree‐Fock (RHF) and single‐point Møller‐Plesset 2 (MP2) calculations at the RHF geometries apparently indicate the carbene cyclization to be the rate‐determining step, contrary to chemical intuition. However, larger‐scale correlated calculations with completely optimized molecular geometries ((8,8) CASSCF/6‐311G**), augmented with a perturbative account for the dynamic correlation contribution to the electronic energy, show vanishing energy barriers to the cyclization step and large activation energies for the acetylene‐vinylidene rearrangement, which is thus confirmed as the rate‐determining step of the title reaction.     

Concerted and stepwise reaction mechanisms for the addition of ozone to acetylene: a computational study

The mechanism of the reaction between acetylene and ozone to form a primary ozonide (POZ) in the gas phase has been studied theoretically. The concerted pathway, HCCH + O3 --> POZ, proceeds via a biradicaloid transition state TS0. The stepwise pathway is a three-step reaction, HCCH + O3 --> M1 --> M2 --> POZ, involving two biradical TSs and two biradical intermediates M1 and M2. The segment of the global potential energy surface (PES) for the concerted pathway is characterized as a R-PES, which is obtained from the restricted (R) density functional theory and Hartree-Fock-based methods. The RDFT and RHF solutions of TS0 and O3 are unstable toward spin-symmetry breaking. The wave function instability for TS0 and O3 results in a discontinuity between the R-PES and the region of the global PES encompassing the biradical TSs and the intermediates of the stepwise pathway, which are characterized with unrestricted (U) methods. The global PES is characterized separately as an U(R)-PES using a combination of the R and U methods. Several different values of barriers for the concerted pathway and the energy of concert (Ec) can be estimated due to complications arising from the discontinuity between the R- and the U(R)-PES and the existence of two different RDFT and UDFT O3 equilibrium geometries. RCCSD(T)//RDFT predicts a barrier of 8.2 kcal/mol. U(R)CCSD(T)/U(R)DFT predicts a barrier of 13.8 kcal/mol for the concerted and 15.3 kcal/mol for the stepwise pathway. Comparison between the R-PES barrier to the concerted pathway and the U(R)-PES barrier to the stepwise pathway suggests the former to be the only significant mechanism. Consideration of the energy difference between TS1, the TS for the first step of the stepwise mechanism, and TS0 within the global PES leads to a significantly smaller Ec. Geometry optimization with CASSCF and energy point calculations with MRMP2 are employed to characterize TS0 and TS1. MRMP2//CASSCF predicts the energy level of TS1 to be higher than that of TS0 by 2 kcal/mol. Analysis of experimental and computational data based on the low estimate of Ec shows that the possibility of the stepwise pathway being a secondary channel at elevated temperatures cannot be ruled out.