60th Annual Report on Research 2015

            Polycyclic aromatic hydrocarbons (PAHs) are byproducts of combustion and a subject of intense scientific interest, in part due to the fact that many PAHs are known or suspected carcinogens.¹  PAHs also have interesting electronic and optical properties which make them attractive as components in novel semiconducting or plasmonic devices.  Repeated computational studies have demonstrated that some electronic excitations in PAHs seem almost plasmonic in nature, particularly when considering dimers or trimers of PAHs.^2-4   Our group is exploring the ground- and excited-state properties of these materials to assess their ability to mimic the properties of conventional plasmonic nanomaterials.  We are approaching this problem from two directions.  First, we are developing and applying real-time time-dependent quantum-mechanical approaches in order to understand the ultrafast dynamics of electrons in PAHs.  Second, we are developing novel electronic structure methods to accurately describe the multireference nature of both the ground and excited states of these materials.

            We are using explicitly time-dependent electronic structure methods to explore the ultrafast dynamics of electrons in PAHs.  We developed a new implementation of the time-dependent configuration interaction singles (TD-CIS) method within the Psi4 electronic structure package that has substantially better performance properties than the implementation we used to generate our preliminary proposal data.  The present version allows us to follow induced electric fields in the time-domain, a capability relevant to assessing the ability of PAHs to mimic the properties of plasmonic materials.  Figure 1 (b) illustrates the enhancement in the electric field between two naphthalene molecules as a function of their separation.  Incident electromagnetic radiation that is resonant with the bright longitudinal excitation at ~6.7 eV induces an oscillating electric field, and the enhancement in the electric field approaches a factor of 20 with decreasing intermolecular distance.

Figure 1. A resonant external electric field induces Rabi oscillations in a naphthalene dimer.  The induced time-dependent electric fields (a) show the characteristic beating usually observed in the dipole moment during the Rabi cycle.  As a function of intermolecular distance, the enhancement in the electric field (b) approaches almost a factor of twenty.

            The TD-CIS approach provides a qualitative description of electron dynamics in small PAHs, but larger PAHs, whose ground states have substantial multireference character, will be difficult to describe at this level of theory.  The usual workhorse for capturing multireference correlation is the complete active space self-consistent field (CASSCF) method.  Unfortunately, most implementations of CASSCF are configuration-interaction (CI)-based, and the exponential scaling of CI severely limits the size of the active space that one can practically employ. The application of CASSCF to large active spaces requires that one abandon CI in favor of polynomial-scaling approaches such as density-matrix renormalization group (DMRG)⁵ or variational two-electron reduced-density matrix (2-RDM) methods.⁶  We have developed a computer implementation of the variational 2-RDM method (v2RDM) and coupled it to an orbital optimization procedure, thereby achieving a polynomial-scaling CASSCF method.  We applied this approach to the ground-state properties of the linear acene series; we assessed the ability of the v2RDM-CASSCF method to capture the emergence of polyradical behavior in longer members of this series and the ability of the method to predict the energy gaps between the lowest-energy singlet and triplet states (see Fig. 2).  The v2RDM method provides a qualitatively similar description of the electronic structure to that provided by other sophisticated methods, such as DMRG.  The largest v2RDM-CASSCF computations in this study were for dodecacene in a cc-pVTZ basis set, which involved an active space of 50 electrons in 50 orbitals and the simultaneous optimization of more than 1800 orbitals.  Such a computation is well beyond the capabilities of CI-driven CASSCF.

Figure 2. (a) Natural orbital occupation numbers convey the emergence of polyradical behavior in the linear acene series. (b) The singlet/triplet state splitting for the linear scene series at the v2RDM-CASSCF/cc-pVTZ level of theory.  Experimental and DMRG results are taken from Ref. 7.

We are also developing methods for higher-quality descriptions of the dynamics of electrons in PAHs.  The extended random phase approximation (ERPA) can yield excitation energies and excited-state wave functions from ground-state information obtained at any level of theory, provided that one has access to the 1- and 2-RDM.  We completed a pilot implementation of the ERPA coupled to the v2RDM method mentioned above, and we have worked out the theory necessary for the application of the ERPA within the context of a time-dependent simulation.  With a general explicitly time-dependent ERPA, it will be possible to simulate ultrafast electron dynamics in PAHs using ground-state information from essentially any level of theory.  We are also developing a real-time time-dependent coupled-cluster code based on the CC2 model.  We completed the ground-state code and are developing both the formalism and code for time-dependent simulations.

            The impact of this work on my career and that of my students has been significant.  We have generated a substantial amount of data that has served as preliminary data for other proposals to federal funding agencies.  The graduate students working on this project are developing valuable research skills and expert knowledge in computer programming and scientific computing.  The programming skills are transferable to virtually any other discipline.

[1] A. Luch, The Carcinogenic Effects of Polycyclic Aromatic Hydrocarbons. Imperial College Press: London, 2005.

[2] A. Manjavacas, F. Marchesin, S. Thongrattanasiri, et al.,  ACS Nano, 7, 3635-3643 (2013).

[3] E. B. Guidez and C. M. Aikens, J. Phys. Chem. C 117, 21466-21475 (2013).

[4] L. Bursi, A. Calzolari, S. Corni, and E. Molinari, ACS Photonics 1, 1049-1058 (2014).

[5] D. Ghosh, J. Hachmann, T. Yanai, and G. K.-L. Chan, J. Chem. Phys. 128, 144117 (2008) .

[6] G. Gidofalvi and D. A. Mazziotti, J. Chem. Phys. 129, 134108 (2008).

[7] J. Hachmann, J. J. Dorand, M. Aviles, and G. K.-L. Chan, J. Chem. Phys. 127, 134309 (2007).