Broken orbital symmetry study of low-lying excited and N15 ionized states of pyrazine

Ab initio ΔE_SCF calculations of the low-lying n-π^* and π-π^* transitions in pyrazines are reported with D_2h and C_2v symmetry adapted molecular orbitals. The use of broken orbital symmetry is essential for interpreting the emission properties of pyrazine at the computational level used. The energy of the N_is orbital is calculated using these two symmetry constraints with C_2v orbitals leading to results in better agreement with experiment.     

The Fock Matrix Analysis for Atomic Orbitals in Molecular Orbitals II. The Electronic Structure of N2 Molecules

Weinhold's natural hybrid orbitals can be chosen as the molecular adapted atomic orbitals to build the canonical molecular orbitals of N₂ molecules. The molecular Fock matrix expanded in the natural hybrid orbitals can reveal deeper insight of the electronic structure and reaction of the N₂ molecule. For example, the magnitude of F_ab can signify the bonding character of the paired electrons as well as the diradical character of the unpaired electrons for both σ‐ and π‐types. Discarding the concept of the overlap between non‐orthogonal atomic orbitals, the different orbitals for different spins in the unrestricted Hartree‐Fock wavefunction reveal that there are three pairs of opposite spin density flows between two atoms, which proceed until the bonding molecular orbitals form.     

Fast calculation of excited-state potentials for rare-gas diatomic molecules: Ne2 and Ar2

A fast method for obtaining excited-state potentials of rare-gas diatomic molecules is described. Two types of excited orbitals are used: molecular orbitals calculated in the field of a singly charged molecular ion, and atomic orbitals (properly symmetrized) obtained in a similar atomic system. The RPA equations are solved within the manifold of excitations from the highest occupied orbital in each symmetry to the lowest excited orbital of either type in each symmetry. A simple model for estimating the dynamic correlation correction to excitation (and ionization) energies is given. Applications to excited states of Ne₂(^1,3Σ⁺_{g, u}, ^1,3Π_{g, u}) and Ar₂(^1,3Σ⁺_{g, u}) are described. Two-electron integral transformations involve only three orbitals of each symmetry, and the RPA matrices are four-dimensional. The computational effort required for all excited-state potentials adds less than one-tenths (in terms of computer time) to the effort involved in the preliminary ground state Hartree—Fock calculations. The resulting potentials compare favorably with more elaborate CI calculations and give good agreement with spectroscopic and scattering data. Potential curves for the molecular ions are also given.     

Time‐Dependent Density Functional Theory Molecular Dynamics Simulations of Liquid Water Radiolysis

The early stages of the Coulomb explosion of a doubly ionized water molecule immersed in liquid water are investigated with time‐dependent density functional theory molecular dynamics (TD–DFT MD) simulations. Our aim is to verify that the double ionization of one target water molecule leads to the formation of atomic oxygen as a direct consequence of the Coulomb explosion of the molecule. To that end, we used TD–DFT MD simulations in which effective molecular orbitals are propagated in time. These molecular orbitals are constructed as a unitary transformation of maximally localized Wannier orbitals, and the ionization process was obtained by removing two electrons from the molecular orbitals with symmetry 1B₁, 3A₁, 1B₂ and 2A₁ in turn. We show that the doubly charged H₂O²⁺ molecule explodes into its three atomic fragments in less than 4 fs, which leads to the formation of one isolated oxygen atom whatever the ionized molecular orbital. This process is followed by the ultrafast transfer of an electron to the ionized molecule in the first femtosecond. A faster dissociation pattern can be observed when the electrons are removed from the molecular orbitals of the innermost shell. A Bader analysis of the charges carried by the molecules during the dissociation trajectories is also reported.     

Relativistic symmetry orbitals for the double groups C2v,C∞v,D∞h,and Oh

Relativistic symmetry orbitals are given for molecular LCAO calculations for the double groups: C_2v, C_∞v, D_∞h, and O_h (6-fold) coordination. The atomic orbitals used in the LCAO are of the four component form. A discussion of the comparison between nonre ativistic and relativistic molecular eigenvalues is presented.     

Relativistic molecular orbitals for the double group D3h

Relativistic symmetry orbitals are given for the double group D_3h. For atomic orbitals at the symmetry center a general expression is presented. The atomic orbitals of the s, p_½, and p_3/2 variety outside the center are also considered. The representation matrices are given in explicit form.     

