Atomic decomposition of molecular properties

In this thesis, new methodology of computing properties aimed for multiple applications is developed. We use quantum mechanics to compute properties of molecules, and having these properties as a basis, we set up equations based on a classical reasoning. These approximations are shown to be quite good in many cases, and makes it possible to calculate linear and non-linear properties of large systems. The calculated molecular properties are decomposed into atomic properties using the LoProp algorithm, which is a method only dependent on the overlap matrix. This enables the expression of the molecular properties in the twosite atomic basis, giving atomic, and bond-centric force-fields in terms of the molecular multi-pole moments and polarizabilities. Since the original LoProp transformation was formulated for static fields, theory is developed which makes it possible to extract the frequency-dependent atomic properties as well. From the second-order perturbation of the electron density with respect to an external field, LoProp is formulated to encompass the first order hyperpolarizability. The original Applequist formulation is extended into a quadratic formulation, which produces the second-order shift in the induced dipole moments of the point-dipoles from the hyperpolarizability. This enables the calculation of a total hyperpolarizability in systems consisting of interacting atoms and molecules. The first polarizability α and the first hyperpolarizability β obtained via the LoProp transformation are used to calculate this response with respect to an external field using the quadratic Applequist equations. In the last part, the implemented analytical response LoProp procedure and the quadratic Applequist formalism is applied to various model systems. The polarizable force-field that is obtained from the decomposition of the static molecular polarizability α is tested by studying the one-photon absorption spectrum of the green fluorescent protein. From the frequency dispersion of the polarizability α(ω), the effect of field perturbations is evaluated in classical and QM/MM applications. Using the dynamical polarizabilities, the Rayleighscattering of aerosol clusters consisting of water and cis–pinonic acid molecules is studied. The LoProp hyperpolarizability in combination with the quadratic Applequist equations is used to test the validity of the model on sample water clusters of varying sizes. Using the modified point-dipole model developed by Thole, the hyper-Rayleigh scattering intensity of a model collagen triplehelix is calculated. The atomic dispersion coefficients are calculated from the decomposition of the real molecular polarizability at imaginary frequencies. Finally, using LoProp and a capping procedure we demonstrate how the QM/MM methodology can be used to compute x-ray photoelectron spectra of a polymer.