Time-dependence of wave functions and the calculation of transition intensities

The standard formalism of the perturbation theory for time-dependent perturbations follows from the assumption that the exact solution of the unperturbed time-independent problem is known. The consequences of this assumption are analyzed. Particular attention is given to the methods used for the evaluation of transition intensities. It is shown that the traditional intensity formula in most cases violates the assumptions underlying its derivation. It is shown that for the given ansatz concerning the form of the approximate wave function, the transition intensities should be determined from the variation treatment of the corresponding time-dependent problem. The wave functions of both states involved in the transition should be given the same amount of variation flexibility. This condition is satisfied if the transition intensity expression follows from the complete timedependent perturbation treatment of the perturbed system.     

HCl solvation at the surface and within methanol clusters/nanoparticles II: Evidence for molecular wires

Condensed-phase solvation of HCl on and within methanol nanoparticles was investigated by Fourier transform infrared (FTIR) spectroscopy, on-the-fly molecular dynamics as implemented in the density functional code Quickstep (which is part of the CP2K package), and ab initio calculations. Adsorption and solvation stages are identified and assigned with the help of calculated infrared spectra obtained from the simulations. The results have been further checked with MP2-level ab initio calculations. The range of acid solvation states extends from the single-coordinated slightly stretched HCl to proton-sharing with Zundel-like methanol O...H+...X- states, and finally to MeOH2+...Cl- units with full proton transfer. Furthermore, once the proton moves to methanol, it is mobilized along methanol molecular chains. Since the proton dynamics reflects the evolving local structures, the "proton" spectra display broad bands usually with underlying continua.     

Reduced-size polarized basis sets for calculations of molecular electric properties. II. Simulation of the Raman spectra

The accuracies of the calculated vibrational frequencies and Raman intensities given by two new, highly compact Pol-type basis sets, Z2PolX and Z3PolX, have been determined and compared to the 6-31G(d), PolX, and aug-cc-pVTZ basis sets. Calculation of accurate Raman intensities has previously required large basis sets, but the ZmPolX basis sets are smaller even than PolX, which are the most compact basis sets able to calculate accurate Raman intensities. For the largest compound studied, C5H10O2, Z3PolX required more than an order of magnitude less CPU time than PolX, which has been shown to be 10 times faster than aug-cc-pVTZ. Two sets of test molecules were studied: one was a series of small molecules for which experimental values for absolute Raman activities were available; the second was a series of medium-sized molecules (mainly common organic solvents) where only relative Raman band intensities were available. The accuracies of the Raman intensities given by both of the ZmPolX basis sets were good compared to those of the PolX and aug-cc-pVTZ sets, and much better than the 6-31G(d) values. The errors in even unscaled frequency values <2000 cm(-1) were also acceptable and were slightly lower for Z3PolX than Z2PolX (30 cm(-1) vs. 48 cm(-1)). The combination of good intensity and frequency data meant that for the medium-sized organic molecules there was a close correspondence between the simulated Raman spectra and experimental data, and that the observed bands could easily be assigned on the basis of these calculations. Achieving this level of accuracy in the simulations at modest computational cost should now allow computational methods to be combined with experimental Raman studies much more widely than is currently the case.     

Electric properties of the water molecule in 1A1, 1B1, and 3B1 electronic states: Refined CASSCF and CASPT2 calculations

Summary The dipole moments and dipole polarizabilities of the ¹A₁, ¹B₁, and ³B₁ electronic states of the water molecule have been calculated by using the CASSCF approach followed by the evaluation of the dynamic electron correlation contribution by the second-order perturbation scheme CASPT2. All calculations have been carried out in a specifically extended ANO basis set which accounts for the Rydberg character of the two excited states. In order to estimate the correctness and accuracy of the present data a scan over a variety of different active spaces for the CASSCF wave function has been made. The present results are superior to earlier CASSCF calculations, although their qualitative features remain essentially the same. The dipole moments in ¹B₁ and ³B₁ states are predicted to be about 0.49 a.u. and 0.33 a.u., respectively, and have the opposite orientation with respect to the ground state dipole moment. The dipole polarizability tensors of the excited states are characterized by high anisotropy and are dominated by the in-plane component perpendicular to the symmetry axis. All their components are found to be about an order of magnitude larger than those of the ground state polarizability tensor. The excitation energy dependence on the choice of the active orbital space in the CASSCF reference function is also considered and the analysis of the present data concludes in the concept of what is called the mutually compatible active spaces for the two states involved in excitation. All CASPT2 results are in good agreement with the results of recent calculations carried out in the framework of the open-shell coupled cluster formalism. This agreement confirms the high efficiency of the CASSCF/CASPT2 approach to the treatment of the electron correlation effects.     

