Approximate MCSCF optimization for multiconfigurational spin‐tensor electron propagator method (MCSTEP): The vertical ionization potentials of CO,HCN, HNC,H2CO,and O3

The multiconfigurational spin tensor electron propagator method (MCSTEP) was developed as an implementation of electron propagator/single particle Green's function methods. MCSTEP was specifically designed for open shell and highly correlated (nondynamically correlated) initial states. The initial state used in MCSTEP is typically a small complete active space (CAS) with multiconfigurational self‐consistent field (MCSCF) state. In some cases, because of our use of a small CAS in MCSTEP, the Lagrangian eigenvalues of the MCSCF reference state are in an undesired order (u). The desired order (d) can usually be obtained by excluding one or more orbital rotations in MCSCF optimization between the doubly occupied and partially occupied orbitals. We systematically examine several cases where the undesired order occurs for the low‐lying vertical MCSTEP ionization potentials (IPs) of the molecules CO, HCN, HNC, H₂CO, and O₃ with our recently established CAS choices for MCSCF/MCSTEP. By excluding one or more orbital rotations between the partially and doubly occupied orbitals, an approximate MCSCF reference state with the same CAS choice is obtained for use in standard MCSTEP calculations that, in general, gives more reliable vertical MCSTEP IPs. © 2007 Wiley Periodicals, Inc. J Quantum Chem, 2008     

Equivalent orbitals for multiconfigurational spin‐tensor electron propagator method (MCSTEP): The vertical ionization potentials of B,NO, CF,and OF

The multiconfigurational spin tensor electron propagator method (MCSTEP) was developed as an implementation of electron propagator/single particle Green's function methods for ionization potentials (IPs) and electron affinities (EAs). MCSTEP was specifically designed for open shell and highly correlated (nondynamically correlated) initial states. For computational efficiency the initial state used in MCSTEP is typically a small complete active space (CAS) multiconfigurational self‐consistent field (MCSCF) state. If in a molecule there are some degenerate orbitals which are not fully or half occupied, usual MCSCF calculations will make these orbitals inequivalent, i.e., the occupied ones will be different from the nonoccupied ones, so that the degeneracy is broken. In this article, we use a state averaged MCSCF method to get equivalent orbitals for the initial state and import the integrals into the subsequent MCSTEP calculations. This gives, in general, more reliable MCSTEP vertical IPs. © 2008 Wiley Periodicals, Inc., 2008     

The multiconfigurational spin tensor electron propagator method (MCSTEP): Comparison with extended Koopmans' theorem results

Summary We applied the multiconfigurational spin tensor electron propagator method (MCSTEP) for determining the lowest few (in energy) vertical ionization potentials (IPs) of HF, H₂O, NH₃, CH₄, N₂, CO, HNC, HCN, C₂H₂, H₂CO, and B₂H₆. We chose these molecules so that we could compare MCSTEP IPs with recently reported extended Koopmans' theorem (EKT) IPs on the same molecules. Using standard Dunning core-valence basis sets with relatively small complete active spaces, MCSTEP results are in very good to excellent agreement with experiment. These MCSTEP IPs are obtained using matrices no larger than 400 × 400. EKT matrices are even smaller; however, to obtain similar but generally slightly worse agreement with experiment, fairly large active spaces are required with EKT.     

Obtaining positions and widths of scattering resonances from a complex multiconfigurational self‐consistent field state using the M1 method

We present a complex multiconfigurational self‐consistent field (CMCSCF)‐based approach to investigate electron‐atom scattering resonances. It is made possible by the use of second quantization algebra adapted for biorthogonal spin orbitals, which has been applied to develop a quadratically convergent CMCSCF method. To control the convergence to the correct CMCSCF stationary point, a modified step‐length control algorithm is introduced. Convergence to a tolerance of 1.0 × 10^?10 a.u. for the energy gradient is found to be typically within 10 iterations or less. A method involving the first block of the M matrix defined in the multiconfigurational spin tensor electron propagator method (MCSTEP) based on the CMCSCF reference state has been implemented to investigate ²P Be^? shape resonances. The position and width of these resonances have been calculated for different complete active space choices. The wide distribution of the position and width of the resonance reported in the literature is explained by the existence of two distinct resonances which are close in energy. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Ab initio interpretation of Hund's rule for the methylene molecule: Variational optimization of its molecular geometries and energy component analysis

