A CAS study on S‐loss and O‐loss dissociation mechanisms of the SO2+ ion in the C,D, and E states

In the present work, we mainly study dissociation of the C ²B₁, D²A₁, and E²B₂ states of the SO₂⁺ ion using the complete active‐space self‐consistent field (CASSCF) and multiconfiguration second‐order perturbation theory (CASPT2) methods. We first performed CASPT2 potential energy curve (PEC) calculations for S‐ and O‐loss dissociation from the X, A, B, C, D, and E primarily ionization states and many quartet states. For studying S‐loss predissociation of the C, D, and E states by the quartet states to the first, second, and third S‐loss dissociation limits, the CASSCF minimum energy crossing point (MECP) calculations for the doublet/quartet state pairs were performed, and then the CASPT2 energies and CASSCF spin‐orbit couplings were calculated at the MECPs. Our calculations predict eight S‐loss predissociation processes (via MECPs and transition states) for the C, D, and E states and the energetics for these processes are reported. This study indicates that the C and D states can adiabatically dissociate to the first O‐loss dissociation limit. Our calculations (PEC and MECP) predict a predissociation process for the E state to the first O‐loss limit. Our calculations also predict that the E²B₂ state could dissociate to the first S‐ and O‐loss limits via the A²B₂ ← E²B₂ transition. On the basis of the 13 predicted processes, we discussed the S‐ and O‐loss dissociation mechanisms of the C, D, and E states proposed in the previous experimental studies. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

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)     

Theoretical studies on quinones I. The structure of p-benzoquinone and two of its excited triplet states

Ab initio calculations on the ground and two excited triplet states (³B_1g and ³B_1u) of p-benzoquinone are described. The geometries of the three states were fully optimised at the SCF level using the 3-21G basis set. For the excited states, both D_2h and C_2v geometries were investigated. Comparison was made between UHF and ROHF levels of theory.     

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.     

Construction and applications of symmetrized valence bond wave functions

A method constructing symmetry-adapted bonded Young tableau bases is proposed, based on the symmetry properties of bonded tableaus and the projection operator associated with a point group. Several examples including the ground states and π excited states of O₃⁻, O₃, O₃⁺, and C₃⁻ are shown for instruction to construct the symmetrized valence bond (VB) wave function. Excitation energies of transitions from the ground states to π excited states of O₃⁻, C₃H₅, and C₃⁻ are calculated with an optimized symmetrized valence bond wave function in the σ–π separation approximation. Good agreement between the VB and experimental excitation energies is observed. The bonding features of the ground state and the first π excited singlet and triplet states for S₃ are discussed according to bonding populations from VB calculations. Both the singlet-biradical and the dipole structures have significant contributions to the ground state X ¹A₁ of S₃, while the excited state 1 ¹B₂ is essentially composed of the dipole structures, and the 1 ³B₂ excited state is comprised from a triplet-biradical structure. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 66 : 1–7, 1998     

Theoretical electronic structure of the molecule ScI

Theoretical investigation of the 18 lowest electronic states of the molecule ScI in the representation ^2S+1Λ^(±) has been performed via CASSCF and MRCI (single and double excitation with Davidson correction) calculations. To the best of our knowledge these calculated electronic states are the first ones from ab initio methods. Thirteen electronic states between 4,500 cm^?1 and 21,000 cm^?1 have been studied for the first time and have not yet been observed experimentally. The harmonic frequency ω_e, the internuclear distance R_e, the electronic transition energy with respect to the ground state T_e, and the rotational constant B_e have been calculated for the considered electronic states. By using the canonical functions approach the eigenvalues E_υ and the rotational constants B_υ have also been calculated for the six lowest‐lying electronic states. The comparison of these results with the theoretical and the experimental data available in the literature shows a good agreement. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Ab initio Study of the Geometrical and Electronic Structures of Sc(MDA)2 and Sc(MDA)3 Molecules

The geometrical parameters, force fields, and vibrational spectra of various geometrical configurations of Sc(MDA)₂ and Sc(MDA)₃ molecules were calculated using the restricted Hartree—Fock method taking into account electron correlation by second–order Möller–Plesset perturbation theory. The calculations were performed using effective pseudopotentials for describing atomic cores and valence double zeta basis sets supplemented by polarization functions. It was shown that the configurations of D ₃ [Sc(MDA)₃] and D _2h [Sc(MDA)₂] symmetry correspond to the minimum on the potential energy surface of the ground electronic state. The configurations of D _3h symmetry for Sc(MDA)₃ and D _2d for Sc(MDA)₂ correspond to first–order saddle points. The ground electronic states of Sc(MDA)₂ and Sc(MDA)₃ molecules are the states of ² A _g and ¹ A ₁ symmetries, respectively. For both configurations (D _2h and D _2d of the Sc(MDA)₂ molecule, the energies of vertical electron transitions were calculated using the CASSCF method. The formation of chemical bonding in the compounds considered was analyzed. It was shown that the Sc–O bond is predominantly ionic and the conjugation is characteristic only of the oxygen–carbon skeleton of the chelate fragment. The results obtained are compared with literature experimental and theoretical data for related compounds.     

