Zuehlsdorff, T. J., & Isborn, C. M. (2018). Combining the ensemble and Franck-Condon approaches for calculating spectral shapes of molecules in solution. The Journal of Chemical Physics, 148, 024110. Website
Kocherzhenko, A. A., Sosa Vazquez, X. A., Milanese, J. M., & Isborn, C. M. (2017). Absorption Spectra for Disordered Aggregates of Chromophores Using the Exciton Model. Journal of Chemical Theory and Computation, 13, 3787-3801. Website Abstract
Optimizing the optical properties of large chromophore aggregates and molecular solids for applications in photovoltaics and nonlinear optics is an outstanding challenge. It requires efficient and reliable computational models that must be validated against accurate theoretical methods. We show that linear absorption spectra calculated using the molecular exciton model agree well with spectra calculated using time-dependent density functional theory and configuration interaction singles for aggregates of strongly polar chromophores. Similar agreement is obtained for a hybrid functional (B3LYP), a long-range corrected hybrid functional (ωB97X), and configuration interaction singles. Accounting for the electrostatic environment of individual chromophores in the parametrization of the exciton model with the inclusion of atomic point charges significantly improves the agreement of the resulting spectra with those calculated using all-electron methods; different charge definitions (Mulliken and ChelpG) yield similar results. We find that there is a size-dependent error in the exciton model compared with all-electron methods, but for aggregates with more than six chromophores, the errors change slowly with the number of chromophores in the aggregate. Our results validate the use of the molecular exciton model for predicting the absorption spectra of bulk molecular solids; its formalism also allows straightforward extension to calculations of nonlinear optical response.
Provorse Long, M. R., & Isborn, C. M. (2017). Combining Explicit Quantum Solvent with a Polarizable Continuum Model. The Journal of Physical Chemistry B, 121, 10105-10117. Website Abstract
A promising approach for accurately modeling both short-range and long-range solvation effects is to combine explicit quantum mechanical (QM) solvent with a classical polarizable continuum model (PCM), but the best PCM for these combined QM/classical calculations is relatively unexplored. We find that the choice of the solvation cavity is very important for obtaining physically correct results since unphysical double counting of solvation effects from both the QM solvent and the classical dielectric can occur with a poor choice of cavity. We investigate the dependence of electronic excitation energies on the definition of the PCM cavity and the self-consistent reaction field method, comparing results to large-scale explicit QM solvent calculations. For excitation energies, we identify the difference between the ground and excited state dipole moments as the key property determining the sensitivity to the PCM cavity. Using a linear response PCM approach combined with QM solvent, we show that excitation energies are best modeled by a solvent excluded surface or a scaled van der Waals surface. For the aqueous solutes studied here, we find that a scaled van der Waals surface defined by universal force field radii scaled by a factor of 1.5 gives reasonable excitation energies. When using an external iteration state-specific PCM approach, however, the excitation energies are most accurate with a larger PCM cavity, such as a solvent accessible surface.
Milanese, J. M., Provorse, M. R., Alameda, E., & Isborn, C. M. (2017). Convergence of Computed Aqueous Absorption Spectra with Explicit Quantum Mechanical Solvent. Journal of Chemical Theory and Computation, 13, 2159-2171. Website Abstract
For reliable condensed phase simulations, an accurate model that includes both short- and long-range interactions is required. Short- and long-range interactions can be particularly strong in aqueous solution, where hydrogen-bonding may play a large role at short range and polarization may play a large role at long range. Although short-range solute–solvent interactions such as charge transfer, hydrogen bonding, and solute–solvent polarization can be taken into account with a quantum mechanical (QM) treatment of the solvent, it is unclear how much QM solvent is necessary to accurately model interactions with different solutes. In this work, we investigate the effect of explicit QM solvent on absorption spectra computed for a series of solutes with decreasing polarity. By adjusting the boundary between QM and classical molecular mechanical solvent to include up to 400 QM water molecules, convergence of the calculated absorption spectra with respect to the size of the QM region is achieved. We find that the rate of convergence does not correlate with solute polarity when excitation energies are calculated using time-dependent density functional theory with a range-separated hybrid functional, but it does correlate with solute polarity when using configuration interaction singles. We also find that larger basis sets converge the computed spectrum with fewer QM solvent molecules. To optimize the computational cost with respect to convergence, we test a mixed basis set with more basis functions for atoms of the chromophore and the solvent molecules that are nearest to it and fewer basis functions for the atoms of the remaining solvent molecules in the QM region. Our results show that using a mixed basis set is a potentially effective way to significantly lower the computational cost while reproducing the results computed with larger basis sets.
