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.     

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.     

Ab initio study of the ground and lower-lying excited electronic states of NiX2 and FeX2 (X=F,Cl, Br,I) molecules

The ground and lower-lying excited electronic states of FeX₂ and NiX₂ (X=F, Cl, Br, I) molecules are systematically investigated by ab initio method at the complete active space self-consistent field (CASSCF) and multiconfigurational quasi-degenerate second-order perturbation (MCQDPT2) levels of theory. It is concluded that the dynamic electron correlation has to be taken into account in the prediction of the properties for such kind of molecules. The equilibrium bond lengths r_e(M–X), force constants and harmonic vibrational frequencies are calculated for the ground and lower-lying excited electronic states. The spin-orbit coupling (SOC) effects are analysed.     

A MS-CASPT2 study of the low-lying electronic excited states of CH2BrCl

The low-lying singlet excited states of CH₂BrCl have been calculated using multiconfigurational CASSCF, second-order perturbation theory CASPT2 and its multistate extension MS-CASPT2. The CASSCF method shows spurious valence–Rydberg mixing and a wrong order of states. Inclusion of dynamical correlation by single root CASPT2 lowers dramatically the energy of the valences states but does not lead to a complete separation between valence and Rydberg states. This situation is improved by the MS-CASPT2 calculations, which gives two valence states for both A^′ and A″ symmetries below the lowest Rydberg state, corresponding to n(Br)→σ^*(C–Br) and n(Cl)→σ^*(C–Cl) transitions at 6.1 eV (203 nm) and 7.2 eV (173 nm), and being repulsive along C–Br and C–Cl coordinates.     

Ab initio calculations for the potential curves and spin–orbit coupling of Mg2

 The ground state and several low-lying excited states of the Mg₂ dimer have been studied by means of a combination of the complete-active-space multiconfiguration self-consistent-field (CASSCF)/CAS multireference second-order perturbation theory (CASPT2) method and coupled-cluster with single and double excitations and perturbative contribution of connected triple excitations [CCSD(T)] scheme. Reasonably good agreement with experiment has been obtained for the CCSD(T) ground-state potential curve but the dissociation energy of the only experimentally known A¹Σ _u ⁺ excited state of Mg₂ is somewhat overestimated at the CASSCF/CASPT2 level. The spectroscopic constants D _e, R _e and ω_e deduced from the calculated potential curves for other states are also reported. In addition, some spin–orbit matrix elements between the excited singlet and triplet states of Mg₂ have been evaluated as a function of internuclear separation. Received: 10 May 2001 / Accepted: 15 August 2001 / Published online: 30 October 2001     

Ab initio investigation on the structures and spectra of the firefly luciferin

The ground state (S₀) geometry of the firefly luciferin (LH2) was optimized by both DFT B3LYP and CASSCF methods. The vertical excitation energies (T _v) of three low-lying states (S₁, S₂, and S₃) were calculated by TD-DFT B3LYP//CASSCF method. The S₁ geometry was optimized by CASSCF method. Its T _v and the transition energy (T _e) were calculated by MS-CASPT2//CASSCF method. Both the TD-DFT and MS-CASPT2 calculated S₁ state T _v values agree with the experimental one. The IPEA shift greatly affects the MS-CASPT2 calculated T _v values. Some important excited states of LH2 and oxyluciferin (oxyLH2) are charge-transfer states and have more than one dominant configuration, so for deeply researching the firefly bioluminescence, the multireference calculations are desired. Supported by the National Natural Science Foundation of China (Grant No. 20673012) and the Major State Basic Research Development Programs (Grant No. 2004CB719903)     

A multireference configuration interaction method based on the separated electron pair wave functions

A multireference configurational interaction method based on the separated electron pair (SEP) wave functions, SEP‐CI approach, has been developed as an approximation to the traditional CASSCF method. It differs from the CASSCF method in that active orbitals are obtained from the SEP wave function without further optimization in the subsequent CI calculations, and the active space is automatically constructed according to the occupation coefficients of SEP natural orbitals. These features make the present SEP‐CI method computationally much less demanding than the CASSCF method. The applicability of the SEP‐CI method is illustrated with sample calculations on the insertion reaction of BeH₂ and dissociation energies of LiH, BH, FH, H₂O, and N₂. © 2005 Wiley Periodicals, Inc. J Comput Chem 27: 39–47, 2006     