2-氢吡喃分子光激发开环反应机理的理论研究

用完全活性空间多组态(CASSCF)方法对2-氢吡喃分子光激发开环反应机理进行了研究。利用价键理论(VB)和自然键道分析(NBO)探究了沿能量最低反应途径电子的重新分布情况。计算结果表明从S0-Min p®p*垂直激发到Franck-Condon点后很容易弛豫到S1-Min,经较低的势垒到达圆锥交叉点S1/S0。而S1/S0与S1-Min相比能量低0.63eV。这样体系沿非绝热最低反应途径从激发单重态经交叉点S1/S0很容易得到产物S0-Prod。     

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.     

Structure of acetyl chloride molecule isotopomers CH<Subscript>3</Subscript>COCl and CD<Subscript>3</Subscript>COCl in the ground and lowest excited singlet and triplet electronic states: a quantum mechanical study

The structures of isotopomers of conformationally flexible acetyl chloride molecule, CH₃COCl and CD₃COCl, in the ground (S₀ and lowest excited singlet (S₁) and triplet (T₁) electronic states were calculated by the RHF, MP2, and CASSCF methods. The equilibrium geometric parameters and harmonic vibrational frequencies of the molecules in these electronic states were estimated. According to calculations, electronic excitation causes considerable conformational changes involving rotation of the CH₃ (CD₃) top and a substantial deviation of the CCOCl fragment from planarity. The results of calculations agree with experimental data. Two dimensional torsional inversion sections of the potential energy surface were calculated and analyzed. Vibrational problems for large amplitude vibrations (torsional vibration in the S₀ state and both torsional and inversion vibrations in the T₁ and S₁ states) were solved in one- and two-dimensional approximations.__________Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 1, pp. 62–70, January, 2005.     

Ab initio study on the photochemical behavior of styrene

Ab initio complete active space self‐consistent field (CASSCF) and the second order multireference Møller‐Plesset calculations have been performed to examine the photochemical behavior of styrene upon the strong S₀‐S₂ electronic excitation in the low‐lying excited states. The optimized structure at the S₂/S₁ conical intersection (CIX) is characterized by a quinoid structure. The transition state (TS) in S₁ is in the vicinity of the S₂/S₁‐CIX. At the S₁‐TS, two reaction paths branch. One is the relaxation into the stable structure in S₁ and then emission into S₀. The other is the radiationless decay through the S₁/S₀‐CIX. © 2002 Wiley Periodicals, Inc. J Comput Chem 10: 950–956, 2002     

硫代樟脑光化学反应的理论研究

运用量子化学方法优化了硫代樟脑的最低5个电子态(S₀, T₁, S₁, T₂和S₂)的结构, 并计算了它们的相对能量. 计算结果表明: S₁, T₁和T₂态的能量非常接近, 而S₂的能量远远高于T₂态, 这与之前对几种小的硫代羰基化合物的研究结论一致. 确定了硫代樟脑分子在T₁态发生β-插入反应和类Norrish II型反应的机理, 计算的势垒相对于S₀的振动零点分别为314.1和332.6 kJ/mol. 在400 nm波长的光的照射下, 分子被激发到S₁态, 此时分子没有足够的能量发生反应, 只能通过内转换回到基态. 当激发光波长在254 nm时, 硫代樟脑分子被激发到S₂态, 这时候体系有了足够的内部能量使反应发生. 实验上已经观察到此激发光波长下, 气态硫代樟脑可以发生β-插入反应和类Norrish II型反应.     

Ab initio MRD-CI study of the rydberg states of methylene

Potential curves have been calculated for the low-lying Rydberg states of CH₂ as well as for a number of its valence-shell species by employing the ab initio MRD-CI method. The first Rydberg transition is found to occur with a vertical energy of 6.38 eV (1b₁ → 3s), but the corresponding upper state is believed to be strongly predissociated since it correlates directly with the CH(²II) + H(²S_g) ground state fragments at lower energy. The assignment of the first observed Rydberg transition at 8.757 eV by Herzberg as 1b₁ → 3dπ is confirmed almost quantitatively in the calculations, while the corresponding minimum 1P value is computed to be 10.21 eV compared to the experimental result of 10.3 ± 0.1 eV. The dissociation energy of methylene in its ground state is calculated to be 4.47 eV, and this result also fits in well with experimental evidence, which determines a lower limit for this quantity of D₀ > 4.23 eV. Finally, it is found that none of the Rydberg states nor any of the higher-lying valence-shell species of methylene are of sufficiently low energy to play a significant role in the experimental determination of the ¹A₁-³B₁ splitting of this system.     

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.     