Wang, L., Isborn, C. M., & Markland, T. E. (2016). Chapter Fifteen - Simulating Nuclear and Electronic Quantum Effects in Enzymes. In G. A. Voth, Computational Approaches for Studying Enzyme Mechanism Part A (Vol. 577, p. 389 - 418). Academic Press. Website Abstract
Abstract An accurate treatment of the structures and dynamics that lead to enhanced chemical reactivity in enzymes requires explicit treatment of both electronic and nuclear quantum effects. The former can be captured in ab initio molecular dynamics (AIMD) simulations, while the latter can be included by performing ab initio path integral molecular dynamics (AI-PIMD) simulations. Both \{AIMD\} and AI-PIMD simulations have traditionally been computationally prohibitive for large enzymatic systems. Recent developments in streaming computer architectures and new algorithms to accelerate path integral simulations now make these simulations practical for biological systems, allowing elucidation of enzymatic reactions in unprecedented detail. In this chapter, we summarize these recent developments and discuss practical considerations for applying \{AIMD\} and AI-PIMD simulations to enzymes.
Provorse, M. R., Peev, T., Xiong, C., & Isborn, C. M. (2016). Convergence of Excitation Energies in Mixed Quantum and Classical Solvent: Comparison of Continuum and Point Charge Models. The Journal of Physical Chemistry B, 120, 12148-12159. Website Abstract
Mixed quantum mechanical (QM)/classical methods provide a computationally efficient approach to modeling both ground and excited states in the condensed phase. To accurately model short-range interactions, some amount of the environment can be included in the QM region, whereas a classical model can treat long-range interactions to maintain computational affordability. The best computational protocol for these mixed QM/classical methods can be determined by examining convergence of molecular properties. Here, we compare molecular mechanical (MM) fixed point charges to a polarizable continuum model (PCM) for computing electronic excitations in solution. We computed the excitation energy of three pairs of neutral/anionic molecules in aqueous solvent, including up to 250 water molecules in the QM region. Interestingly, the convergence is similar for MM point charges and a PCM, with convergence achieved when at least one full solvation shell is treated with QM. Although the van der Waals (VDW) definition of the PCM cavity is adequate with small amounts of QM solvent, larger QM solvent layers had gaps in the VDW PCM cavity, leading to asymptotically incorrect excitation energies. Given that the VDW cavity leads to unphysical solute–solvent interactions, we advise using a solvent-excluded surface cavity for QM/PCM calculations that include QM solvent.
Provorse, M. R., & Isborn, C. M. (2016). Electron dynamics with real-time time-dependent density functional theory. International Journal of Quantum Chemistry, 116, 739–749. Website Abstract
Real-time time-dependent functional theory (RT-TDDFT) directly propagates the electron density in the time domain by integrating the time-dependent Kohn–Sham equations. This is in contrast to the popular linear response TDDFT matrix formulation that computes transition frequencies from a ground state reference. RT-TDDFT is, therefore, a potentially powerful technique for modeling atto- to picosecond electron dynamics, including charge transfer pathways, the response to a specific applied field, and frequency dependent linear and nonlinear properties. However, qualitatively incorrect electron dynamics and time-dependent resonant frequencies can occur when perturbing the density away from the ground state due to the common adiabatic approximation. An overview of the RT-TDDFT method is provided here, including examples of some cases that lead to this qualitatively incorrect behavior. © 2016 Wiley Periodicals, Inc.
