Polarization molecular Hamiltonians

H is the molecular hamiltonian in the absence of the field. This anharmonic energy profile is plotted in Figure 2 for three choices of 2 A/t. A taylor series expansion of this equation around the equilibrium polarization, Vo, gives the effective cubic anharmonicity in the potential, where V replaces the classical position x... 

We add the operator —p, ER to the total molecular Hamiltonian. According to Eq. (3.1), the electronic Hamiltonian of the molecule in the field due to the solvent is then He — p ER. The electronic Schrodinger equation is then solved using this modified Hamiltonian. This leads to a self-consistent solution where the electronic wave function and the electronic energy are modified due to the solvent field. Thus, polarization of the molecular electronic density (as described approximately above) is automatically included in this approach. 

As an example of application of the method we have considered the case of the acrolein molecule in aqueous solution. We have shown how ASEP/MD permits a unified treatment of the absorption, fluorescence, phosphorescence, internal conversion and intersystem crossing processes. Although, in principle, electrostatic, polarization, dispersion and exchange components of the solute-solvent interaction energy are taken into account, only the firsts two terms are included into the molecular Hamiltonian and, hence, affect the solute wavefunction. Dispersion and exchange components are represented through a Lennard-Jones potential that depends only on the nuclear coordinates. The inclusion of the effect of these components on the solute wavefunction is important in order to understand the solvent effect on the red shift of the bands of absorption spectra of non-polar molecules or the disappearance of... 

The traditional a—ir description of multiple bonding and the expectation that conformational effects could somehow be derived from a molecular Hamiltonian function can both safely be discounted. Looking for a fresh approach in terms of quantum potential, returns the argument to the general form of polar wave functions... 

Interpretation of nonlinear molecular measurements on molecules, and indeed our intuitive understandings of any polarization, is almost always based on a state model of the molecule the applied fields mix the levels of the molecular Hamiltonian so that spectral analysis (in the sense of sums over states, or SoS) becomes a very useful description. While more recent and more sophisticated electronic structure calculations have important direct-response methods, the SoS techniques, like the very simple two-level formula of Oudar and Chemla, have tremendous advantages in terms of generality and understanding. 

Here, Ho is the molecular Hamiltonian in the BO approximation, and V is the nonadiabatic coupling operator. U(t) = —/x e(r)cos(a)/t) is the pulse excitation operator. Here, e t) is the amplitude of the laser pulse with photon polarization vector e, and coi is laser central frequency. In Eq. 6.18, i] denotes the parameter depending on photon polarization direction of the linearly polarized laser pulse = 1 for the polarization vector e+, while r] = -l for e. ... 

For condensed-phase and macromolecular simulations, we have written an X-Pol software package using the C-p-p language, which has been incorporated into NAMD and CHARMM. The X-Pol program can be used with the popular NDDO-based semiempirical Hamiltonians as well as the recently developed polarized molecular orbital (PMO) model. - Molecular d3mamics simulations of liquid water have been carried out using the NAMD/X-Pol interface. In addition, we have used an earlier version of the X-Pol model in Monte Carlo simulations of liquid water. 

Finally, the whole system (molecule + metal nanoparticle) can be treated atomistically via TD-DFT or other quantum chemical methods. The interaction between the metal nanoparticle and the molecule are treated on the same foot as the intra-molecule and intra-nanoparticle ones. This method is therefore able to include much more than just the electrodynamics coupling, as it can include mutual polarization, chemical bonding, charge transfers (also in excited states). On the down side, at present this approach is limited to very small metal particles (a few tens of atoms, a few nm in size). Moreover, electrodynamics coupling is limited to the quasi-static limit, as standard molecular Hamiltonian includes only non-retarded Coulombic potential. Nevertheless, this method represents a fully ab initio approach to molecular plasmonics. 

In the quantum mechanical continuum model, the solute is embedded in a cavity while the solvent, treated as a continuous medium having the same dielectric constant as the bulk liquid, is incorporated in the solute Hamiltonian as a perturbation. In this reaction field approach, which has its origin in Onsager s work, the bulk medium is polarized by the solute molecules and subsequently back-polarizes the solute, etc. The continuum approach has been criticized for its neglect of the molecular structure of the solvent. Also, the higher-order moments of the charge distribution, which in general are not included in the calculations, may have important effects on the results. Another important limitation of the early implementations of this method was the lack of a realistic representation of the cavity form and size in relation to the shape of the solute. 

Dipole Moments (Debyes) in Gas Phase and in Aqueous Solution," and Aqueous Polarization Energies (kcal/mole),4 Computed by a QM/MM Discrete Molecular Solvent Method, Using The AMI Solute Hamiltonian. 

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