Theoretical studies on structures and electronic spectra of linear carbon chains C2nH+ (n = 1−5)

The density functional theory (DFT) and the complete active space self‐consistent‐field (CASSCF) method have been used for full geometry optimization of carbon chains C_2nH⁺ (n = 1–5) in their ground states and selected excited states, respectively. Calculations show that C_2nH⁺ (n = 1–5) have stable linear structures with the ground state of X³Π for C₂H⁺ or X³Σ^? for other species. The excited‐state properties of C_2nH⁺ have been investigated by the multiconfigurational second‐order perturbation theory (CASPT2), and predicted vertical excitation energies show good agreement with the available experimental values. On the basis of our calculations, the unsolved observed bands in previous experiments have been interpreted. CASSCF/CASPT2 calculations also have been used to explore the vertical emission energy of selected low‐lying states in C_2nH⁺ (n = 1–5). Present results indicate that the predicted vertical excitation and emission energies of C_2nH⁺ have similar size dependences, and they gradually decrease as the chain size increases. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Initial excited‐state relaxation of locked retinal protonated schiff base chromophore. An insight from coupled cluster and multireference perturbation theory calculations

The initial S₁ excited‐state relaxation of retinal protonated Schiff base (RPSB) analog with central C11C12 double bond locked by eight‐membered ring (locked‐11.8) was investigated by means of multireference perturbation theory methods (XMCQDPT2, XMS‐CASPT2, MS‐CASPT2) as well as single‐reference coupled‐cluster CC2 method. The analysis of XMCQDPT2‐based geometries reveals rather weak coupling between in‐plane and out‐of‐plane structural evolution and minor energetical relaxation of three locked‐11.8 conformers. Therefore, a strong coupling between bonds length inversion and backbone out‐of‐plane deformation resulting in a very steep S₁ energy profile predicted by CASSCF/CASPT2 calculations is in clear contradiction with the reference XMCQDPT2 results. Even though CC2 method predicts good quality ground‐state structures, the excited‐state structures display more advanced torsional deformation leading to ca. 0.2 eV exaggerated energy relaxation and significantly red shifted (0.4–0.7 eV) emission maxima. According to our findings, the initial photoisomerization process in locked‐11.8, and possibly in other RPSB analogs, studied fully (both geometries and energies) by multireference perturbation theory may be somewhat slower than predicted by CASSCF/CASPT2 or CC2 methods. © 2018 Wiley Periodicals, Inc.     

CASSCF and CASPT2 studies on the structures, transition energies, and dipole moments of ground and excited states for azulene

The electronic structure of azulene molecule has been studied. We have obtained the optimized structures of ground and singlet excited states by using the complete active space self-consistent-field (CASSCF) method, and calculated vertical and 0-0 transition energies between the ground and excited states with second-order M?ller-Plesset perturbation theory (CASPT2). The CASPT2 calculations indicate that the bond-equalized C(2v) structure is more stable than the bond-alternating C(s) structure in the ground state. For a physical understanding of electronic structure change from C(2v) to C(s), we have performed the CASSCF calculations of Duschinsky matrix describing mixing of the b(2) vibrational mode between the ground (1A(1)) and the first excited (1B(2)) states based on the Kekule-crossing model. The CASPT2 0-0 transition energies are in fairly good agreement with experimental results within 0.1-0.3 eV. The CASSCF oscillator strengths between the ground and excited states are calculated and compared with experimental data. Furthermore, we have calculated the CASPT2 dipole moments of ground and excited states, which show good agreement with experimental values.     

Description of excited states in [Re(Imidazole)(CO)3(Phen)]+ including solvent and spin‐orbit coupling effects: Density functional theory versus multiconfigurational wavefunction approach

The low‐lying electronic excited states of [Re(imidazole)(CO)₃(phen)]⁺ (phen = 1,10‐phenanthroline) ranging between 420 nm and 330 nm have been calculated by means of relativistic spin‐orbit time‐dependent density functional theory (TD‐DFT) and wavefunction approaches (state‐average‐CASSCF/CASPT2). A direct comparison between the theoretical absorption spectra obtained with different methods including SOC and solvent corrections for water points to the difficulties at describing on the same footing the bands generated by metal‐to‐ligand charge transfer (MLCT), intraligand (IL) transition, and ligand‐to‐Ligand‐ charge transfer (LLCT). While TD‐DFT and three‐roots‐state‐average CASSCF (10,10) reproduce rather well the lowest broad MLCT band observed in the experimental spectrum between 420 nm and 330 nm, more flexible wavefunctions enlarged either by the number of roots or by the number of active orbitals and electrons destabilize the MLCT states by introducing IL and LLCT character in the lowest part of the absorption spectrum. © 2016 Wiley Periodicals, Inc.     

