We present a simple algorithm, which we call the maximum overlap method (MOM), for finding excited-state solutions to self-consistent field (SCF) equations. Instead of using the aufbau principle, the algorithm maximizes the overlap between the occupied orbitals on successive SCF iterations. This prevents variational collapse to the ground state and guides the SCF process toward the nearest, rat...

The photochemical control of ground- and excited-state chirality of (M)-cis-(1) and (P)-trans-(2)-2-nitro-7-(dimethylamino)-9-(2',3'-dihydro-1'H-naphtho[2,1-b]-thiopyran-1'-ylidene)-9H-thioxanthene is described. It is shown that while ground state chirality can be controlled photochemically by irradiation with light of different wavelengths, the excited state chirality can be tuned either photo...

We consider the focusing energy-critical nonlinear Schrödinger equation of fourth order iut + ∆ u = |u| 8 d−4u. We prove that if a maximal-lifespan radial solution u : I × R → C obeys sup t∈I ‖∆u(t)‖2 < ‖∆W‖2, then it is global and scatters both forward and backward in time. Here W denotes the ground state, which is a stationary solution of the equation. In particular, if a solution has both en...

We examine the ground state and excitations of the one dimensional extended Hubbard model with long range interaction. The ground state wavefunction and low lying excitations are given explicitly in the form of a Jastrow product of two-body terms. This result motivates an asymptotic Bethe ansatz solution for the model. We present evidence that this solution is in fact exact and spans the comple...

Bi-local mean field theory is applied to one dimensional quantum liquid with long range 1/r2 interaction, which has exact ground state wave function. We obtain a mean field solution and an effective action which expresses a long range dynamics. Based on them the ground state energy and correlation functions are computed. The ground state energy agrees fairly well with the exact value and expone...

This paper is concerned with ground state solutions for the Hénon type equation −∆u(x) = |y|αup−1(x) in Ω, where Ω = B(0, 1) × Bn−k(0, 1) ⊂ R and x = (y, z) ∈ R × Rn−k. We study the existence of cylindrically symmetric and non-cylindrically symmetric ground state solutions for the problem. We also investigate asymptotic behavior of the ground state solution when p tends to the critical exponent...

The D dimensional quasi exact solutions for the singular even power anharmonic potential V (q) = aq2 + bq−4 + cq−6 are reported. We show that whilst Dong and Ma’s [5] quasi exact ground state solution (in D=2) is beyond doubt, their solution for the first excited state is exotic. Quasi exact solutions for the ground and first excited states are also given for the above potential confined to an ...

The D dimensional quasi exact solutions for the singular even power anharmonic potential V (q) = aq2 + bq−4 + cq−6 are reported. We show that whilst Dong and Ma’s [5] quasi exact ground state solution (in D=2) is beyond doubt, their solution for the first excited state is exotic. Quasi exact solutions for the ground and first excited states are also given for the above potential confined to an ...

asphaltenes are the n-pentane or n-heptane insoluble fractions of crude oil that remain in solution under reservoir temperature and pressure conditions. they are destabilized and start to precipitate when the pressure, temperature and/or composition changes occur during primary production. the precipitated asphaltene particles will then grow in size and may start to deposit onto the production ...