Genistein complexes with amines. Part II: ab initio study of the complexes with piperazine and triethylamine

The piperazine and triethylamine complexes of genistein, exhibiting high immunosuppressant activity, were ab initio modeled at RHF/6-31G^** level and results were compared with those obtained for genistein–morpholine complexes by X-ray, NMR, and theoretical methods. The most stable genistein–piperazine complex is formed due to hydrogen bonding of genistein's OH group at position C7 to piperazine's nitrogen atom. In the most stable genistein–triethylamine complex genistein's OH group at position C4′ (position para to phenyl substituent) and trimethylamine nitrogen atom are engaged in hydrogen bond formation. The calculations confirmed our previous NMR conclusion that piperazine is more strongly complexed by genistein than is morpholine or triethylamine. The theoretical ¹³C NMR spectra correlate fairly well with the experimental spectra.     

Ground-state dipole polarizability of lithium hydride. Accurate SCF and CAS SCF calculations

Accurate calculations of the dipole polarizability tensor of lithium hydride are performed using the finite-field perturbation approach in the SCF and CAS SCF method. The SCF results (α_? = 22.1, α_⊥ = 25.4 au) are expected to be very close to the HF values. The CAS SCF calculations predict a positive correlation contribution, giving α_? = 26.3 and α_⊥ = 29.3 au.     

Size-Nonextensive Contributions in Singles-Only CI

The size-nonextensivity (SNE) of the configuration interaction scheme with single excitations only (CIS) is discussed. On the basis of model considerations the method is explicitly shown to give energies which have wrong dependence on the number of particles. The same model of a multimer of N noninteracting subsystems, each in the same singly excited state, is analyzed in terms of the many-body perturbation theory expansion. This suggests new computational schemes which will be either completely free of the size-nonextensive contributions or may have them removed a posteriori. The extension of the perturbation scheme leads to the singles-only coupled cluster approach with a singly excited reference function. The consequences of the present model study for computational methods for inexpensive calculations of the electronic spectra of molecules, are investigated.     

Polarized basis sets and the calculation of infrared intensities from nuclear electric shielding tensors

The idea of the basis set polarization which follows from the known dependence of basis set functions on the perturbation strength is applied to the calculation of the dipole moment derivatives with respect to nuclear displacements. The differentiation of the dipole moment function is replaced by the straightforward evaluation of derivatives of the intramolecular electric field with respect to the external electric field strength. The method and its efficiency are illustrated by a series of calculations of the dipole moment derivatives for the water molecule. Already a polarized basis set of 26 CGTO's derived from the minimal CGTO basis set provides fairly reasonable results.     

On the improvement of expectation values in the uncoupled SCF and HF perturbation theories

The exact derivation of the formula for the first-order ‘correlation’ correction to the second-order uncoupled Hartree-Fock energies, computed with approximate Hartree-Fock orbitals, is presented. A comparison with the corresponding formula derived under the assumption of the exact solution of the Hartree-Fock equations indicates that also the second-order perturbed orbitals do contribute. However, their contribution can be expressed in terms of the first-order correction to the SCF orbitals which accounts for the difference between the Hartree-Fock and SCF solution. These additional terms can be either positive or negative and can influence significantly the final result for the correlation-corrected second-order energies.     

Ab Initio SCF Calculations Relating to the Cls Chemical Shifts for Some Alkanes

Ab initio calculatios have been made for a series of simple alkanes and the atomic charges have been estimated in two ways, using the Mulliken population analysis and also using an analysis due to Karlström where the charges are fitted to describe the electrical moments derived from the SCF wave function. Also the orbital energies were calculated. The results were used to interpret experimental data of the carbon core electron binding energies. It is found that the Karlström technique is best suited to describe the XPS data.