Random Phase Approximation and Beyond

Density functional methods based on the random phase approximation (RPA) balance accuracy and computational efficiency and have lead to a paradigm shift in electronic structure theory recently. My group has pioneered the development of these methods during the past decade [2-4, 19, 20]. Perhaps the most important result so far is that RPA-type methods are capable of treating small-gap systems efficiently [5] and with high accuracy. Small gaps are the signature of highly reactive and thus interesting species in chemistry and materials science, such as transition metal compounds, radicals, transition states, metal clusters, and small-gap semiconductors. This has profound implications, e.g., for chemical catalysis, whose high complexity has eluded accurate predictions and rational design in the past. RPA makes it possible, for the first time, to compute reaction barriers for large and small-gap systems in the ~100 atoms range with high accuracy [6].

RPA methods have also inspired fundamentally new developments in the area of weak intermolecular interactions. As nano-sized and biological systems as well as soft condensed matter are moving into the focus of computational chemists, it has become clear that weak non-covalent intermolecular interactions are much more important than previously thought. As opposed to standard semi-local density functionals, RPA contains the correct physics to capture long-range van-der-Waals interactions without any empiricism, and greatly improves upon binding energies and structures [7,8].

Non-Adiabatic Molecular Dynamics

Another area where computational tools can have a large impact on the rate of breakthrough discoveries are non-adiabatic processes involving strong coupling of more than one electronic state through nuclear motion. For example, non-adiabatic transitions are the key limiting factor for the efficiency of photovoltaic devices and light emitting diodes (LEDs). Non-adiabatic molecular dynamics (NAMD) simulations are the method of choice to attack these problems, but were hardly useful in the past due to extremely high computational demands.

Our group has developed highly efficient analytical derivative techniques for computing excited state forces [9-11] and non-adiabatic couplings [12] within time-dependent density functional theory. This has made possible NAMD simulations of moderately large molecules including several vitamin D derivatives with unprecedented accuracy and detail [13,14].

The breakdown of the Born-Oppenheimer approximation is reflected in the non-adiabatic transitions which is captured in form of a ‘Surface Hop’ in the NAMD. This has lead to discoveries of new mechanisms of photodissociation of Acetaldehyde[18].

Figure 1. The NAMD of acetaldehyde excited with 157 nm light. The yellow background represents the excited state, and the white represents the ground state. The arrows represent the direction in which the dynamics is being biased in a non-adiabatic transition.


An important impact measure for theoretical chemistry are successful applications to novel systems that have never been observed before. We have applied our methods to lanthanide and actinide complexes in collaboration with the group of Professor William Evans at UCI. This lead to the discovery of a series of new lanthanide oxidation states [15], and most recently the discovery of the first +2 compound of uranium [16]. The new +2 compounds differ radically in their chemical behavior from traditional lanthanide and actinide complexes. This new chemistry is due to an effective d1 occupation of the metal atom predicted by our calculations and supported by spectroscopic data.


The most tangible product of our research is Turbomole, a commercial quantum chemistry program with thousands of users in academia, government, and industry world-wide [17]. Prof. Furche co-founded Turbomole GmbH in 2007, served as its first CEO, and continue to contribute to it as core-developer and scientific coordinator. Commercialization of the code pays for a support network, which can reach a large number of users, and allows investments in long-term code stability. Turbomole exemplifies how fundamental science and commercial enterprise can complement each other.


[1] R. S. Mulliken: G. N. Lewis Award Lecture, Vortex 21, 182, 1960.

[2] F. Furche: Molecular tests of the random phase approximation to the exchange-correlation energy functional, Phys. Rev. B 64, 195120, 2001.

[3] F. Furche and T. Van Voorhis: Fluctuation-dissipation theorem density functional theory, J. Chem. Phys. 122, 164106, 2005.

[4] F. Furche: Developing the random phase approximation into a practical post-Kohn-Sham correlation model, J. Chem. Phys. 129, 114105, 2008.

