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     

Molecular electric properties in electronic excited states: multipole moments and polarizabilities of H2O in the lowest1 B 1 and3 B 1 excited states

Summary The dipole and quadrupole moments and the dipole polarizability tensor components are calculated for the¹ B ₁ and³ B ₁ excited states of the water molecule by using the complete active space (CAS) SCF method and an extended basis set of atomic natural orbitals. The dipole moment in the lowest¹ B ₁ (0.640 a.u.) and³ B ₁ (0.416 a.u.) states is found to be antiparallel to that in the ground electronic state of H₂O. The shape of the quadrupole moment ellipsoid is significantly modified by the electronic excitation to both states investigated in this paper. All components of the excited state dipole polarizability tensor increase by about an order of magnitude compared to their values in the ground electronic state. The present results are used to discuss some aspects of intermolecular interactions involving molecules in their excited electronic states.     

Absorption spectrum of manganian andalusite: Cluster calculation by an ab initio method

The ground state and the first few excited states of an MnO₆^9? cluster are calculated in the unrestricted Hartree–Fock model. The state ordering is ⁵B_{1 g}, ⁵A_{1 g}, ⁵B_{2 g}, and ⁵E_g as can be expected from simpler models. Consistent with the results by the same method for copper complexes, we obtain d–d transition energies about one half or less of the experimental energies. The charge transfer spectrum is subject to a large spin polarization in the sense that the lowest charge transfer state (⁵E_u) has five unpaired spins on Mn.     

Semiempirical local spin: Theory and implementation of the ZILSH method for predicting Heisenberg exchange constants of polynuclear transition metal complexes

The local spin formalism ( 3 ) for computing expectation values 〈S_A · S_B〉 that appear in the Heisenberg spin model has been extended to semiempirical single determinant wave functions. An alternative derivation of expectation values in restricted and unrestricted cases is given that takes advantage of the zero differential overlap (ZDO) approximation. A formal connection between single determinant wave functions (which are not in general spin eigenfunctions) and the Heisenberg spin model was established by demonstrating that energies of single determinants that are eigenfunctions of the local spin operators with eigenvalues corresponding to high‐spin radical centers are given by the same Heisenberg coupling constants {J_AB} that describe the true spin states of the system. Unrestricted single determinant wave functions for transition metal complexes are good approximations of local spin eigenfunctions when the metal d orbitals are local in character and all unpaired electrons on each metal have the same spin (although spins on different metals might be reversed). Good approximations of the coupling constants can then be extracted from local spin expectation values 〈S_A · S_B〉 energies of the single determinant wave functions. Once the coupling constants are obtained, diagonalization of the Heisenberg spin Hamiltonian provides predictions of the energies and compositions of the spin states. A computational method is presented for obtaining coupling constants and spin‐state energies in this way for polynuclear transition metal complexes using the intermediate neglect of differential overlap Hamiltonian parameterized for optical spectroscopy (INDO/S) in the ZINDO program. This method is referred to as ZILSH, derived from ZINDO, Davidson's local spin formalism, and the Heisenberg spin model. Coupling constants and spin ground states obtained for 10 iron complexes containing from 2 to 6 metals are found to agree well with experimental results in most cases. In the case of the complex [Fe₆O₃(OAc)₉(OEt)₂(bpy)₂]⁺, a priori predictions of the coupling constants yield a ground‐state spin of zero, in agreement with variable‐temperature magnetization data, and corroborate spin alignments proposed earlier on the basis of structural considerations. This demonstrates the potential of the ZILSH method to aid in understanding magnetic interactions in polynuclear transition metal complexes. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

Ab initio calculations on urea

Multiconfiguration wave functions constructed from contracted Gaussian-lobe functions have been found for the ground and valence-excited states of urea. ICSCF molecular orbitals of the excited states were used as the parent configurations for the CI calculations except for the ¹A₁(π → π*) state. The ¹A₁(π → π*) state used as its parent configuration an orthogonal linear combination of natural orbitals obtained from the second root of a three-configuration SCF calculation. The lowest excited states are predicted to be the n π → π* and π → π* triplet states. The lowest singlet state is predicted to be the n π → π* state with an energy in good agreement with the one known UV band at 7.2 eV. The π → π* singlet state is predicted to be about 1.9 eV higher, contrary to several previous assignments which assumed the lowest band was a π → π* amide resonance band. The predicted ionization energy of 9.0 eV makes this and higher states autoionizing.     