Hund's spin‐multiplicity rule for the ground state of the methylene molecule CH₂ is interpreted by Hartree‐Fock (HF) and multi‐reference configuration interaction (MRCI) methods. The stabilization of the triplet ground state ( ³B₁) relative to the second singlet excited state ( ¹B₁) is ascribed to the greater electron‐nucleus attraction energy that is gained at the cost of increasing the electron‐electron repulsion energy and with the aid of a reduction in the nucleus‐nucleus repulsion energy. The highest spin‐multiplicity in the ground state of CH₂ is accompanied by a set of three characteristic features, i.e., elongation of the internuclear distances, reduction in the bond angle, and contraction of the valence electron density distribution around the nuclei involving expansion of the core electron density distribution. The present calculations fulfill the virial theorem to an accuracy of ?V/T = 2.000 for both HF and MRCI. Accordingly, the molecular geometries are optimized for each of the two states. The inclusion of correlation by MRCI method reduces the energy splitting between the two states by about 14%. The energy splitting is analyzed by the correlational virial theorem 2T^c + V^c = 0 to make a clear interpretation of the correlation effect.© 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

EOM/Propagator ionization potentials: Extension of the excitation operator manifold

The excitation operator manifold required for the calculation of vertical IPs in the EOM/propagator formalism is extended to include products of five spin orbital field operators (refered to as the h₅ basis). Spin symmetry adaptation is used for all the operators of this manifold. Using a direct diagonalization technique introduced previously the effect of inclusion of the h₅ basis on calculated IPs is illustrated for various levels of approximation to the electron density by numerical applications to ethylene and water. The fourth-order terms thus introduced are shown to have greater magnitude than previously included third-order terms, in agreement with earlier work.     

Towards Magnetic Carbo‐meric Molecular Materials

Numerous studies have underlined the putative diradical character of π‐conjugated molecules that can be described by closed‐shell Lewis structures, for instance, p‐dimethylene p–n phenylenes, or long polyacenes. In the latter compounds, the only way to save the aromaticity of the six‐membered rings is to give up the Lewis electron pairing in the singlet biradical ground state. The present work considers the possibility of doing the same by using the basic C₂ units of carbo‐meric architectures. A series of acyclic and cyclic carbo‐meric architectures is studied by using UB3LYP DFT broken‐symmetry calculations, including spin decontaminations and subsequent geometry optimization of the singlet diradical. The C₂ units are shown to stabilize the singlet biradical by spin delocalization, two of them playing approximately the same role as one radical‐insulating 1,4 phenylene moiety. The results are generalized to the investigation of open‐shell polyradical singlet states of rigid hydrocarbon structures, the symmetry and rigidity of which can assist cooperativity and self spin polarization effect. Several synthesis targets with challenging magnetic/spin properties are suggested in the carbo‐mer series.     

The full 2p-h tda and other self-energy approximants: a comparative investigation

A super-operator formulation for decoupling symmetry blocks of the full 2p-h TDA electron propagator matrix is presented, accuracy is explored using the full 2p-h TDA overlap amplitudes to calculate relative ionization intensities for N₂ and H₂O. The effect of excluding orbitais on IPs and relative ionization cross sections is reported.     

