Role of electronic structure of ruthenium polypyridyl dyes in the photoconversion efficiency of dye‐sensitized solar cells: Semiempirical investigation

ZINDO/S calculations on cis‐Ru(4,4′‐dicarboxy‐2,2′‐bipyridine)₂(X)₂ and cis‐Ru(5,5′‐dicarboxy‐2,2′‐bipyridine)₂(X)₂ complexes where X = Cl^?, CN^?, and NCS^? reveal that the highest occupied molecular orbital (HOMO) of these complexes has a large amplitude on both the nonchromophoric ligand X and the central ruthenium atom. The lowest‐energy metal to ligand charge transfer (MLCT) transition in these complexes involves electron transfer from ruthenium as well as the halide/pseudohalide ligand to the polypyridyl ligand. The contribution of the halide/pseudohalide ligand(X) to the HOMO affects the total amount of charge transferred to the polypyridyl ligand and hence the photoconversion efficiency. The virtual orbitals involved in the second MLCT transition in 4,4′‐dicarboxy‐2,2′‐bipyridine complexes have higher electron density on the ? COOH group compared to the lowest unoccupied molecular orbital and hence a stronger electronic coupling with the TiO₂ surface and higher injection efficiency at shorter wavelengths. In comparison, the virtual orbitals involved in the second MLCT transition in 5,5′‐dicarboxy‐2,2′‐bipyridine complexes have lesser electron density on the ? COOH group, leading to a weaker electronic coupling with the TiO₂ surface and therefore lower efficiency for electron injection at shorter wavelengths for these complexes. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Use of addition theorems in evaluation of multicenter nuclear-attraction and electron-repulsion integrals with integer and noninteger n Slater-type orbitals

Multicenter integrals appearing in the Hartree–Fock–Roothaan equations for molecules are calculated using different kinds of series expansion formulas obtained from the expansions of integer and noninteger n Slater-type orbitals, in terms of Ψ ^α -exponential-type orbitals (where α=1, 0, –1, –2,...) at a displaced center, that form complete orthonormal sets and are represented by linear combinations of integer n Slater-type orbitals. The convergence of these series is tested by calculating concrete cases. The accuracy of the results is quite high for quantum numbers, screening constants, and location of orbitals. Received: 13 February 2002 / Accepted: 11 March 2002 / Published online: 4 July 2002     

Electron correlation effects on the shape of the Kohn–Sham molecular orbital

Even systems in which strong electron correlation effects are present, such as the large near-degeneracy correlation in a dissociating electron pair bond exemplified by stretched H₂, are represented in the Kohn–Sham (KS) model of non-interacting electrons by a determinantal wavefunction built from the KS molecular orbitals. As a contribution to the discussion on the status and meaning of the KS orbitals we investigate, for the prototype system of H₂ at large bond distance, and also for a one-dimensional molecular model, how the electron correlation effects show up in the shape of the KS σ _g orbital. KS orbitals φ^HL and φ^FCI obtained from the correlated Heitler-London and full configuration interaction wavefunctions are compared to the orbital φ^LCAO, the traditional linear combination of atomic orbitals (LCAO) form of the (approximate) Hartree-Fock orbital. Electron correlation manifests itself in an essentially non-LCAO structure of the KS orbitals φ^HL and φ^FCI around the bond midpoint, which shows up particularly clearly in the Laplacian of the KS orbital. There are corresponding features in the kinetic energy density t _s of the KS system (a well around the bond midpoint) and in the one-electron KS potential v _s (a peak). The KS features are lacking in the Hartree-Fock orbital, in a minimal LCAO approximation as well as in the exact one. Received: 11 December 1996 / Accepted: 10 January 1997     

Ab initio study of the transition-metal carbene cations

The geometries and bonding characteristics of the first-row transition-metal carbene cations MCH_2~ were investigated by ab initio molecular orbital theory (HF/LANL2DZ). All of MCH_2~ are coplanar. In the closed shell structures the C bonds to M with double bonds; while in the open shell structures the partial double bonds are formed, because one of the σ and π orbitals is singly occupied. It is mainly the π-type overlap between the 2p_x orbital of C and 4p_x, 3d_(xz), orbitals of M~ that forms the π orbitals. The dissociation energies of C—M bond appear in periodic trend from Sc to Cu. Most of the calculated bond dissociation energies are close to the experimental ones.     

Analysis of chemical bonding in C2 using Dyson orbitals

Multireference configuration interaction wave functions with single and double excitations were calculated for the ¹Σ⁺_g ground state of the C₂ molecule and the excited states of C⁺₂ with symmetries ²Σ⁺_g, ²Σ^-_u, ²Π_u, and ²Π_g. The corresponding σ_g, σ_u, π_u, and π_g valence Dyson orbitals were calculated. Most of the density due to the valence electrons is accounted for by three σ_g, one σ_u, and one degenerate pair of π_u Dyson orbitals. Electron correlation plays an important role in the bond strength of C₂ by increasing the occupation of the σ_g valence orbitals and decreasing the occupation of the σ_u and π_u valence orbitals. © 1996 John Wiley & Sons, Inc.     

A new algorithm for inactive orbital optimization in valence bond theory

This paper presents an efficient algorithm for energy gradients in valence bond self-consistent field (VBSCF) method with non-orthogonal orbitals. The frozen core approximation method is extended to the case of non-orthogonal orbitals. The expressions for the total energy and its gradients are presented by introducing auxiliary orbitals, where inactive orbitals are orthogonal, while active orbitals are non-orthogonal themselves but orthogonal to inactive orbitals. It is shown that our new algorithm has a low scaling of (N _a + 1)m ⁴, where N _a and m are the numbers of the active orbitals and basis functions, respectively, and is more efficient than the existing VBSCF algorithms.     

Metallomacrocycle (MacM) complex with cyanide as bridged ligand: Electronic structures of [MacMCN]n

The electronic structures of complexes and one‐dimensional metallomacrocycles with cyanide as bridged ligand, such as [MacM(CN)₂]^? and [MacM(CN)]_n [Mac=phthalocyanine, tetrabenzoporphyrine; M=Co(III), Rh(III)] have been investigated using density functional theory. The results of this study show that the intrinsic semiconductivity properties depend on the frontier bands. The valence band is composed by the π‐macrocycle orbital. The conduction band for the cobalt polymers is a mixture of orbitals between this metal and the cyanide ligand along of the stacking direction. However, in the rhodium polymers such a band is exclusively composed of the π* system of the macrocycles. © 2002 John Wiley & Sons, Inc. Int J Quantum Chem, 2002     

Unrestricted CNDO-MO calculations. II. MnO 4 2− and CrO 4 3−

The electronic structures of the tetrahedral molecule ions MnO ₄ ^2– and CrO ₄ ^3– have been investigated within an unrestricted CNDO-MO approximation [Theoret. Chim. Acta (Berl.)20, 317 (1971)]. Calculations assuming the unpaired electron occupies the 3a ₁, 2e, and 4t2 molecular orbitals indicate that the 3a ₁ and2e orbitals have similar orbital energies and that the 4t ₂ orbital is at a higher energy. The experimentally indicated2e orbital for the unpaired electron is obtained with expanded O^1– type atomic orbitals for oxygen and valence metal orbitals of the expanded 3d and plus one ion 4p types. The metal 4s orbitals must be held to the neutral atom type. The optimum valence orbitals above with a slightly contracted 4s type metal orbitals yield the minimum total energy and places the unpaired electron in the 3a ₁ orbital. Since the contracted 4s metal orbital produces results that are not in agreement with experimental data, the method used apparently does not adequately take into account the increased electron-electron repulsions that contracted 4s orbitals produce.     

Extended Hartree–Fock calculations for the helium ground state

The extended Hartree–Fock (EHF) wave function of an n-electron system is defined (Löwdin, Phys. Rev. 97 , 1509 (1955)) as the best Slater determinant built on one-electron spin orbitals having a complete flexibility and projected onto an appropriate symmetry subspace. The configuration interaction equivalent to such a wavefunction for the ¹S state of a two-electron atom is discussed. It is shown that there is in this case an infinite number of solutions to the variational problem with energies lower than that of the usual Hartree–Fock function, and with spin orbitals satisfying all the extremum conditions. Two procedures for obtaining EHF spin orbitals are presented. An application to the ground state of Helium within a basic set made up of 4(s), 3(p₀), 2(d₀) and 1 (f₀) Slater orbitals has produced 90% of the correlation energy.     

Convergence of the partial wave expansion of the He ground state

The configuration interaction (CI) method, using a very large Laguerre orbital basis, is applied to the calculation of the He ground state. The largest calculations included a minimum of 35 radial orbitals for each ? ranging from 0 to 12, resulting in basis sets in excess of 400 orbitals. The convergence of the energy and electron–electron δ‐function with respect to J (the maximum angular momenta of the orbitals included in the CI expansion) were investigated in detail. Extrapolations to the limit of infinite angular momentum using expansions of the type ΔX_J = A_X[J + 1/2]^?p + B_X[J + 1/2]^?p?1 + …, gave an energy accurate to 10^?7 Hartree and a value of 〈δ〉 accurate to about 0.5%. Improved estimates of 〈E〉 and 〈δ〉, accurate to 10^?8 Hartree and 0.01%, respectively, were obtained when extrapolations to an infinite radial basis were done prior to the determination of the J → ∞ limit. Round‐off errors were the main impediment to achieving even higher precision, since determination of the radial and angular limits required the manipulation of very small energy and 〈δ〉 differences. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

A configuration interaction study of the spin dipole-dipole parameters for formaldehyde and methylene

The electron spin dipole-dipole contribution to the zero field splitting has been evaluated for the ³A₂ (n → π*) and ³A₁ (π → π*) states of formaldehyde using a CI wave function constructed from contracted Gaussian-lobe functions. The values D = 0.539 cm^?1 and E = 0.031 cm^?1 were obtained for the ³A₂(n → π*) state and D = ?0.588 cm^?1 and E = 0.058 cm^?1 were obtained for the ³A₁ (π → π*) state using the CI wave function constructed from SCF orbitals of the respective parent configurations. An analysis of the effect of CI on the parameters is given for the ³A₂ (n n → π*) state of formaldehyde and the ³B₁ ground state of methylene. Numerical results are given which show that internally consistent self-consistent field orbitals (ICSCF ) are superior to canonical SCF orbitals as a starting point for a CI calculation. Our CI wave function for the ¹A₁ ground state gave an energy of ?114.13658 hartrees which is significantly lower than any previously reported energy calculation. This wave function gives a dipole moment of 2.22 Debye (C⁺O^?) in good agreement with the experimental value of 2.33 ± 0.02 Debye.     

锂离子电池镍掺杂尖晶石LiMn2O4正极材料的电子结构

采用密度泛甬平面波赝势方法对LiMn2O4和LiNi0.5Mn1.5O4的几何结构进行了优化,并计算了相应的电子结构.计算的结果表明:在Li 脱嵌前后,LiMn2O4和LiNi0.5Mn1.5O4均为导体,且锂元素主要以离子形式存在于两种材料中,O2p轨道与Mn(Ni)的3d轨道形成了较强的共价键.Li 嵌入导致Mn(Ni)3d轨道的态密度峰发生移动.Ni的掺杂导致Mn(Ni)和O2p轨道的成键作用得以加强,电子在Mn(Ni)3d轨道的填充发生变化,从而提高了电池的充放电电压.     

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.     

Theoretical analysis of the electronic structure and reactivity of the CoP3 core in [(triphos)CoP3]

Summary The electronic structure and reactivity of the compound [(triphos)-CoP₃] [triphos=1, 1, 1-tris(diphenylphosphinomethyl)ethane] have been investigated using the semiempirical, extended Hückel (EH) approach, and density functional theory (DFT). The calculations have been performed on the model complex [(PH₃)₃CoP₃]. The orientation of the P₃ ring with respect to the (triphos)Co unit and electrophilic addition reactions have been investigated within the local density approximation (LDA). The staggered and eclipsed conformations of the P₃ group have been found to have comparable energies and the molecule is stabilized by a strong interaction within thee atomic orbitals (C_3v symmetry) mainly involving the 3p _z orbitals of phosphorus and 3d _xz and 3d _yz hybrid metal orbitals. Using H⁺ as the electrophilic reagent four preferential sites of attack have been probed. The optimized structure of the most stable arrangement of the adduct corresponds to that experimentally observed in the monopositive cation [(triphos)CoP₃H]⁺, which was obtained by protonation of the neutral species. The arrangements of two other favourable sites for the attack correspond to the geometries observed in the derivatives obtained by the electrophilic additions of CH ₃ ⁺ and, respectively, HgCH ₃ ⁺ . The geometry of the model complex [(PH₃)₃Co(P₃CH₃)]⁺ has been optimized using DFT-LDA and compared to that of [(triphos)Co(P₃CH₃)]⁺.     