Potential energy surfaces for OsH2

Summary We compute the potential energy surfaces of 12 electronic states of OsH₂ (four quintet, four triplet, and four singlet) arising from⁵ D ground state of the Os atom as well as triplet and singlet excited states using the complete active space multiconfiguration self-consistent field (CAS-MCSCF) followed by multireference configuration interaction (MRCI) and relativistic CI (RCI) calculation which include up to 430,000 configurations. We find that the⁵ D ground state of Os atom does not insert into H₂ while the excited³ F state of Os does. The³ B ₁ ground state of OsH₂ (there are two other nearly degenerate states) in the absence of spin-orbit coupling was found to be 22 kcal/mol more stable than Os(⁵ D)+H₂. The spin-orbit mixing of³ B ₁,³ B ₂,³ A ₂, and¹ A ₁ states was so strong that it induces significant change in bond angles (up to 10°) for OsH₂.Dedicated to Prof. Klaus RuedenbergCamille and Henry Dreyfus Teacher-Scholar     

Theoretical evidence for bound electronic excited states of ozone

Extensive configuration interaction calculations (up to 1532 spin eigenfunctions) have been carried out on ozone with both minimal and extended bases. Vertical and adiabatic excitation energies to 14 excited states are reported, including seven states with vertical excitation energies less than 4 eV. Our calculations indicate that in addition to the ground state there are four other states of ozone (³B₂, ³A₂, ¹A₂ and ³B₁) bound with respect to dissociation to ground state O₂ and O (by 0.4, 0.3, 0.1 and 0.0 eV, respectively). With such small bonding energies, the current results cannot be said to show definitively (except perhaps for ³B₂) these four states to be bound with respect to O₂ + O. However, the theoretical evidence is sufficiently strong as to warrant careful experimental studies. Such bound excited electronic states could play important roles in the chemistry of the upper atmosphere and in the chemistry of oxygen discharge systems. One (or more) of these states may be responsible for the short-lived intermediate (‘ozone precursor’) recently observed in oxygen radiolysis.     

Bonding in the ground state and excited states of copper-alkene complexes

The ground state and ¹B₂ excited state of Cu(C₂H₄)⁺ and of CuX(C₂H₄) (X  F, Cl) have been investigated by the Hartree-Fock-Slater (HFS) method. The main metal-ligand interactions in the ground state are ethene π → Cu 4s donation and Cu 3d_π → ethene π^* backdonation, which have comparable contributions to the metal-ligand bond strength. The excitation of CuX(C₂H₄) does not involve an alkene π → metal charge transfer (LMCT), but instead is metal 3d → alkene π^* charge transfer (MLCT) in character. The implications for the photochemistry of olefin-copper(I) complexes are discussed.     

High‐spin behavior of molecular crystals and extended π systems

The qualitative rules for the existence of high‐spin ground states in extended systems and molecular crystals are examined here on a firmer theoretical footing. Extended systems have been categorized into three groups, namely, type I, type II, and type III, depending on the type of bonding interactions. The general form of the spin Hamiltonian operators have been written down. The active spaces have been restricted to the minimum size for each of these three types of spin systems. The zeroth‐order state vectors and the Hartree–Fock ground‐state energies have been identified for unit species of each type. The extended system Hamiltonian operators are further truncated in such a way that only the nearest‐neighbor interactions are retained. Expressions have been derived for the energy gap from a molecular orbital approach. The relatively small effects of electron correlation on the energy gaps have been estimated for the type I systems, which belong to the systems of solid‐state physics. In particular, it has been shown that for the type I systems the singlet–triplet gap, and hence the ferromagnetic coupling constant, primarily depends upon the difference of one‐electron kinetic energies and not on the two‐electron exchange integrals. This result agrees with the concept of kinetic exchange that was introduced in the context of a resonating valence‐bond formalism. Type II systems are exemplified by extended systems that can be prepared from conjugated molecules while organic molecular crystals form examples of type III species. For these systems, however, the Coulomb exchange interaction has been shown to dominate the energy gap. A quick review of the Heisenberg spin Hamiltonian for the H₂ molecule is sufficient to point out that the sign of the calculated ferromagnetic coupling constant depends on the method of calculation, the nature of the basis set, and the bond length. This is amply supported by ab initio calculations on this species. Numerical data have also been obtained from computations on m‐phenylene‐coupled nitroxy radicals and stacks of α‐nitronyl nitroxide, but these calculations have been based on a semiempirical quantum chemical methodology (INDO) since some of the species involved are exceedingly large. Computed energy gaps are in good agreement with experimental and other theoretical (AM1, PM3) results. Nevertheless, for the dimer, trimer, tetramer, and pentamer of the type II specimen, the important π orbitals are far from being degenerate. The quantitative results clearly deviate from the criterion of degeneracy that was suggested from qualitative theories for the existence of a high‐spin ground state. Therefore, the criteria for the existence of high spins have been reformulated in terms of the monomer orbitals. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 79: 308–324, 2000     

Studies on the singlet and triplet states of unsaturated carbenes

Quantum chemical calculations and studies have been made on the different spin states of unsaturated carbenes X₂C?C: and X₂C?C?C: (X?H, Li, F). The geometries and relative stabilities of these carbenes with various groups X have been outlined. The ground states of unsaturated carbenes are all singlet. The energy splittings between the ground states and first excited states ΔE (¹A₁-³B₁) are generally within the value of 60 kcal/mol and change greatly with the electronegativities of groups X, but little with the sizes of the cumulidenes. The equilibrium conformations of ¹A₁ and ³B₁ are different.     

STEREOELECTRONIC PROPERTIES OF PHOTOSYNTHETIC AND RELATED SYSTEMS—VII. AB INITIO QUANTUM MECHANICAL CHARACTERIZATION OF THE ELECTRONIC STRUCTURE AND SPECTRA OF CHLOROPHYLLIDE a AND BACTERIOCHLOROPHYLLIDE a CATION RADICALS

Abstract— Ab initio configuration interaction wavefunctions and energies are reported for 29 doublet states and three quartet states of the cation radicals of ethyl chlorophyllide a (Et-Chl a⁺) and ethyl bacteriochlorophyllide a (Et-BChl a⁺). In Et-Chl a.⁺ I the lowest excited doublet state D₁ is estimated to lie 5220 cm^-1 above the ground state D₀, with a negligibly small D₁← D₀ transition probability. The lowest quartet state, Q₁, is estimated to lie 7980 cm^-1 above D₁. The absorption spectrum up to 20,000cm^-1 is shown to consist primarily of numerous low-intensity ‘background’ transitions, with transitions to D₅ and D₁₁ accounting for the observed peaks at 12,200cm^-1 and 17,500cm^-1, respectively. The large intense band at 25,000cm^-1 is due primarily to transitions to D₂₂ and D₂₃, with numerous lower-intensity transitions to neighboring states. In Et-BChl a.⁺ D₁ is estimated to lie 7112 cm-¹ above D₀, and Q, is approximately 5725 cm^-1 above D. A pair of states, D₃ and D₅, account for the absorption at 11,000 cm^-1, while another pair of states, D₁₃ and D₁₄, are associated with the broad, weak absorption near 20,000 cm^-1. The two prominent intense peaks at 23,700 cm^-1 and 27,700 cm^-1 are assigned to D₂₃ and D₂₈, respectively, while the shoulder located at 25,500cm^-1 is attributed to transitions to D₂₄ and D₂₆. As in Et-Chl at, numerous background transitions are found throughout the spectrum. The π spin density distribution in D₀ of both molecules is similar, with spin density found predominantly on the α-carbon atoms. In both systems, approximately 65% of the π spin density in D₁ is found on the methine carbon atoms, with the remainder found largely on the nitrogen atoms.     