Whittleton, S. R., Sosa Vazquez, X. A., Isborn, C. M., & Johnson, E. R. (2015). Density-functional errors in ionization potential with increasing system size. The Journal of Chemical Physics, 142, 184106. Website
Provorse, M. R., Habenicht, B. F., & Isborn, C. M. (2015). Peak-Shifting in Real-Time Time-Dependent Density Functional Theory. Journal of Chemical Theory and Computation, 11, 4791-4802. Website Abstract
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 and properties that require going beyond a linear response of the electron density. However, the RT-TDDFT method within the adiabatic approximation can unphysically shift absorption peaks throughout the electron dynamics. Here, we investigate the origin of these time-dependent resonances observed in RT-TDDFT spectra. Using both exact exchange and hybrid exchange-correlation approximate functionals, adiabatic RT-TDDFT gives time-dependent absorption spectra in which the peaks shift in energy as populations of the excited states fluctuate, while exact wave function methods yield peaks that are constant in energy but vary in intensity. The magnitude of the RT-TDDFT peak shift depends on the frequency and intensity of the applied field, in line with previous studies, but it oscillates as a function of time-dependent molecular orbital populations, consistent with a time-dependent superposition electron density. For the first time, we provide a rationale for the direction and magnitude of the time-dependent peak shifts based on the molecular electronic structure. For three small molecules, H2, HeH+, and LiH, we give contrasting examples of peak-shifting to both higher and lower energies. The shifting is explained as coupled one-electron transitions to a higher and a lower lying state. Whether the peak shifts to higher or lower energies depends on the relative energetics of these one-electron transitions.
Sosa Vazquez, X. A., & Isborn, C. M. (2015). Size-dependent error of the density functional theory ionization potential in vacuum and solution. The Journal of Chemical Physics, 143, 244105. Website
Garrett, K., Sosa Vazquez, X. A., Egri, S. B., Wilmer, J., Johnson, L. E., Robinson, B. H., & Isborn, C. M. (2014). Optimum Exchange for Calculation of Excitation Energies and Hyperpolarizabilities of Organic Electro-optic Chromophores. Journal of Chemical Theory and Computation, 10, 3821-3831. Website Abstract
Organic electro-optic (OEO) materials integrated into silicon–organic hybrid devices afford significant improvements in size, weight, power, and bandwidth performance of integrated electronic/photonic systems critical for current and next generation telecommunication, computer, sensor, transportation, and defense technologies. Improvement in molecular first hyperpolarizability (β), and in turn electro-optic activity, is crucial to optimizing device performance. Common hybrid density functional theory (DFT) methods, while attractive due to their computational scaling, often perform poorly for optical properties in systems with substantial intramolecular charge-transfer character, such as OEO chromophores. This study evaluates the utility of the long-range corrected (LC) DFT methods for computation of the molecular second-order nonlinear optical response. We compare calculated results for a 14-molecule benchmark set of OEO chromophores with the corresponding experimentally measured β and one-photon absorption energy, λmax. We analyze the distance dependence of the fraction of exact exchange in LC-DFT methods for accurately computing these properties for OEO chromophores. We also examine systematic tuning of the range-separation parameter to enforce Koopmans’/ionization potential theorem. This tuning method improves prediction of excitation energies but is not reliable for predicting the hyperpolarizabilities of larger chromophores since the tuning parameter value can be too small, leading to instabilities in the computation of βHRS. Additionally, we find that the size dependence of the optimal tuning parameter for the ionization potential has the opposite size dependence of optimal tuning parameter for best agreement with the experimental λmax, suggesting the tuning for the ionization potential is unreliable for extended conjugated systems.
Habenicht, B. F., Tani, N. P., Provorse, M. R., & Isborn, C. M. (2014). Two-electron Rabi oscillations in real-time time-dependent density-functional theory. The Journal of Chemical Physics, 141, 184112. