Hylleraas' variational method with orthogonality restrictions.

In this paper, we suggest a new computational technique for the minimization of Hylleraas' functional with additional orthogonality restrictions imposed on the desired vectors. It is shown how Hylleraas' constrained problem can be reduced to an unconstrained one by minimal computational efforts. The asymptotic projection (AP) method proposed earlier to minimize Rayleigh's quotient subject to some orthogonality restrictions is applied to construct a modified Hylleraas' functional whose solution fulfills the required constraints automatically. Specifically, equivalence between the original problem and the one for the modified Hamilton operator is derived. It is shown that the AP methodology allows additional restrictions to be treated in a unified approach for both Rayleigh's quotient and Hylleraas' functional. Specific features of the method are demonstrated on the electronic parallel polarizability of H2+. Some emphasis is put on the choice of specific distributed basis set adapted for polarizability computation. A comparison with other methods, considered exact or extremely accurate, is also given.

On the orthogonality of states with approximate wavefunctions.

A variational solution to the eigenvalue problem for the Hamiltonian H, with orthogonality restrictions on eigenvectors of H to the vector H ∣ Φ0〉, where ∣Φ0〉 is an approximate ground-state vector, is proposed as a means to calculate excited states. The asymptotic projection (AP) method proposed previously is further developed and applied to solve this problem in a simple way. We demonstrate that the AP methodology does not require an evaluation of the matrix elements of operator H2, whereas conventional approaches-such as the elimination of off-diagonal Lagrange multipliers method, projection operator techniques, and other methods-do. It is shown, based on the results obtained for the single-electron molecular ions H2+, HeH2+, and H32+, that applying the new method to determine excited-state wavefunctions yields the upper bounds for excited-state energies. We demonstrate that regardless of whether the orthogonality constraint for states (〈Φ| Φ0〉 = 0) is applied, the zero-coupling constraint (〈Φ| H| Φ0〉 = 0) is imposed, or both of these restrictions are enforced simultaneously, practically the same excited-state energy is obtained if the basis set is almost complete. For the systems considered here, all schemes are capable of giving a sub-µhartree level of accuracy for the ground and excited states computed with different basis sets.

Novel quinoxalinone-based push-pull chromophores with highly sensitive emission and absorption properties towards small structural modifications.

The photophysical properties of a series of novel push-pull quinoxalinone-based chromophores that strongly absorb and emit light in the broad visible spectrum were comprehensively studied both experimentally and through quantum chemical methods. The drastic influence of the position of the electron-donor dimethylaminostyryl (DMAS) in the quinoxalinone core on its absorption and emission intensities as well as on the solvatochromic behavior of the concerned isomers has been established. No dependence of the photophysical properties of the chromophores on the conformation of the DMAS group was found. Quantum chemical computations provided a reliable theoretical rationalization of the observed spectral features, in particular, the important one related to Stokes shift. The local or intramolecular charge-transfer (ICT) character of the key electronic transitions has been assessed using a quantitative natural transition orbitals analysis and based on the novel topological descriptors of the electronic density rearrangement. This study shows that the ICT effects are not the primary factors contributing to the drastic difference in the emission efficiency of push-pull chromophores that are structurally very similar.

Probing halogen-halogen interactions in solution.

Halogen-halogen interactions are a particularly interesting class of halogen bonds that are known to be essential design elements in crystal engineering. In solution, it is likely that halogen-halogen interactions also play a role, but the weakness of this interaction makes it difficult to characterize or even simply detect. We have designed a supramolecular balance that allows detecting BrBr interactions between CBr3 groups in solution and close to room temperature. The sensitivity and versatility of the chosen platform have allowed accumulating consistent data. In halogenoalkane solvents, we propose estimates for the free energy of these weak halogen bond interactions. In toluene solutions, we show that the interactions between Br atoms and the solvent aromatic groups dominate over the BrBr interactions.

On orthogonality constrained multiple core-hole states and optimized effective potential method.