Half-metallic ferromagnetism in Ag-doped ZnO: An ab initio study

The spin-resolved electronic structures of ZnO doped with 6.25% Ag have been studied with the first-principles calculations based on the spin density functional theory. The substitutional Ag impurities and their nearest neighbor O atoms are shown to be in a spin polarized state with a global magnetization of 1.0μ_B. Ag-doped ZnO is in a ferromagnetic ground state which can be explained by Zener's double exchange mechanism. Furthermore, band structure calculations show a half-metallic behavior of the Ag-doped ZnO. These results indicate that Ag-doped ZnO shows promise as a dilute magnetic semiconductor free of magnetic precipitation and may find applications in the field of spintronics.     

Theoretical study on S<Subscript>1</Subscript>(<Superscript>1</Superscript>B<Subscript>3u</Subscript>) state electronic structure and absorption spectrum of pyrazine

Making use of a set of quantum chemistry methods, the harmonic potential surfaces of the ground state (S₀(¹ A _g)) and the first (S₁(¹ B _3u)) excited state of pyrazine are investigated, and the electronic structures of the two states are characterized. In the present study, the conventional quantum mechanical method, taking account of the Born-Oppenheimer adiabatic approximation, is adopted to simulate the absorption spectrum of S₁(¹ B _3u) state of pyrazine. The assignment of main vibronic transitions is made for S₁(¹ B _3u) state. It is found that the spectral profile is mainly described by the Franck-Condon progression of totally symmetric mode ν_6a. For the five totally symmetric modes, the present calculations show that the frequency differences between the ground and the S₁(¹ B _3u) state are small. Therefore the displaced harmonic oscillator approximation along with Franck-Condon transition is used to simulate S₁(¹ B _3u) absorption spectra. The distortion effect due to the so-called quadratic coupling is demonstrated to be unimportant for the absorption spectrum, except the coupling mode ν_10a. The calculated S₁(¹ B _3u) absorption spectrum is in reasonable agreement with the experimental spectra. Supported by Taiwan National Science Council (Grant Nos. NSC 96-2113-M-009-021 and NSC 96-2811-M-009-023)     

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.     

A density matrix renormalization group study of low-lying excitations of polythiophene within a Pariser-Parr-Pople model

Symmetrized density-matrix-renormalization-group calculations have been carried out, within Pariser-Parr-Pople Hamiltonian, to e_xplore the nature of the ground and low-lying e_xcited states of long polythiophene oligomers. We have e_xploitedC ₂ symmetry and spin parity of the system to obtain e_xcited states of experimental interest, and studied the lowest dipole allowed e_xcited state and lowest dipole forbidden two photon state, for different oligomer sizes. In the long system limit, the dipole allowed e_xcited state always lies below the lowest dipole forbidden two-photon state which implies, by Kasha rule, that polythiophene fluoresces strongly. The lowest triplet state lies below two-photon state as usual in conjugated polymers. We have doped the system with a hole and an electron and obtained the charge e_xcitation gap and the binding energy of the 1¹B _u ⁻ exciton. We have calculated the charge density of the ground, one-photon and two-photon states for the longer system size of 10 thiophene rings to characterize these states. We have studied bond order in these states to get an idea about the equilibrium e_xcited state geometry of the system. We have also studied the charge density distribution of the singly and doubly doped polarons for longer system size, and observe that polythiophenes do not support bipolarons. Dedicated to Prof J Gopalakrishnan on his 62nd birthday.     

Electronic states and nature of the chemical bond in the molecule CrC by all-electron ab initio calculations

All-electron ab initio Hartree–Fock (HF ), valence configuration interaction (CI ), and multiconfiguration self-consistent-field (CASSCF ) calculations have been applied to investigate the electronic states of the CrC molecule. The molecule is predicted as having four low-lying electronic states, ³∑^?, ⁵∑^?, ⁷∑^?, and ⁹∑^?, separated by an energy gap of 0.55 eV from the next higher-lying state, ¹∑^?, which is followed by the states ⁵Π and ⁷Π. The four lowest-lying electronic states are due to the coupling of the angular momenta of the ⁶S_g Cr⁺ ion with those of the ⁴S_u C^? anion. The chemical bond in the ³∑^? ground state can be viewed as a quadruple bond composed of two σ and two π bonds. One σ bond is due to the formation of a molecular orbital that is doubly occupied. The remaining bonds, i.e., one σ and two π bonds, arise from valence-bond couplings. The π bonds originate from the valence-bond couplings of the electrons in the C 2pπ orbitals with those in the Cr 3dπ orbitals. The σ bond originates from the valence-bond coupling of the C 2pσ electron with an electron in the Cr 4s, 4p hybrid that is polarized away from the C atom.     