Theoretical study of structure, vibrational frequencies, and electronic spectra of dibenzofuran and its polychlorinated derivatives

Minimum structures and harmonic vibrational frequencies of dibenzofuran (DF), 2,3,7,8-tetrachlorodibenzofuran (TCDF), and octachlorodibenzofuran (OCDF) were calculated using the multiconfigurational complete active space self-consistent field (CASSCF) and density functional theory (DFT) methods. The electronic transitions in these compounds were studied via the single-state multireference second-order perturbation theory (CASPT2) based on the CASSCF(14,13) references, as well as the time-dependent DFT (TD-B3P86) employing the cc-pVDZ (CASSCF/CASPT2) and 6-31G(d,p) (TD-B3P86) basis sets. The B3P86 geometry and harmonic vibrational frequencies of ground state DF agree very well with the experimental data, and the CASSCF/CASPT2 excitation energies and oscillator strengths are accurate enough to provide a reliable assignment of the absorption bands in the 200-300 nm region. The close agreements with experiment for the parent DF give the present theoretical approaches a valuable credit in predicting the properties of the environmentally toxic polychlorinated congeners, which is all the more important considering the difficulties and hazards in obtaining the experimental data.     

Conical Intersections and Low‐Lying Electronic States of Tetrafluoroethylene

The low‐lying electronic states of tetrafluoroethylene (C₂F₄) are characterized theoretically for the first time using equation‐of‐motion coupled cluster theory (EOM‐CCSD), and complete active space self‐consistent field (CASSCF) and second‐order perturbation theory (CASPT2). Computations are performed for vertical excitation energies, equilibrium geometries, minimum‐energy conical intersections, and potential energy curves along three geometric coordinates: 1) twisting of the F?C?C?F dihedral angle, 2) pyramidalization of the CF₂ group, and 3) migration of a fluorine atom resulting in an ethylidene‐like (CF₃CF) structure. The results suggest two relaxation pathways from the Rydberg‐3s excited electronic state to the ground state. These relaxation pathways are discussed in conjunction with the femtosecond photoionization spectroscopy results of Trushin et al. [ChemPhysChem­ 2004 , 5, 1389].     

Unusual magnetic properties of mixed-valence system: multiconfigurational method theoretical study on Mn2+ cation

The geometry structure, dissociation energy, vibrational frequencies, and low-lying spin-state energy spectrum of Mn2+ are investigated by using ab initio CASSCF/ECP10MDF, complete active space self-consistent field/atomic natural orbital basis sets (CASSCF/ANO-s), CASPT2/ECP10MDF, and second-order perturbation theory with CASSCF reference function/atomic natural orbital basis sets (CASPT2/ANO-s) levels of theory. For the ground state the dissociation energy of 1.397 eV calculated at the CASPT2/ANO-s level supports Jarrlod's experimental value of 1.39 eV. The equilibrium bond length and vibrational frequency are 2.940 A calculated at the CASPT2/ANO-s level of theory and 214.4 cm-1 calculated at the CASSCF/ANO-s level of theory, respectively. On the basis of the mixed-valence model, the Heisenberg exchange constant J(-71.2 cm-1) and the double-exchange constant B(647.7 cm-1) are extracted explicitly from the low-lying energy spectrum calculated at the higher levels of theory. The magnetic competition between the weaker Heisenberg exchange interactions and the stronger double-exchange interactions makes the ground state a 12Sigmag+ state, consistent with electron paramagnetic resonance experimental observation, which explains unusual magnetic properties of Mn2+, quite different from the antiferromagnetic ground state of Mn2 and Cr2. On the other hand, the results calculated at the higher levels of theory show the consistent antiferromagnetic Heisenberg exchange interactions between 3d-3d for Cr2, Mn2+, and Mn2.     