An attempt to construct a multiple core-hole state within the optimized effective potential (OEP) methodology is presented. In contrast to the conventional Δ-self-consistent field method for hole states, the effects of removing an electron is achieved using some orthogonality constraints imposed on the orbitals so that a Slater determinant describing a hole state is constrained to be orthogonal to that of a neutral system. It is shown that single, double, and multiple core-hole states can be treated within a unified framework and can be easily implemented for atoms and molecules. For this purpose, a constrained OEP method proposed earlier for excited states (Glushkov and Levy, J. Chem. Phys. 2007, 126, 174106) is further developed to calculate single and double core ionization energies using a local effective potential expressed as a direct mapping of the external potential. The corresponding equations, determining core-hole orbitals from a one-particle Schrödinger equation with a local potential as well as correlation corrections derived from the second-order many-body perturbation theory are given. One of the advantages of the present direct mapping formulation is that the effective potential, which plays the role of the Kohn-Sham potential, has the symmetry of the external potential. Single and double core ionization potentials computed with the presented scheme were found to be in agreement with data available from experiment and other calculations. We also discuss core-hole state local potentials for the systems studied.

Doubly, triply, and multiply excited states from a constrained optimized effective potential method.

This article further develops and applies a constrained optimized effective potential (COEP) approach for the practical calculations of doubly and multiply excited states of atoms and molecules. The COEP method uses the time-independent theory of pure excited states and implements a simple asymptotic projection method to take orthogonality constraints into account. We show that, in contrast with the common time-dependent density functional method, the COEP methodology is capable of treating doubly, triply, and multiply excited states and can be easily applied to both atoms and molecules. In particular, doubly excited energies of each state are calculated through a constrained minimization procedure including constraints that make its Slater determinantal functions orthogonal to those of the ground and all lower-lying doubly excited states. The performance of the proposed method is examined by calculations of doubly excited state energies for the He atom and H(2) molecule at exchange-only and exchange-correlation level of approximation.

An ab initio and DFT study of structure and vibrational spectra of disiloxane H3SiOSiH3 conformers. Comparison to experimental data.

The structural and vibrational properties of siloxane monomers may account in the physical and chemical properties of silicone polymers. Because disiloxane (H(3)SiOSiH(3)) is the smallest molecule in the set which runs through small siloxanes like hexamethyldisiloxane (CH(3))3SiOSi(CH(3))3 to silicone polymers, its energetic, structural and vibrational features have been investigated in detail using density functional theory (B3LYP), post Hartree-Fock methods (MP2 and CCSD(T)) and basis sets up to spdfg quality. Five conformations were considered: three bent structures with C2v (double staggered, SS, and double eclipsed, EE, conformations) and Cs symmetries, and two linear forms with D3d and D3h symmetries. At all levels of theory, the relative stability was C2v(SS) approximately C2v(EE)>Cs>D3h>D3d. The difference of energy between the two C2v conformers is lower than 0.04 kcal/mol. At the highest level of theory (CCSD(T)/cc-pVQZ), the barrier to linearisation from C(2v) to D(3h) conformers was calculated at 0.43 kcal/mol, which is extremely low. Most of the structural and vibrational features of the disiloxane do not depend on the conformation of the molecule but are strongly influenced by the SiOSi angle. Anharmonic calculations allowed, without any scaling factor, an exhaustive reinvestigation of the assignments of observed wavenumbers in the infrared and Raman spectra of gaseous disiloxane. Particularly, in the gas phase spectrum, the SiOSi symmetric and antisymmetric stretches have been assigned at 599 and 1105, 596 and 1060, 527 and 1093 cm(-1) for H(3)SiOSiH(3), H(3)Si(18)OSiH(3) and D(3)SiOSiD(3), respectively. The experimental wavenumber splitting of SiOSi symmetric and antisymmetric stretches of H(3)SiOSiH(3) gave an estimation of the SiOSi angle at around 145 degrees . Ab initio methods were revealed more accurate for structural parameters, when DFT/B3LYP was enough for spectral assignments, even at the harmonic level using a single scaling factor.