Are atoms sic to molecular electronic wavefunctions? II. Analysis of fors orbitals

Electronic wavefunctions that describe molecules in the full optimized reaction space (FORS) are multiconfigurational wavefunctions which are invariant under non-singular linear transformations of the occupied molecular orbitals. They offer therefore a considerably wider scope for orbital interpretations than the single-configuration Hartree-Fock approximation. For example they can be analyzed in terms of natural MOs and in terms of localized MOs. The latter turn out to be remarkably atomic in character and a new localization procedure can be formulated which yields atom-adapted molecular orbitals. These have the character of minimal-basis-set AOs that are optimally adapted to the molecular environment and furnish an unambigious atomic population analysis. On the other hand, chemically adapted molecular orbitals can be defined by an appropriate compromise between natural orbitals and localized orbitals. The freedom to use, as configuration-generating molecular orbitals, atom-adapted FORS MOs as well as chemically adapted FORS MOs makes FORS wavefunctions particularly suitable for chemical interpretations. The ensuing analysis establishes the minimal basis set (in molecule-adapted form) as a theoretically sound concept for the understanding of accurate molecular wavefunctions. An illustrative example is discussed.     

Symmetry simplifications of space types in configuration interaction induced by orbital degeneracy

Symmetry simplifications are introduced in configuration interaction (CI ) by reducing the number of symmetry-allowed space types if there is degeneracy in some of the molecular orbitals by constructing the unique space types. A new symmetry group which we call the configuration symmetry group is defined and is shown to be expressible as a generalized wreath product group. Generating functions are derived for enumerating the equivalence classes of space types. A double coset method is expounded which constructs the representatives of all equivalence classes of space types using the cycle index of generalized wreath product and the double cosets of label subgroup with generalized wreath product in the symmetric group S_n, if n is twice the number of occupied and virtual orbitals. Method is illustrated with CI using the localized orbitals of polyenes, CI in benzene, and atomic CI for several reference states.     

An ab initio evaluation of the role of p,π interaction: II. Molecules of the CH3COX series

The RHF/6-311G(d) and MP2/6-311G(d) calculations with full geometry optimization were performed for CH₃COX molecules (X = F, Cl, Br, CH₃). Variations in the populations of the p _y orbitals of their halogen and carbon atoms (orbitals whose symmetry axes are perpendicular to the molecular plane) from X = F to X = Cl, Br, and CH₃ are not associated with variations in the extent of the p,π conjugation between the lone electron pair of the halogen atom and the π-electron system of the carbonyl group. The bonding molecular orbitals formed by these atomic p _y orbitals are not determined by this interaction. The RHF/6-311G(d) and MP2/6-311G(d) calculations give similar results.     

A method for population and bonding analyses in calculations with extended basis sets

Summary A method for population and bonding analyses in the calculations with extended basis sets is proposed. The definition and evaluation method of the atomic orbitals in molecular environments (AOIMs) are described. It is shown that the AOIMs can be divided into two subsets, the strongly occupied minimal compact subset {AOIM}_B and the very weakly occupied “Rydberg” subset {AOIM}_R, according to the orbital population obtained from Mulliken analysis with AOIMs as basis sets. The viewpoint of “molecular orbitals consisting of minimal atomic orbital sets” can be optimally realized in terms of {AOIM}_B. The Mulliken population based on AOIMs is reasonable and fairly stable to changes of basis sets. The Mayer bond orders calculated based on {AOIM}_B are quite stable to the changes of basis sets; therefore they can be used to measure objectively the contribution of individual atomic orbitals to bonding.     

On the defects of molecular symmetry-lobe orbitals

It is proved that two molecular symmetry-lobe orbitals, belonging to different irreducible representations, can have a non-negligible overlap. Using a previously reported multipolar analysis of Gaussian-lobe orbitals (GLOs), it is demonstrated that such defects occur when individual symmetry orbitals (SOs) are both contaminated in a given Y_1m subspace, even if such contaminations are very small. A numerical application illustrates this result in the case of the NH₃ molecule, and it is shown that axial-GLOs allow for the exact cancellation of the symmetry defects.     

Characterization of the excited states of ethylene by MRCI

The excited states of ethylene are systematically analyzed and characterized according to the natural orbitals (NOs) resulting from multireference configuration interaction singles and doubles (MRCISD) calculations. By comparing the shapes and nodal structures of the NOs with those of hydrogen atomic orbitals, the Rydberg series can be classified. Two or three different types of Rydberg series appear within five excited states for each symmetry of D_2h. For example, in the ¹A_g symmetry there are three series having np and two nf hydrogen‐like atomic orbitals. Electronic correlation effects for the (π→π*) V state are also discussed on the basis of a complete active space self‐consistent field (CASSCF) calculation, showing that electron correlation effects merely within the valence space cannot explain contraction of the V state. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Symmetry and equivalence restrictions in electronic structure calculations

A simple method for obtaining MCSCF orbitals and CI natural orbitals adapted to degenerate point groups, with full symmetry and equivalence restrictions, is described. Among several advantages accruing from this method are the ability to perform atomic SCF calculations on states for which the SCF energy expression cannot be written in terms of Coulomb and exchange integrals over real orbitals, and the generation of symmetry-adapted atomic natural orbitals for use in a recently proposed method for basis set contraction.     

