The structure of molecules and the details of chemical bonding can be accurately predicted by electronic structure (ES) methods. Thousands of research groups worldwide apply or further develop ES theories. The logical second step, the quantum equations for nuclear motion, is not considered in such calculations and theories (apart from the rudimentary harmonic oscillator calculations). However, advanced ES methods and programs provide essential input for calculating the electronic energies needed for constructing potential energies surfaces (PESs).
Classical molecular dynamics (MD) is widely used to create illustrative models and “movies”, e.g. for systems of biochemical interest such a proteins, as well as for simulation of liquids. While such studies are useful and justified in a classical statistical mechanical sense, it should be stressed that the individual classical trajectories have no basis in reality! In the simplest case, a swarm of classical trajectories will give predictions fairly similar to quantum mechanics, but generally, basic physics tell us that quite different results will be obtained from classical and quantum mechanics. The emergence of classical behavior for macroscopic systems is well-established, but this still does not mean that accurate molecular predictions can be made using classical equations of motion. Standard MD uses classical potentials and classical equations of motion. Classical simulations using direct ES calculations of the forces on nuclei are increasingly used. However, the equations for the motion of nuclei are still classical in such calculations.
In contrast to the widespread approaches above, my vision is to abandon the classical trajectories altogether and instead perform approximate adaptive quantum simulations using wave functions. Quantum mechanics will always provide both forces and equations of motion.
Today, many quantum dynamical phenomena are well-understood for few-atomic systems and very nice theoretical and computational tools exists. However, a problem is that the available accurate quantum dynamical calculation methods are generally subject to serious restrictions in the size of the systems that can be treated reliably (up to about 10 atoms). In addition, much work that is specific to the particular system is usually required, certainly preventing such methods from becoming widespread in use.
I have defined new formulations and theories with the goal of taking computational quantum dynamics out of the few-atom world. This includes very fundamental work such as the definition of a second-quantization (SQ) formulation for many-mode quantum dynamics and introduction of vibrational coupled cluster (VCC) theory. Coupled cluster (CC) theory has long been accepted as providing the golden standard for electronic structure calculations. The key to the success of CC methods is the ability to describe correlation accurately. In the vibrational context correlation is also central, albeit the degrees of freedom are very different. The accuracy of VCC for energies and spectra and its time dependent analogues [TDVCC, TDMVCC) for wave packets is now well-established and is the foundation of the work in the group.
