Explicitly Correlated Wave Function Methods
Standard wave function methods are capable of very high accuracy necessary for computing reaction enthalpies, atomization energies, and even reaction rates. Unfortunately, very large basis sets are usually needed to reduce the error due to the basis to acceptable level. This is because such methods have difficulty describing behavior of electrons at short distance rij from each other. Explicitly correlated methods include terms the wave function which depend explicitly on rij and can describe the pairs of electrons well when rij->0. In our group we develop explicitly correlated Linear R12 methods of Kutzelnigg, Klopper, and co-workers. Our recent developments of the linear R12 methods promise to match the best accuracy of standard methods using some of the smallest available basis sets (aug-cc-pVDZ).
The first-order wave function for the ground state computed with a conventional method is smooth everywhere whereas the exact function has a cusp when electrons are at the same point, i.e., phi=0. This discrepancy if the artifact of the two-electron basis used in the standard wave function methods.
Our developments in explicitly correlated methods are included into the freely-available Massively Parallel Quantum Chemistry program. Prof. Valeev is also the author of the older explicitly correlated MP2 code in PSI3 package.
Charge Transport in Organic Materials
Electronic devices based on organic materials have several important advantages over their silicone and other "inorganic" counterparts: lower weight, ease of processing, ability to tune properties by changing the chemical composition, and cost, among others. Description of charge transport in such devices is challenging because geometric structure and electronic properties are subtly related and are very sensitive to changes in chemical composition.
A face-to-face one-dimensional stack of pentacene molecules is a better conductor than the face-to-edge stack because the site enegries in the latter split due to polarization.
We are working towards developing the understanding how the geometric, electronic, and chemical structures are related. For example we recently established how local geometric structure can dramatically affect the transport parameters via an often-ignored mutual polarization of molecules. We also added a capability to compute transport parameters to MPQC.
Development of Non-Born-Oppenheimer Molecular Structure Methods
Born-Oppenheimer approximation is the basic assumption of the vast majority of quantum computations on molecules. In many situations one must go beyond the Born-Oppenheimer framework, e.g., nonradiative decay of excited states, electron-phonon coupling in metals, or even accurate prediction of rovibrational spectra. Unfortunately, general and practical non-Born-Oppenheimer methods are still lacking.
Our group's contributions to this area is a general method to evaluate the adiabatic correction to the Born-Oppenheimer surface using general configuration interaction wave functions (implemented in PSI3) and investigation of methods which treat electrons and some nuclei quantum-mechanically.
Robust Scientific Software: Scalability, Design, Compiler Techniques
Computational electronic structure program can easily be hundreds of thousands lines long, developed by many scientific programmers over several decades, and often poorly documented. Over such long periods of time not only the algorithms change, but also the hardware and middleware. Good design is therefore very important for computational chemistry software. We subscribe to several key ideas about design: 1) software must be scalable; 2) modern techniques (object oriented, generic, etc.) should be utilized for at least coarse-grain design; 3) domain-specific compilers (code generators) can be extremely beneficial. We apply these principles in our work (see Software for more information).