Multireference Calculation of the Photodissociation of Benzyl Chloride

The photodissociation mechanism of benzyl chloride （BzCl） under 248 nm has been investigated by the complete active space SCF （CASSCF） method by calculating the geometries of the ground （S0） and lower excited states, the vertical （Tv） and adiabatic （T0） excitation energies of the lower states, and the dissociation reaction pathways on the potential energy surfaces （PES） of SI, TI and T2 states. The calculated results clearly elucidated the photodissociation mechanism of BzCl, and indicated that the photodissociation on the PES of T1 state is the most favorable.     

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.     

Tetra-hydrides of the third-row transition elements: spin–orbit coupling effects on geometrical deformation in WH4 and OsH4

The dissociation energies of MH₄ (M =  La, Hf–Hg) were computed using full optimized reaction space (FORS) multi-configuration self-consistent field (MCSCF) and second-order multi-reference Møller–Plesset perturbation methods with the SBKJC basis sets augmented by a set of polarization functions (SBKJC(f,p)). It was shown that of the molecules examined, only four tetra-hydrides HfH₄, TaH₄, WH₄, and OsH₄ with T_d symmetry are lower in energy than the corresponding dissociation limits. For WH₄ and OsH₄, the potential energy surfaces from the D_4h to the T_d structure were explored from both theoretical calculations and symmetry arguments based on the pseudo-Jahn- Teller effect. As for WH₄, it is found that the ground state could be ³E_g, ³A_2g, or ³B_2g at the D_4h structure. The present calculations suggest that the ground state is ³E_g, and that this state is stabilized by the e_u deformation into a C_2v structure (³B₁) and then sequentially to the most stable T_d structure (³A₂). If the molecular system is promoted to the lowest ³B_2g state, the D_4h structure can directly deform into the most stable T_d structure along the b_2u vibrational mode. For OsH₄, the ground state (⁵B_1g) at the D_4h structure deforms into a D_2d structure and the resulting ⁵B₂ state strongly interacts with the lowest ³E and ¹A₁ states due to the spin-orbit couplings (SOCs). As a result, it was shown that the relativistic potential energy of the lowest spin-mixed state (ground state) monotonically decreases along the D_2d deformation path from the D_4h to the T_d structure.     

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.     

Diagrammatic valence-bond theory for finite model Hamiltonians

Valence bond (VB ) diagrams form a complete basis for model Hamiltonians that conserve total spin, S, and have one valence state, ?_p, per site. Hubbard and Pariser–Parr–Pople (PPP ) models illustrate ionic problems, with zero, one, or two electrons in each ?_p, while isotropic Heisenberg models illustrate spin problems, with only purely covalent VB diagrams. The difficulty of nonorthogonal VB diagrams is by-passed by exploiting the finite dimensionality of the complete basis and working with unsymmetric sparse matrices. We introduce efficient bit manipulations for generating, storing, and handling VB diagrams as integers and describe a new coordinate relaxation method for the ground and lowest excited states of unsymmetric sparse matrices. Antiferromagnetic spin-½ Heisenberg rings and chains of N ? 20 spins, or 2^N spin functions, are solved in C₂ symmetry as illustrative examples. The lowest S = 1 and 0 excitations are related to domain walls, or spin solitons, and studied for alternations corresponding to polyacetylene. VB diagrams with arbitrary S and nonneighbor interactions are constructed for both spin and ionic problems, thus extending diagrammatic VB theory to other topologies.     

Structure and Chemical Bonding of the B<Subscript>3</Subscript>S<Stack><Subscript>n</Subscript><Superscript>0/−</Superscript></Stack> (<Emphasis Type="Italic">n</Emphasis> = 2–4) Boron Sulfide Clusters: A Density Functional Theory Investigation

A density functional theory investigation on the structural and bonding properties of B₃S _n ^?/0 (n = 2–4) series has been performed. Based on B3LYP and CCSD(T) calculations, we present the linear D _∞h B₃S₂ ^? (1, ³Σ_g) and D _∞h B₃S₂ (2, ²Π_u), the Y-shaped C _2v B₃S₃ ^? (3, ¹A₁) and C _2v B₃S₃ (4, ²B₂), and perfectly planar structures C _2v B₃S₄ ^? (5, ¹A₁) and C _2v B₃S₄ (6, ²B₂) that contain rhombic B₂S₂ rings. The 1–6 ground-state structures are planar with linear “B–B–B” core, in which the first and the second S atoms prefer to bond terminally to the terminal B, and the third S atom bonds to the center B, however, when the third S atom is added with the fourth, the atoms tend to be in the bridging positions of two adjacent B atoms. The growth pattern of B₃S _n ^?/0 (n = 2–4) clusters helps to understand the structural properties of the other small boron sulfide clusters. Bonding analyses reveal that a dual or single three-center one-electron (3c–1e) π hypervalent bonds located over the “B–B–B” core of D _∞h B₃S₂ ^? (1) and B₃S₂ (2), respectively. While C _2v B₃S₄ ^? (5) and B₃S₄ (6) with rhombic B₂S₂ rings as the center with –BS and –S units all possess 4c–4e bonds (o-bonds) in the rhombic B₂S₂ rings.