Theoretical study of spectroscopic and molecular properties of several low‐lying electronic states of CO molecule

The potential energy curves (PECs) of eight low‐lying electronic states (X¹Σ⁺, a³Π, a′³Σ⁺, d³Δ, e³Σ^?, A¹Π, I¹Σ^?, and D¹Δ) of the carbon monoxide molecule have been studied by an ab initio quantum chemical method. The calculations have been performed using the complete active space self‐consistent field method, which is followed by the valence internally contracted multireference configuration interaction (MRCI) approach in combination with the correlation‐consistent aug‐cc‐pV5Z basis set. The effects on the PECs by the core‐valence correlation and relativistic corrections are included. The way to consider the relativistic corrections is to use the third‐order Douglas–Kroll Hamiltonian approximation at the level of a cc‐pV5Z basis set. Core‐valence correlation corrections are performed using the cc‐pCVQZ basis set. To obtain more reliable results, the PECs determined by the MRCI calculations are corrected for size‐extensivity errors by means of the Davidson modification (MRCI+Q). The spectroscopic parameters (D_e, T_e, R_e, ω_e, ω_ex_e, ω_ey_e, B_e, α_e, and γ_e) of these electronic states are calculated using these PECs. The spectroscopic parameters are compared with those reported in the literature. Using the Breit–Pauli operator, the spin–orbit coupling effect on the spectroscopic parameters is discussed for the a³Π electronic state. With the PECs obtained by the MRCI+Q/aug‐cc‐pV5Z+CV+DK calculations, the complete vibrational states of each electronic state have been determined. The vibrational manifolds have been calculated for each vibrational state of each electronic state. The vibrational level G(ν), inertial rotation constant B_ν, and centrifugal distortion constant D_ν of the first 20 vibrational states when the rotational quantum number J equals zero are reported and compared with the experimental data. Comparison with the measurements demonstrates that the present spectroscopic parameters and molecular constants determined by the MRCI+Q/aug‐cc‐pV5Z+CV+DK calculations are both reliable and accurate. © 2012 Wiley Periodicals, Inc.     

Theoretical electronic studies of aluminum monobromide and aluminum monoiodide

By using CASSCF/MRCI methods, theoretical molecular calculations have been performed for 12 electronic states for AlBr molecule and 12 electronic states for AlI molecule in the representation ^2s+1Λ (neglecting spin‐orbit effects). Calculated potential energy curves are displayed. Spectroscopic constants including the harmonic vibrational wave number ω_e, the electronic energy T_e referred to the ground state and the equilibrium internuclear distance R_e are predicted for these singlet and triplet electronic states for both AlBr and AlI molecules. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

A Heteroleptic Push–Pull Substituted Iron(II) Bis(tridentate) Complex with Low‐Energy Charge‐Transfer States

A heteroleptic iron(II) complex [Fe(dcpp)(ddpd)]²⁺ with a strongly electron‐withdrawing ligand (dcpp, 2,6‐bis(2‐carboxypyridyl)pyridine) and a strongly electron‐donating tridentate tripyridine ligand (ddpd, N,N′‐dimethyl‐N,N′‐dipyridine‐2‐yl‐pyridine‐2,6‐diamine) is reported. Both ligands form six‐membered chelate rings with the iron center, inducing a strong ligand field. This results in a high‐energy, high‐spin state (⁵T₂, (t_2g)⁴(e_g*)²) and a low‐spin ground state (¹A₁, (t_2g)⁶(e_g*)⁰). The intermediate triplet spin state (³T₁, (t_2g)⁵(e_g*)¹) is suggested to be between these states on the basis of the rapid dynamics after photoexcitation. The low‐energy π^* orbitals of dcpp allow low‐energy MLCT absorption plus additional low‐energy LL′CT absorptions from ddpd to dcpp. The directional charge‐transfer character is probed by electrochemical and optical analyses, Mößbauer spectroscopy, and EPR spectroscopy of the adjacent redox states [Fe(dcpp)(ddpd)]³⁺ and [Fe(dcpp)(ddpd)]⁺, augmented by density functional calculations. The combined effect of push–pull substitution and the strong ligand field paves the way for long‐lived charge‐transfer states in iron(II) complexes.     