[5] H. Eshuis, J. Yarkony, and F. Furche: Fast computation of molecular random phase approximation correlation energies using resolution of the identity and imaginary frequency integration, J. Chem. Phys. 132, 234114, 2010, also published in Virtual Journal of Biological Physics Research 20 (2010).

[6] H. Eshuis, J. E. Bates, and F. Furche: Electron Correlation Methods Based on the Random Phase Approximation, Theor. Chem. Acc. 131, 1084, 2012.

[7] H. Eshuis and F. Furche: A parameter-free density functional that works for non-covalent interactions, J. Phys. Chem. Lett. 2, 983–989, 2011.

[8] H. Eshuis and F. Furche: Basis set convergence of molecular correlation energy differences within the random phase approximation, J. Chem. Phys. 136, 084105, 2012.

[9] F. Furche and R. Ahlrichs: Adiabatic time-dependent density functional methods for excited state properties, J. Chem. Phys. 117, 7433–7447; J. Chem. Phys. 121 (2004), 12772 (E), 2002.

[10] D. Rappoport and F. Furche: Analytical time-dependent density functional derivative methods within the RI-J approximation, an approach to excited states of large molecules, J. Chem. Phys. 122, 064105, 2005.

[11] F. Furche and D. Rappoport: Density functional methods for excited states: equilibrium structure and electronic spectra, in M. Olivucci, editor, Computational photochemistry, volume 16 of Theoretical and Computational Chemistry, chapter III, pp. 93–128, Elsevier, Amsterdam, 2005.

[12] R. Send and F. Furche: First-order nonadiabatic couplings from time-dependent hybrid density functional response theory: Consistent formalism, implementation, and performance, J. Chem. Phys. 132, 044107, 2010.

[13] E. Tapavicza, A. M. Meyer, and F. Furche: Unravelling the details of vitamin D photosynthesis by non- adiabatic molecular dynamics simulations, Phys. Chem. Chem. Phys. 13, 20986–20998, 2011.

[14] E. Tapavicza, G. Bellchambers, J. C. Vincent, and F. Furche: Ab initio non-adiabatic dynamics, Phys. Chem. Chem. Phys. 2013, accepted, DOI: 10.1039/C3CP51514A.

[15] M. R. MacDonald, J. E. Bates, J. W. Ziller, F. Furche, and W. J. Evans: Completing the Series of +2 Ions for the Lanthanide Elements: Synthesis of Molecular Complexes of Pr2+ , Gd2+ , Tb2+ , and Lu2+ , J. Am. Chem. Soc. 135, 2013.

[16] M. R. MacDonald, M. E. Fieser, J. E. Bates, J. W. Ziller, F. Furche, and W. J. Evans: Identification of the +2 Oxidation State for Uranium in a Crystalline Molecular Complex, [K(2.2.2-Cryptand)][(C5 H4 SiMe3 )3 U], J. Am. Chem. Soc. 2013, article ASAP, DOI: 10.1021/ja406791t.

[17] F. Furche, R. Ahlrichs, C. Hättig, W. Klopper, F. Weigend, and M. Sierka: Turbomole, WIREs Comput. Mol. Sci. 2013, early view, DOI: 10.1002/wcms.1162.

[18] J. C. Vincent, M. Muuronen, K. C. Pearce, L. N. Mohanam, E. Tapavicza, F. Furche: That Little Extra Kick: Nonadiabatic Effects in Acetaldehyde Photodissociation, J. Phys. Chem. Lett., 7, (2016), 4185 − 4190; doi: 10.1021/acs.jpclett.6b02037.

[19] J. E. Bates, F. Furche: J. Chem. Phys. 139, 171103, 2013.

[20] A. M. Burow, J. E. Bates, F. Furche, H. Eshuis: J. Chem. Theory Comput. 10, 180, 2014.