60th Annual Report on Research 2015

Through the support from the ACS-PRF Doctoral New Investigator grant in 2014-2015, we have performed investigations of how electron removal (ionization) and excitation (absorption) is treated with density-functional theory (DFT) and time-dependent DFT (TDDFT) in both vacuum and solution phase environments. 

I. Size-dependent delocalization error in vacuum and solution.

We investigated the effects of molecular size on the accuracy of density-functional ionization potentials (IPs) for a set of 28 hydrocarbons, including series of alkanes, alkenes, and oligoacenes. As the system size increases, delocalization error introduces a systematic underestimation of the IP. The computation of the IP with many density-functional approximations is not size-extensive due to excessive delocalization of the incipient positive charge. These results emphasize that good performance of a functional for small molecules is not necessarily transferable to larger systems. Due to the local nature of exchange and the accompanying size-dependent delocalization error, we show that most density functionals in use do not yield a constant IP for an increasing number of identical isolated molecules in vacuum. Instead, as the number of molecules increases, the total energy required to ionize the system decreases (see Figure 1).

Figure 1. Difference in DFT computed ionization potential (IP) with increasing number of molecules for methane, ethene, and benzene in vacuum.

Rather surprisingly, this is still the case in solution, whether using a polarizable continuum model (PCM) or with explicit solvent that breaks the degeneracy of each solute. The decrease in the IP is not as great when using a PCM compared to vacuum, while we find that including explicit solvent in the calculation can exacerbate the size-dependent delocalization error by extending the size of the quantum mechanical region. Difference densities show that instead of the electron being removed from a single solute molecule, DFT with local exchange (BLYP) removes some electron density from many molecules; using exact nonlocal exchange (M06-HF) fixes the error (see Figure 2). In vacuum and explicit solvent, the amount of exact exchange needed to make the computed ionization potential size extensive agrees with optimally tuning long-range corrected hybrid functionals. However, this is not the case when using a PCM, which tends to over-polarize the electron density.

Figure 2. The BLYP and M06-HF density differences for the neutral and cation systems of five identical ethene molecules separated by 10 Angstrom.  Density differences are shown for three solvent environments: PCM, all MM point charge solvent, and a combination of QM and MM solvent molecules, with the twenty-five solvent molecules closest to a solute being treated as QM and the remaining sphere of waters treated as MM.

II. Convergence of excitation energy with layers of QM solvent

One approach to modeling both the short- and long-range effects of solvation is to partition the system into a quantum mechanical region (QM) and a classical region treated by molecular mechanics (MM) or a PCM. Ideally one would like to include enough solvent molecules in the QM region to yield a converged result. Our results show that the amount of solvent required in the QM region to compute converged spectra depends on the basis set (see Figure 3) and the character of the excitations, rather than the charge on the solute.

The QM/PCM model requires fewer QM solvent molecules than QM/MM to reach convergence (Figure 4). The QM/MM and QM/PCM models converge to different excitation energies for the main peak (~0.05 eV difference) for our tests with anion solutes, and the QM/PCM model leads to a significantly more intense HOMO to LUMO peak compared to the QM/MM model.

Figure 4. TDDFT absorption spectra of the anionic PYP chromophore computed using QM/MM (top) and QM/PCM (middle), and the difference in excitation energy with respect to the converged value (bottom).

When comparing QM/MM and QM/PCM for ionization, non-equilibrium PCM must be used to take into account the vertical ionization that is modeled when no relaxation of the solvent positions are considered. In this case PCM again shows accelerated convergence compared to an MM point charge water model, requiring 25-50 explicit solvent molecules (one solvation shell) to reach a close to converged value.

III. Peak-Shifting in Real-Time Time-Dependent Density Functional Theory.

In recent years, the development and application of real-time time-dependent density functional theory (RT-TDDFT) has gained momentum as a computationally efficient method for modeling electron dynamics. However, the RT-TDDFT method within the adiabatic approximation can unphysically shift absorption peaks. We investigated the origin of these time-dependent resonances observed in RT-TDDFT spectra (Figure 5). We showed that the magnitude of the RT-TDDFT peak shift depends on the applied field, in line with previous studies, but it oscillates as a function of time-dependent molecular orbital populations, and the direction and magnitude of the time-dependent peak shifts is due to the relative transition energies.

Figure 5. TDCI and RT-TDDFT spectra at three different field durations.

Impact on career and training.

This project supported by ACS-PRF has allowed my group to obtain initial results that have been used to apply for, and be successful with, other grants. Therefore, not only has it led to productivity during the time of the award, it has helped my group obtain the funds to continue to be productive in the future. It has also supported my travel to present some of these results at the ACS meeting in Denver, which was key as a new professor for promoting my research to the theoretical and physical chemistry communities.

The funds have also been used to support 2^nd year graduate Joel Milanese and post-doc Dr. Makenzie Provorse. Joel was able to concentrate on research full-time rather than having to balance research with teaching assistant duties, which has led to him being able to understand his project at a deeper level, and to be more productive with his calculations and analysis. Makenzie has made good research progress, has been able to mentor students, and plans to go on the academic job market. The funds also supported her travel to the ACS Denver meeting to give a talk.