TiO2基态和激发态的几何结构、激发能和偶极矩

采用二阶微扰理论MP2、密度泛函B3LYP方法和含时密度泛函TD-B3LYP方法分别优化了TiO₂分子的基态¹A₁和六个激发态¹B₂、³B₂、¹B₁、³B₁、¹A₂和³A₂的几何结构. ¹A₁、¹B₂、³B₂、¹B₁和³B₁具有弯曲几何结构, ¹A₂和³A₂具有线性对称结构. 我们发现激发态¹B₂、³B₂、¹B₁和³B₁键偶极矩的数值大小顺序和相应的键角大小顺序完全一致. 另外, 采用完全活化空间自洽场(CASSCF)CASSCF(6,6)、CASSCF(8,8)、多参考组态相互作用(MRCI)和含时密度泛函TD-B3LYP 计算了TiO₂ 分子各激发态的垂直激发能和绝热激发能. 对¹B₂、³B₂和¹B₁三个态, MRCI/CASSCF(6,6) 计算的垂直激发能和绝热激发能与已有的实验值最接近. 对其他三个激发态³B₁、¹A₂和³A₂, 计算的激发能和文献报道的激发能计算值基本一致. 最后, 还计算了TiO₂分子的基态和激发态的偶极矩. 对¹A₁和¹B₂态, 偶极矩的计算值与已有的实验值相吻合. 采用原子偶极矩校正的Hirshfeld 布居方法计算了TiO₂分子在¹A₁、¹B₂、³B₂、¹B₁和³B₁态时各原子的电荷, 发现从基态到激发态偶极矩的变化与电荷从氧原子向钛原子的转移有关. 整个计算中还考察了基函数cc-pVDZ、cc-pVTZ和cc-pVQZ对计算结果的影响.     

Full CI benchmark calculations for molecular properties

Full CI calculations of first- and second-order properties are presented to provide benchmark results for comparisons with other methods, such as multireference CI(MRCI). The full CI(FCI) polarizability of F^– is computed using a double zeta plus polarization plus diffuse basis set. These FCI results are compared to those obtained at other levels of theory; the CASSCF/MRCI with Davidson correction results are in excellent agreement with the FCI. Differences between the polarizability results computed as a (numerical) second derivative of the energy or as an induced dipole moment are also discussed. FCI calculations are presented for the dipole moment and polarizability of HF, CH₂ and SiH₂ using a DZP basis set. Again, the CASSCF/MRCI values are in excellent agreement with the FCI results, whereas SDCI values, whether computed as an expectation value or as an energy derivative, are much worse. The results obtained using the CPF approach are in considerably better agreement with the FCI results than SDCI, and are similar in quality to the SDCI energy derivative results with the inclusion of Davidson's correction.     

Theoretical studies on the low-lying electronic states of the HSO neutral radical and its cation

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

Molecular Structure,Thermodynamic and Spectral Characteristics of Metal-Free and Nickel Complex of Tetrakis(1,2,5-thiadiazolo)porphyrazine

The Knudsen effusion method with mass spectrometric control of the vapor composition was used to study the possibility of a congruent transition to the gas phase and to estimate the enthalpy of sublimation of metal-free tetrakis(1,2,5-thiadiazolo)porphyrazine and its nickel complex (H₂TTDPz and NiTTDPz, respectively). The geometrical and electronic structure of H₂TTDPz and NiTTDPz in ground and low-lying excited electronic states were determined by DFT calculations. The electronic structure of NiTTDPz was studied by the complete active space (CASSCF) method, following accounting dynamic correlation by multiconfigurational quasi-degenerate second-order perturbation theory (MCQDPT2). A geometrical structure of D_2h and D_4h symmetry was obtained for H₂TTDPz and NiTTDPz, respectively. According to data obtained by the MCQDPT2 method, the nickel complex possesses the ground state ¹A_1g, and the wave function of the ground state has the form of a single determinant. Electronic absorption and vibrational (IR and resonance Raman) spectra of H₂TTDPz and NiTTDPz were studied experimentally and simulated theoretically.     

Theoretical study of Pu and Am tetracarbide molecules

The electronic structure and ground‐state molecular properties of Pu and Am tetracarbides have been investigated by relativistic multireference calculations using CASSCF/CASPT2 theory as well as by density functional theory in conjunction with relativistic pseudopotentials. The CASSCF/CASPT2 treatment has been extended by spin–orbit coupling effects for selected species using the CAS state‐interaction method. The five atoms can form various structural isomers, from which 12 ones have been identified in our study. The electronic ground state in both molecules corresponds to a planar fan‐type structure of C_2v symmetry, in which the actinide atom is connected to a bent C₄ moiety. The other structures are much higher in energy, the ones computed in this study appear between 250 and 1050 kJ/mol. The bonding characteristics in the most relevant structures have been analyzed on the basis of the valence molecular orbitals and natural bond orbital analysis. The most stable structures have been characterized by their spectroscopic (vibrational and electron) properties. © 2014 Wiley Periodicals, Inc.     

Generalized brillouin theorem multiconfiguration method for excited states

The Generalized Brillouin Theorem Multiconfiguration Method (GBT-MC) of Grein and Chang is extended and applied to the calculation of excited states. Orthogonality constraints to lower states as well as second-order interaction effects of states lying close together have been taken into account. In this way quadratic convergence can be guaranteed. Difficulties with coupling coefficients and Lagrangian multipliers of SCF methods can be circumvented. Test calculations have been performed on valence electron excited states of C, H₂O, and CH₂O, and on core excited states of Li.     