Combining Open-Shell Verdazyl Environment and Co(II) Spin-Crossover: Spinmerism in Cobalt Oxoverdazyl Compound

The spin states of a Co(II) oxoverdazyl compound are investigated by means of wavefunction-based calculations. Within a ca. 233 K energy window, the ground state and excited states display a structure-sensitive admixture of low-spin S_M=1/2 in a dominant high-spin S_M=3/2 Co(II) ion as indicated by the localized molecular orbitals. The puzzling spin zoology that results from the coupling between open-shell radical ligands and a spin-crossover metal ion gives rise to this unusual scenario, which extends the views in molecular magnetism. In agreement with experimental observation, the low-energy spectroscopy is very sensitive to deformations of the coordination sphere, and a growing admixture of Co(II) low-spin is evidenced from the calculations. In analogy with mesomerism that accounts for charge delocalization, entanglement combines different local spin states to generate a given total spin multiplicity, a spinmerism phenomenon.     

Synthesis and Magnetic Properties of (Pyrrolidin‐1‐oxyl)–(Nitronyl Nitroxide)/(Iminonitroxide)‐Dyads

Unlike extensively studied diradicals linked by π‐conjugated systems, only a few studies have investigated weakly coupled diradicals linked by an sp³ carbon atom. Herein, we prepared pyrrolidin‐1‐oxyl–(nitronyl nitroxide)‐dyad 5 and pyrrolidin‐1‐oxyl–iminonitroxide‐dyad 6 . From the observed temperature dependence of the magnetic susceptibility, 5 and 6 were determined to be in singlet ground states with 2J_intra/k_B=?35.2 K and ?13.6 K, respectively. From these results and theoretical calculations of related diradicals, the spin‐polarization model counting the small spin density of the sp³ carbon atom could be used as a spin‐prediction model.     

A Valence Bond Study of the Low‐Lying States of the NF Molecule

The electronic structures of the three lowest‐lying states of NF are investigated by means of modern valence bond (VB) methods such as the VB self‐consistent field (VBSCF), breathing orbital VB (BOVB), and VB configuration interaction (VBCI) methods. The wave functions for the three states are expressed in terms of 9–12 VB structures, which can be further condensed into three or four classical Lewis structures, whose weights are quantitatively estimated. Despite the compactness of the wave functions, the BOVB and VBCI methods reproduce the spectroscopic properties and dipole moments of the three states well, in good agreement with previous computational studies and experimental values. By analogy to the isoelectronic O₂ molecule, the ground state ³Σ^? possesses both a σ bond and 3‐electron π bonds. However, here the polar σ bond contributes the most to the overall bonding. It is augmented by a fractional (19 %) contribution of three‐electron π bonding that arises from π charge transfer from fluorine to nitrogen. In the singlet ¹Δ and ¹Σ⁺ excited states the π‐bonding component is classically covalent, and it contributes 28 % and 37 % to the overall bonding picture for the two states, respectively. The resonance energies are calculated and reveal that π bonding contributes at least 24, 35 and 42 kcal mol^?1 to the total bonding energies of the ³Σ^?, ¹Δ and ¹Σ⁺ states, respectively. Some unusual properties of the NF molecule, like the equilibrium distance shortening and bonding energy increasing upon excitation, the counterintuitive values of the dipole moments and the reversal of the dipole moments as the bond is stretched, are interpreted in the light of the simple valence bond picture. The overall polarity of the molecule is very small in the ground state, and is opposite to the relative electronegativity of N vs F in the singlet excited states. The values of the dipole moments in the three states are quantitatively accounted for by the calculated weights of the VB structures.