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.     

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.     

DFT study of vibrational circular dichroism spectra of D-lactic acid-water complexes

This paper presents a discussion of the interaction energies, conformations, vibrational absorption (VA, harmonic and anharmonic) and vibrational circular dichroism (VCD) spectra for conformers of monomeric chiral d(-)-lactic acid and their complexes with water at the DFT(B3LYP)/aug-cc-pVDZ and DFT(B3LYP)/aug-cc-pVTZ levels. A detailed analysis has been performed principally for the two most stable complexes with water, differing by lactic acid conformation. The VCD spectra were found to be sensitive to conformational changes of both free and complexed molecules, and to be especially useful for discriminating between different chiral forms of intermolecular hydrogen bonding complexes. In particular, we show that the VCD modes of an achiral water molecule after complex formation acquire significant rotational strengths whose signs change in line with the geometry of the complex. Using the theoretical prediction, we demonstrate that the VCD technique can be used as a powerful tool for structural investigation of intermolecular interactions of chiral molecules and can yield information complementary to data obtained through other molecular spectroscopy methods.     

The properties of weak and strong dihydrogen-bonded D-H...H-A complexes.

The properties of six dihydrogen-bonded (DHB) dimers with the BeH2 molecule as a proton acceptor were calculated by MP2, CCSD(T) and B3LYP methods. The structural, energetic and spectroscopic parameters are presented and analyzed in terms of their possible correlation with the interaction energy and the intermolecular H...H separation. The symmetry-adapted perturbation theory (SAPT) calculations were performed to gain more insight into the nature of the H...H interactions. The studied complexes are divided into three groups based on the calculated intermolecular distances and the interaction energies which range from approximately -1 to -42 kJ mol(-1). The analysis of the interaction energy components indicates that, in contrast to conventional hydrogen bonds, the induction energy is the most important term in the BeH2NH4+ complex. On the other hand, there is no sharp boundary between the DHB complexes classified as hydrogen bonded and van der Waals systems. The complexation-induced changes in vibrational frequencies and in proton shielding constants show a relationship with the interaction energy. The values of the 2hJXH and 3hJBeX coupling constants correlate well with the interaction energy and with the intermolecular distance.