Assessment of semiempirical methods for the photoisomerisation of a protonated Schiff base

The potential energy surfaces and non-adiabatic dynamics of the C₅H₆NH ₂ ⁺ protonated Schiff base (PSB3) have been investigated using the OM2 semiempirical Hamiltonian with GUGA configuration interaction. Three approaches to selecting the GUGA-CI active space are evaluated using closed-shell and open-shell molecular orbitals. Energy minima and minimum energy crossing points (MECPs) have been compared with ab initio CASSCF and CASPT2 results. Only the open-shell calculations give a qualitatively correct MECP. Minimum energy path (MEP) calculations demonstrate that a minimal active space gives a barrierless path from the planar S₁ minimum to the ground state, whereas larger active spaces result in a small barrier to torsional motion. Surface hopping dynamics calculations indicate that this barrier induces bi-exponential dynamics. The comparable CASSCF S₁ energy surface is barrierless, but the CASPT2 surface features an energy plateau, which may also lead to more complex dynamics.     

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

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

A CASSCF/CASPT2 insight into excited‐state intramolecular proton transfer of four imidazole derivatives

Excited‐state intramolecular proton transfer (ESIPT) of four imidazole derivatives, 2‐(2′‐hydroxyphenyl)imidazole (HPI), 2‐(2′‐hydroxyphenyl)benzimidazole (HPBI), 2‐(2′‐hydroxyphenyl)‐1H‐phenanthro[9,10‐d]imidazole (HPPI) and 2‐(2′‐hydroxyphenyl)‐1‐phenyl‐1H‐phenanthro[9,10‐d]imidazole (HPPPI), were studied by the sophisticated CASSCF/CASPT2 methodology. The state‐averaged SA‐CASSCF method was used to optimize their geometry structures of S₀ and S₁ electronic states, and the CASPT2 calculations were used for the calibration of all the single‐point energies, including the absorption and emission spectra. A reasonable agreement is found between the theoretical predictions and the available experimental spectral data. The forward ESIPT barriers of four target compounds gradually decrease with the increase of molecular size. On the basis of the present calculations, it is a plausible speculation that the larger the size, the faster is the ESIPT rate, and eventually, HPPPI molecule can undergo a completely barrierless ESIPT to the more stable S₁ keto form. Additionally, taking HPI as a representative example, the radiationless decays connecting the S₀ and S₁/S₀ conical intersection structures were also studied by constructing a linearly interpolated internal coordinate (LIIC) reaction path. The qualitative analysis shows that the LIIC barrier of HPI in the keto form is remarkably lower than that of its enol‐form, indicating that the former has a big advantage over the latter in the nonradiative process. © 2015 Wiley Periodicals, Inc.     

Assignment on the X,A, B,C, and D states of the C6H5Br+ cation based on high‐level calculations

Geometries, frequencies, and energies of the 1²B₁, 1²A₂, 1²B₂, 2²B₁, 2²B₂, and 1²A₁, of the C₆H₅Br⁺ ion were calculated by using CASSCF and CASPT2 methods in conjunction with an ANO‐RCC basis. The CASPT2//CASSCF adiabatic excitation energies and CASPT2 relative energies for the six states are in good agreement with experiment. The X, A, B, C, and D electronic states of the C₆H₅Br⁺ ion were assigned to be X²B₁, A²A₂, B²B₂, C²B₁, and D²B₂ based on the CASSCF and CASPT2 calculations. The assignment on the D state of the C₆H₅Br⁺ ion is different from the previously published works. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Relativistic effects on inversion barriers of pyramidal group 15 hydrides

Quantum chemistry is an important tool for determining general molecular properties, although relativistic corrections are usually required for systems containing heavy and super heavy elements. Non‐relativistic along with relativistic two‐ and four‐component electronic structure calculations done with the CCSD‐T method and the new RPF‐4Z basis set have therefore been applied for determining inversion barriers, corresponding to the change from a pyramidal (C_3v) ground‐state structure to the trigonal planar (D_3h) transition state, TS, of group 15 hydrides, XH₃ (X= N, P, As, Sb, and Bi). The ground‐state structure of the McH₃ molecule, which contains the super heavy element Moscovium, is also predicted as pyramidal (C_3v), with an atomization energy of 90.8 kcal mol⁻¹. However, although non‐relativistic calculations still provided a D_3h planar TS for McH₃, four‐component relativistic calculations based on single‐reference wave functions are unable to elucidate the definitive TS geometry in this case. Hence, the results show that relativistic effects are crucial for this barrier determination in those hydrides containing Bi and Mc. Moreover, while the scalar relativistic effects predominate, increasing barrier heights by as much as 17.6 kcal mol⁻¹ (32%) in BiH₃, the spin‐orbit coupling cannot be disregarded in those hydrides containing the heaviest group 15 elements, decreasing the barrier by 2.5 kcal mol⁻¹ (4.5%) in this same molecule.     