叠氮化氰的光解离机理

采用多参考态方法,在MRCI+Q//CAS(10,9)/6-311+G(2df)水平上对叠氮化氰(N3CN)的光解离机理进行理论研究.优化得到基态(S0)和低激发态(S1、S2、T1)势能面上的极小点、过渡态、内转换交叉点(IC-S1/S0)和隙间窜跃交叉点(ISC-S1/T1)的结构和能量,构建反应势能面.在MRCI+Q//CAS(10,9)水平上计算N3CN的垂直激发能,并和实验值进行对比.结果表明,在S0、S1、S2和T1态势能面上,N—N键断裂生成N2+NCN是主要解离途径,而C—N键断裂通道是次要通道.实验观测到220 nm处的吸收峰对应分子由S0态到S1态的激发,对应主要光解离产物为NCN[a1△g];而在275 nm处的吸收峰则对应分子被激发到T1态,然后直接生成基态产物NCN[X3Σg-].我们的理论结果与实验测量符合得很好.     

Theoretical investigation of half‐metallicity in Co/Ni substituted AlN

Results of Co and Ni substituted AlN in the zinc blende phase are presented. For spin up states, the hybridized N‐2p and Co/Ni‐3d states form the valance bands with a bandgap around the Fermi level for both materials, while in the case of the spin down states, the hybridized states cross the Fermi level and hence show metallic nature. It is found that, Al_0.75Co_0.25N and Al_0.75Ni_0.25N are ferromagnetic materials with magnetic moments of 4 μ_B and 3 μ_B, respectively. The integer magnetic moments and the full spin polarization at the Fermi level make these compounds half‐metallic semiconductors. Furthermore it is also found that the interaction with the N‐2p state splits the 5‐fold degenerate Co/Ni‐3d states into t_2g and e_g states. The t_2g states are located at higher energies than the e_g states caused by the tetrahedral symmetry of these compounds. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Bis{2,6‐bis[3‐(2,4,6‐trimethylphenyl)pyrazol‐1‐yl‐κN2]pyridine‐κN}cobalt(II) dinitrate at 290 and 150 K

The title compound, [Co(C₂₉H₂₉N₅)₂](NO₃)₂, contains a six‐coordinate high‐spin Co^II ion with approximate local D_2d symmetry. The bond lengths and angles at cobalt undergo only small changes between the two temperatures, which confirms that the Co^II ion does not undergo a spin‐state transition over this temperature range.     

Ground and low‐lying excited C2v states of FeO2—A challenge to computational methods

DFT (BPW91 and B3PW91), CCSD, CCSD(T), and MP2 geometry optimizations were performed on the lowest A₁, A₂, B₁, and B₂ singlet to septet states (a total of 16 states) of FeO₂, using in most cases the 6‐311+G(3df) basis set. With few exceptions, the different methods led to similar geometries. The lowest state is ³B₁ or ⁵B₂, depending on the method used. The quality of the various computational methods was tested by a comparison of vertical excitation energies with corresponding high‐level MRCI values. The best agreement with MRCI was found for BPW91 and B3PW91, with average deviations of about 0.2 eV. MRCI calculations were carried to extremely low configuration selection thresholds (0.025 μh) in order to find the lowest state of FeO₂. The full CI estimate (including Davidson correction and energy extrapolation to 0 μh) gave ³A₁ as the lowest state, followed by ⁵B₂ (0.03 eV) and ³B₁ (0.06 eV). Both ³B₁ and ³A₁ have geometries and vibrational frequencies consistent with the observed IR spectrum. The calculated adiabatic electron affinity of FeO₂ (from ³B₁ of FeO₂ to ⁴B₂ of FeO) is 2.46 eV with CCSD(T), and 2.22 eV with BPW91, compared with the experimental value of 2.36 eV. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Tetracyclopenta[def,jkl,pqr,vwx]tetraphenylene: A Potential Tetraradicaloid Hydrocarbon

