Description of Research Focuses of the Nooijen Group

Synopsis of research: Our long term goal is to develop accurate wave function based electronic structure methods that are applicable to general open-shell systems, in particular transition metal compounds. The electronic structure technique should be coupled to an efficient scheme to describe non-adiabatic nuclear dynamics such that one can make direct comparisons with experimental results. The ideal electronic structure methodology in my mind would be a local, AO-based, multireference coupled cluster method, combined with an efficient explicit correlation (r12) technique, and including important relativistic effects. Nuclear dynamics would be based on vibronic model Hamiltonians obtained from a suitable diabatization of the electronic states.

The availability of the above methodology would mean that we could study small to medium sized clusters and molecules in their full complexity. This is very much needed in the field of transition metal chemistry. Transition metal compounds typically have a manifold of close lying electronic states, while chemical bonds tend not to be very strong. The potential presence of unpaired electrons yields further flexibility. This provides all the ingredients for a very rich chemistry that is only poorly understood. It is very likely that multiple electronic states and non-adiabatic dynamics play an important role in the reactivity of transition metal compounds and in catalysis. Transition metal atoms, even small clusters, are widely present in the active sides of biological systems and the relevance of this kind of chemistry needs little discussion. Another rich area of application for the above technology would be photochemistry. Photochemical processes often involve crossings to doubly excited states, while non-radiative transitions to the ground state typically occur at positions of the potential energy surfaces close to a conical intersection. The electronic states involved are inherently multiconfigurational and non-adiabatic dynamics is at the heart of photochemical processes.

The research in our group is partitioned in various seemingly disjoint pieces that come together in the above mentioned long term goals of our research. A brief summary follows, and further information can be found in presentations and links that are referred to below.

Similarity Transformed Equation Of Motion Coupled Cluster Theory (STEOM)

Single reference Coupled Cluster theory is a highly accurate method in quantum chemistry that is applicable to systems that are relatively well described by a single determinant obtained from Hartree-Fock Theory. In equation of motion CC theory (EOMCC) one uses the exponential CC ground state wave function to effect a similarity transformation of the Hamiltonian. Diagonalization of the transformed Hamiltonian over the proper Hilbert space provides accurate results for excitation and ionization energies, as well as for electron affinities. In STEOM a second similarity transform of the Hamiltonian is used, and this allows us to map the doubly transformed Hamiltonian on a very small subspace. Subsequent diagonalization yields highly accurate excitation energies, for a very modest computational price tag. The STEOM method as well as analytical gradients for this approach are implemented in the ACES II electronic structure package The following document contains a brief overview of the STEOM method: STEOM.pdf

Adiabatic and non-adiabatic nuclear dynamics to simulate eletronic spectra

Recent years have witnessed a mature development of electronic structure methods for both ground and singly excited states. A next step is to use the output from electronic structure calculations to describe the actual spectroscopy. This involves consideration of (non-adiabatic) nuclear dynamics. We are actively involved in many aspects of this field of research. Our aim is to simulate UV/VIS absorption spectra, resonance Raman and circular dichroism spectra with predictive accuracy. This is also a step towards the simulation of photochemical processes. In brief, we use a vibronic model Hamiltonian that provides an adequate representation of the electronic states in the vicinity of the absorbing state geometry. Based on the vibronic Hamiltonian we can either obtain adiabatic potential energy surfaces and calculate spectra in the Franck-Condon approximation, or we can solve the full vibronic problem. The latter is rather expensive, and we are developing many-body transformation approaches to reduce the complexity of full-dimensional vibronic calculations. From a comparison of the FC and vibronic approaches we obtain insight in the importance of non-adiabatic effects. A brief presentation on vibronic coupling can be found in vibronic.pdf. Hannah Chang has written her undergraduate thesis on this topic hannah_thesis.pdf which provides a detailed overview of the theory underlying our approach as well as sample calculations. Anirban Hazra is a graduate student in the Nooijen group who has recently graduated on this topic. He worked extensively on the UV/VIS and photoelectron spectrum of ethylene. Recently the VIBRON program has also been interfaced with the Amsterdam Density Functional program This means that diabatic vibronic models can be extracted from time-dependent DFT calculations using ADF, and simulations of spectra are then done with VIBRON. Using ADF / VIBRON the UV/VIS absorption spectrum of the permanganate anion, involving 24 electronic states and normal modes was simulated, and we have also obtained the vibrational fine structure of the CD spectrum of dimethyloxirane (DMO). The various excited states in DMO show very different vibrational finestructure and this greatly affects the overall CD spectrum.

Multireference Coupled Cluster

The generalization of single reference coupled cluster theory to genuine multireference situations (e.g. magnetic transition metal compounds, bond-breaking and bond-formation, much of photochemistry) is a challenging task We have developed a new strategy that uses an efficient internally contracted formulation, and we have developed an initial implementation. Future work will concern a fully general and more efficient implementation of this new methodology. This work is pursued by Dr. K. R. Shamasundar ("Sham") and myself. More information on this topic can be found in MRCC.pdf

Local Correlation Methods

Highly efficient local AO-based implementations are needed to perform calculations on larger systems of direct experimental interest. Our goal is to develop highly accurate local correlation methods that are reasonably efficient, and which scale linearly with the size of the system. The most important ingredients to our approach are the use of a set of atom-centered localized orbitals that are invariant to chemical changes in the molecule, and the use of dynamical thresholding to decide on the level of treatment for a given set of wave function amplitudes: Small amplitudes are treated with a lower level method than the larger amplitudes, such that an overall level of accuracy is obtained. This selection is made during the calculation of the correlated wave function and energy. Alexander Auer started work on this as a Post-doctoral associate in my group and recently took a position as a junior professor in Chemnitz, Germany, where he is continuing the work on this topic For more information see LOCAL.pdf

Automated Implementation of Many-Body Methods

Much of the tedious work in implementing quantum chemistry methods can be done by computer. Together with other groups we are developing software to automate the derivation of equations, to factorize them in computable units, and to provide an efficient Fortran implementation. At present there is a prototype of the so-called Tensor Contraction Engine (TCE), developed by So Hirata at Pacific Northwest National Laboratory, which is interfaced to the NWChem package ( So Hirata recently took up a position as assistant professor at the University of Florida The prototype TCE has been used to develop single reference CC, CI and EOMCC methods (up to quadruple excitations). We are using these tools in our group to develop local correlation methods (see above). The multireference coupled cluster methods have been developed with a precursor of these tools, which we called the Automatic Program Generator (APG). Moreover, a next generation TCE is being developed together with computer scientists at Ohio State University and Oak Ridge National Laboratory (, that aims to produce highly optimized parallel codes that are tailored to the precise computer architecture of interest. The goal of the TCE project is to provide a tool that can be used by the quantum chemistry community at large. There will be a workshop at this year's Sanibel Symposium on the use and capabilities of the TCE. For more information see A presentation on the motivation behind using automated computation and the present status can be found here:TCE.pdf

Density Matrix Renormalization Group

DMRG is an effective approach to the full-CI limit, in particular for highly correlated systems. We have been working on an efficient DMRG implementation that can perform a CI type of calculation in a large active space. In the near future we plan to combine this approach with an orbital optimization scheme for the active space, and with a perturbative treatment to include dynamical correlation. In principle this might extend the applicability of DMRG-CAPT2 type of approaches to significantly larger active spaces. We also hope to interface the DMRG method with our multireference CC method in due time. At present our DMRG effort is in the initial stage. Dominika Zgid is the student working on this project and you can find a presentation of her work here: DMRG.pdf