Theoretical study of the dipole moment of oxygen monofluoride (OF)

Theoretical X²II potentials and dipole moment functions for OF are presented at the CASSCF, externally contracted Cl, and MRCI(SD) levels using DZP and extended gaussian basis sets. The best theoretical results (with experiment in parentheses) are μ_ν =0 = ?0.0089 (?0.0043) and μ_ν=1 = ?0.0318 (?0.0267) D, where the minus sign implies O⁺F^?.     

Low-lying electronic states of HNCS and its ions: a CASSCF/CASPT2 study

Complete active space self-consistent-field (CASSCF) and multiconfigurational second-order perturbation theory (CASPT2) calculations in conjunction with the ANO-L basis set were performed to investigate systematically the low-lying electronic states of HNCS and its ions in C _s symmetry. Our highly accurate calculation indicated that theoretically determined geometric parameters and harmonic vibrational frequencies for the ground-state X ¹A′ are in good agreement with observed experimental data. The geometry of triplet HNCS is clearly favored C ₁ symmetry, and the relative energy is predicted to be 3.000 eV (69.2 kcal/mol). The vertical transition energies for the selected excited states of HNCS were calculated at CASSCF/CASPT2/ANO-L level of theory based on CASSCF optimized geometry. Except for a few linear states of X ²Π (1²A′, 1²A″), 1⁴Σ⁻ (1⁴A″), and 1²Σ⁺ (3²A′) states of HNCS⁺, our results confirmed that the majority of excited states are twisted trans-bend structures. The existence of bound excited anion states has been found for the first time in HNCS⁻. A more elaborate examination of ionization potential of HNCS (AIP, VIP) than previous reports has been presented.     

Potential energy surfaces of pseudoaromatic molecules: An MMVB and CASSCF study of pentalene

The S₀ and S₁ potential energy surfaces of pentalene were studied using MMVB—a hybrid force-field/parametrized valence bond (VB) method designed to simulate CASSCF calculations for ground and covalent excited states. The results were calibrated against full CASSCF calculations. Four distinct critical points were optimized: on S₀, a C_2h minimum (with alternating single and double bonds) and a D_2h transition structure; and on S₁, a D_2h minimum and an adjacent S₁/S₀ conical intersection. A VB exchange density matrix (which is independent of the choice of the spin-coupled basis) was used to rationalize the S₀ and S₁ surface topologies. Craig defined pseudoaromatic molecules to be those with nontotally symmetric electronic ground states. For pentalene, this is true for both CASSCF and MMVB calculations: the CASSCF S₀ transition structure is an open-shell B_1x singlet, and the VB ground state is dominated by a spin-coupling which transforms as B_1g. A C_2v minimum and a D_2h transition structure were located on the CASSCF S₂ potential energy surface. This state cannot be represented by MMVB because of the importance of ionic configurations. The characters of the S₁ S₂ states of pentalene are shown to be reverse of the S₁ and S₂ states of benzene. © 1996 John Wiley & Sons, Inc.     

Mechanistic Photodissociation of Glycolaldehyde: Insights from Ab Initio and RRKM Calculations

Herein we report a theoretical study on mechanistic photodissociation of glycolaldehyde, HOCH₂CHO. Equilibrium structures, transition states, and intersection structures for the α‐C? C and ‐C? H bond fissions and the β‐C? O bond fission in the excited states are determined by the complete active space self‐consistent field (CASSCF) method. Based on the CASSCF optimized structures, the potential energy profiles for the dissociations are refined by performing single‐point calculations using the multi‐state multi‐reference CASSCF second order perturbation (MS‐MR‐CASPT2) method. With a low excitation energy of 280–340 nm, the T₁ α‐C? C and β‐C? O bond fissions following intersystem crossing from the S₁ state are the predominant and comparable channels, whereas the α‐C? H bond fissions both in the S₁ and in the T₁ states are nearly prohibited due to the relevant high barriers. The rate constants for the T₁ α‐C? C and β‐C? O bond fissions are also calculated by RRKM theory. Furthermore, the S₀ reactions can occur as a consequence of intersystem crossing via T₁/S₀ intersection points resulting from the T₁ C? C and C? O bond cleavages. This photodissociation mechanism is consistent with recent experimental studies.     

Electroanalytical simulations. Orthogonal collocation simulation of fast second-order chemical reactions coupled to an electron transfer with a heterogeneous equivalent formulation

The combination of orthogonal collocation and the heterogeneous equivalent technique is extended to simulate cyclic voltammograms of fast second-order follow-up reactions coupled to an electron transfer at an electrode surface. The $\text{ED}$ (reversible electron transfer with irreversible follow-up dimerization) and $\text{EC}$₂ (reversible electron transfer with irreversible second-order follow-up reaction) models are considered. The non-linear boundary equations are solved numerically. No linear approximation of the concentration profiles is required. The use of non-linear space coordinate transformations is described. Peak potential and peak current function results are compared with literature values and agreement is found. The transition between the second-order $\text{EC}$₂ and the corresponding first-order mechanisms is discussed.