Substituent Effects in the Absorption Spectra of Phenol Radical Species: Origin of the Redshift Caused by 3,5‐Dimethoxyl Substitution

The ground‐state equilibrium geometries, electronic structures and vertical excitation energies of methyl‐ and methoxyl‐substituted phenol radical cations and phenoxyl radicals have been investigated using time‐dependent density‐functional theory (namely TD‐B3LYP) and complete‐active‐space second‐order perturbation theory (CASPT2). The “anomalous” large redshifts of the absorption maxima of the phenol radical species observed in the ultraviolet–visible spectral region upon di‐meta‐methoxyl substitution are reproduced by the calculations. Furthermore, these “anomalous” shifts which were unexplained to date can be rationalized on the basis of a qualitative molecular orbital perturbation analysis.     

Quantum-chemical study of the geometric and electronic structure of the CoC2 molecule

DFT (B3LYP) calculations have been performed to study the CoC₂ molecule in its different geometric conformations and electronic states. The energies have been refined using ab initio multiconfigurational CASSCF/CASPT2 calculations. Both approaches are in a good semi-quantitative agreement between themselves and predict the symmetric triangular (C_2v) structure to be more stable than the linear (C_∞v) conformation. The ground state has been found to be a quartet, which can formally be regarded as an ionic Co²⁺–C₂²⁻ complex, resulting from a transfer of the two 4s electrons of the cobalt atom to the 3σ_g orbital of the C₂ ligand and distributing the remaining seven valence electrons over the split 3d orbitals.     

Theoretical study of low-lying electronic states of Mn2 using a newly developed relativistic model core potential

We investigated the electronic structure of low-lying electronic states of Mn₂ 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 Mn₂, which requires a highly correlated calculation. The wave functions of low-lying states are also analyzed at the CASSCF level.     

HSO自由基电子基态激发态的CAS计算研究

使用CASSCF方法和ANO-L基组优化了HSO自由基的基态和3个低占据激发态的结构, 并采用包括更多电子动态相关能的CASPT2方法进行了单点能校正. 频率计算结果表明, 优化的4个几何为势能面上的稳定点. 通过电子结构的研究合理地解释了各个激发态相对于电子基态的结构变化.     

Theoretical computation of low‐lying electronic states of HCNS: A CASPT2 study

Complete active space self‐consistent field (CASSCF) and complete active space second‐order perturbation theory (CASPT2) calculations in conjunction with the aug‐cc‐pVTZ basis set have been used to investigate the low‐lying electronic states of thiofulminic acid (HCNS), HCNS⁺, and HCNS^?. The result of geometry optimization using CASPT2/aug‐cc‐pVTZ shows that theoretically determined geometric parameters and harmonic vibrational frequencies for the HCNS ground state X¹Σ⁺(X¹A′) are in agreement with previous studies. The ionization energies, the electron affinity energies, the adiabatic excitation energies, and vertical excitation energies have been calculated and the corresponding cation and anion states are identified. By calculating adiabatic electron affinity, the states of HCNS^? have been identified to contain both π orbital states (X²A′ and 1²A″) and dipole‐bond states (1⁴A′ and 1⁴A″). © 2012 Wiley Periodicals, Inc.     

Regulatory Mechanism of the Enantioselective Intramolecular Enone [2+2] Photocycloaddition Reaction Mediated by a Chiral Lewis Acid Catalyst Containing Heavy Atoms

The asymmetric catalysis of the intramolecular enone [2+2] photocycloaddition has been subject of extensive experimental studies, however theoretical insight to its regulatory mechanism is still sparse. Accurate quantum chemical calculations at the CASPT2//CASSCF level of theory associated with energy‐consistent relativistic pseudopotentials provide a basis for the first regulation theory that the enantioselective reaction is predominantly controlled by the presence of relativistic effects, that is, spin–orbit coupling resulting from heavy atoms in the chiral Lewis acid catalyst.