A tetramesityl derivative of hitherto unknown tetracyclopenta[def,jkl,pqr,vwx]tetraphenylene (TCPTP), which is a potential tetraradicaloid hydrocarbon, was synthesized. Theoretical calculations based on spin‐flip time‐dependent density functional theory predict that the closed‐shell D_2h form of TCPTP is more stable than the open‐shell D_4h form with its slightly tetraradical character. The tetramesityl derivative (Mes)₄‐TCPTP exhibits remarkable antiaromaticity as a result of the peripheral 20‐π‐electron circuit, which causes an absorption maximum at a long wavelength and a small HOMO–LUMO gap. In solution, (Mes)₄‐TCPTP most likely adopts rapidly equilibrating D_2h structures that interconvert via the D_4h transition state. X‐ray crystallographic analysis showed (Mes)₄‐TCPTP as an approximate D_2h structure.     

Electron localizability indicators ELI–D and ELIA for highly correlated wavefunctions of homonuclear dimers. I. Li2, Be2, B2, and C2

Electron localizability indicators based on the parallel‐spin electron pair density (ELI–D) and the antiparallel‐spin electron pair density (ELIA) are studied for the correlated ground‐state wavefunctions of Li₂, Be₂, B₂, and C₂ diatomic molecules. Different basis sets and reference spaces are used for the multireference configuration interaction method following the complete active space calculations to investigate the local effect of electron correlation on the extent of electron localizability in position space determined by the two functionals. The results are complemented by calculations of effective bond order, vibrational frequency, and Laplacian of the electron density at the bond midpoint. It turns out that for Li₂, B₂, and C₂ the reliable topology of ELI–D is obtained only at the correlated level of theory. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Excited‐State Dynamics of the Metal String Complex Co3(dpa)4(NCS)2 from Femtosecond Transient Absorption Spectra

Transient absorption spectroscopy is used to study the excited‐state dynamics of Co₃(dpa)₄(NCS)₂, where dpa is the ligand di(2‐pyridyl)amido. The ππ*, charge‐transfer, and d–d transition states are excited upon irradiation at wavelengths of 330, 400 and 600 nm, respectively. Similar transient spectra are observed under the experimental temporal resolution and the transient species show weak absorption. We thus propose that a low‐lying metal‐centered d–d state is accessed immediately after excitation. Analyses of the experimental kinetic traces reveal rapid conversion from the ligand‐centered ππ* and the charge‐transfer states to this metal‐centered d‐d state within 100 fs. The excited molecule then crosses to a second d–d state within the ligand‐field manifold, with a time coefficient of 0.6–1.4 ps. Because the ground‐state bleaching band recovers with a time coefficient of 10–23 ps, we propose that an excited molecule crosses from the low‐lying d–d state either directly within the same spin system or with spin crossing via the state ²B to the ground state ²A₂ (symmetry group C₄). In this trimetal string complex, relaxation to the ground electronic surface after excitation is thus rapid.     

Spin Flip Models in the Spin Coupling Method of Many-Particle Amplitudes

A special class of models is presented in which correlation effects for quasidegenerate electronic states are calculated without resorting to complete MRCI schemes. The high-spin reference determinant is transformed into the desired low-spin state by the spin flip procedure with concomitant electron elimination or addition. For the given spin flip process, variational equations that define the corresponding spin coupling matrix have been obtained. For the simplest spin flip model presented by A. Krylova as the SF-CIS method, a sequential spin projection procedure has been carried out. Illustrative calculations for the excited and dissociative states of small molecules have revealed the high quality of the suggested approximate schemes.Original Russian Text Copyright © 2004 by A. V. Luzanov__________Translated from Zhurnal Strukturnoi Khimii, Vol. 45, No. 5, pp. 771–782, September–October, 2004.