Molecular shape,shape of the geometrically active atomic states,and hybridization

In a recent publication [C. A. Nicolaides and Y. Komninos, Int. J. Quant. Chem. 67 , 321 (1998)], we proposed that in certain classes of molecules the fundamental reason for the formation of covalent polyatomic molecules in their normal shape is to be found in the existence of a geometrically active atomic state (GAAS) of the central atom, whose shape, together with its maximum spin‐and‐space coupling to the ligands, predetermines the normal molecular shape (NMS). The shape of any atomic state was defined as that which is deduced from the maxima of the probability distribution ϱ(cos θ₁₂) of the angle formed by the position vectors of two electrons of an N‐electron atom. Because the shape of the GAAS determines the NMS and because the NMS allows the construction of corresponding hybrid orbitals, we examined and discovered the connection between the GAAS shape and Pauling's function for the strength of two equivalent orthogonal orbitals at angle θ₁₂ with one another. It is shown that the computed ϱ(cos θ₁₂) of the GAAS can be cast in a form which allows the deduction of the composition of the hybrid orbitals of maximum spin states with configurations sp³, sp³d⁵, sp³d⁵f⁷, slⁿ, s²lⁿ and the demonstration of the central atom's tendency to form bonds in directions which coincide with the nodal cones of the hybrid bond orbitals. These results not only reinforce the validity of the theory as to the fundamental “mechanism” for the formation in the normal shape of coordination compounds and covalently bonded polyatomic molecules, but also provide the justification for the relevance and importance of the hybridization model. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 71: 25–34, 1999     

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     

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.     

Radical Anion of Azuleno[5.6.7-cd]phenalene,a Failure of the Simple HMO Model

Hyperfine proton coupling constants are reported for the radical anions of azuleno-[5.6.7-cd]phenalene (I), 6-phenylazulene (II) and the corresponding 1,3-dideuterio-derivatives (I-d₂ and II-d₂). The singly occupied orbitals of both I^? and II^? are found to be symmetric with respect to the mirror plane perpendicular to the plane of the molecule. In the case of I, surprisingly, such an orbital corresponds not to the first, but to the second lowest antibonding HMO. A correlation diagram for the relevant orbitals of I and II indicates that the correct energy order in the HMO model of I can be achieved by a decrease in the absolute value of the parameter β_μν for the bonds 4a–5, 6–6a, 9a–10 and 11–11a.     

Octacarbonyl Anion Complexes of Group Three Transition Metals [TM(CO)8]− (TM=Sc,Y, La) and the 18‐Electron Rule

We report the gas‐phase synthesis of stable 20‐electron carbonyl anion complexes of group 3 transition metals, TM(CO)₈⁻ (TM=Sc, Y, La), which are studied by mass‐selected infrared (IR) photodissociation spectroscopy. The experimentally observed species, which are the first octacarbonyl anionic complexes of a TM, are identified by comparison of the measured and calculated IR spectra. Quantum chemical calculations show that the molecules have a cubic (O_h) equilibrium geometry and a singlet (¹A_1g) electronic ground state. The 20‐electron systems TM(CO)₈⁻ are energetically stable toward loss of one CO ligand, yielding the 18‐electron complexes TM(CO)₇⁻ in the ¹A₁ electronic ground state; these exhibit a capped octahedral structure with C_3v symmetry. Analysis of the electronic structure of TM(CO)₈⁻ reveals that there is one occupied valence molecular orbital with a_2u symmetry, which is formed only by ligand orbitals without a contribution from the metal atomic orbitals. The adducts of TM(CO)₈⁻ fulfill the 18‐electron rule when only those valence electrons that occupy metal–ligand bonding orbitals are considered.     

Octacarbonyl Anion Complexes of Group Three Transition Metals [TM(CO)8]− (TM=Sc,Y, La) and the 18‐Electron Rule

We report the gas‐phase synthesis of stable 20‐electron carbonyl anion complexes of group 3 transition metals, TM(CO)₈^? (TM=Sc, Y, La), which are studied by mass‐selected infrared (IR) photodissociation spectroscopy. The experimentally observed species, which are the first octacarbonyl anionic complexes of a TM, are identified by comparison of the measured and calculated IR spectra. Quantum chemical calculations show that the molecules have a cubic (O_h) equilibrium geometry and a singlet (¹A_1g) electronic ground state. The 20‐electron systems TM(CO)₈^? are energetically stable toward loss of one CO ligand, yielding the 18‐electron complexes TM(CO)₇^? in the ¹A₁ electronic ground state; these exhibit a capped octahedral structure with C_3v symmetry. Analysis of the electronic structure of TM(CO)₈^? reveals that there is one occupied valence molecular orbital with a_2u symmetry, which is formed only by ligand orbitals without a contribution from the metal atomic orbitals. The adducts of TM(CO)₈^? fulfill the 18‐electron rule when only those valence electrons that occupy metal–ligand bonding orbitals are considered.