A short CI expansion for a symmetry-adapted description of localized hole states: Application to the 3dσu hole state of the Cu2 + ion

A simple formalism is developed to describe by means of a symmetry-adapted wavefunction the localized hole states which may arise in symmetric systems. A short CI expansion is generated in a systematic way from the delocalized molecular orbitals of the SCF ground state. For the 3dσ_u hole state of the _Cu2 ⁺ ion, the symmetry adapted and the broken symmetry solutions approximately correspond to the same energy at that level of CI.     

M(o)bius环并苯的分子对称性

一般来说,点群理论认为M(o)bius带环分子最高的对称性只能是C2.本文讨论了由18个苯环组成的环并苯的异构体分子,包括柱面的Hückel型分子(HC-[18])和扭转180°的M(o)bius带环分子(MC-[18]).结果表明除了点对称性外,M(o)bius带环分子还存在一种可称为环面螺旋旋转(TSR)变换的对称性,为此还引用了环面正交曲线坐标系.此外,还讨论了这些分子关于TSR对称性匹配的原子集和原子轨道(AO)集.根据TSR对称性的循环群特征,可以建立此类群的不可约表示及有关特征标.这类分子的分子轨道(MO)关于TSR群的不可约表示是纯的,然而所含的相应的原子轨道对称性匹配的线性组合(SALC-AO)成分可以是多种的.     

Pseudosymmetry analysis of molecular orbitals

We introduce a pseudosymmetry analysis of molecular orbitals by means of the newly proposed irreducible representation measures. To do that we define first what we consider as molecular pseudosymmetry and the relationships of this concept with those of approximate symmetry and quasisymmetry. We develop a general algorithm to quantify the pseudosymmetry content of a given object within the framework of the finite group algebra. The obtained mathematical expressions are able to decompose molecular orbitals by means of the irreducible representations of any reference symmetry point group. The implementation and usefulness of the pseudosymmetry analysis of molecular orbitals is demonstrated in the study of σ and π orbitals in planar and nonplanar polycyclic aromatic hydrocarbons and the t_2g and e_g character of the d‐orbitals in the [FeH₆]^3? anion in its high spin state along the Bailar twist pathway. © 2013 Wiley Periodicals, Inc.     

Use of the bond-projected superposition principle in determining the conditional probabilities of orbital events in molecular fragments

The problem of defining and determining the multi-conditional probabilities of many-orbital events in the chemical bond system of a molecule is addressed anew within theoretical framework of the one-determinantal orbital representation of molecular electronic structure. Its solution is vital for determining the information-theoretic indices of bond couplings between molecular fragments or the reactant/product subsystems in chemical reactions. The superposition principle of quantum mechanics, appropriately projected into the occupied subspace of molecular orbitals, is used to condition the atomic orbitals or general basis functions of the self-consistent-field calculations. The conditional probabilities between the subspaces of basis functions (atomic orbitals) are derived from an appropriate generalization of the bond-projected superposition principle. They are then used to define the triply-conditional probabilities, relating one conditional event to another. The resulting expression is shown to satisfy the relevant non-negativity and symmetry requirements. It is applied to probe the π-bond coupling in butadiene and benzene.     

Möbius环并苯的分子对称性

一般来说, 点群理论认为Möbius带环分子最高的对称性只能是C₂. 本文讨论了由18个苯环组成的环并苯的异构体分子, 包括柱面的Hückel型分子(HC-[18])和扭转180°的Möbius带环分子(MC-[18]). 结果表明除了点对称性外, Möbius带环分子还存在一种可称为环面螺旋旋转(TSR)变换的对称性, 为此还引用了环面正交曲线坐标系. 此外, 还讨论了这些分子关于TSR对称性匹配的原子集和原子轨道(AO)集. 根据TSR对称性的循环群特征, 可以建立此类群的不可约表示及有关特征标. 这类分子的分子轨道(MO)关于TSR群的不可约表示是纯的, 然而所含的相应的原子轨道对称性匹配的线性组合(SALC-AO)成分可以是多种的.     

Nature of coordination bond in silatranes and its formation dynamics according to the ab initio calculations

Quantum-chemical calculations of 1-hydrosilatrane molecule with complete optimization of its geometry and at various fixed Si…N distances (2.0 to 3.7 Å) has been carried out at the MP2/6-31G(d) level. The silatranes coordination bond is formed of different atomic orbitals of Si and N atoms participating in a series of molecular orbitals. With the Si…N distance decreasing, contributions of the atomic orbitals in these molecular orbitals have been changed, number of the molecular orbitals has increased, and total energy of the molecule has decreased. At the coordination centers are getting closer, population of the nitrogen valence s and p _z orbitals have changed due to the corresponding bond angle change; the populations of Si and H orbitals are not significantly changed.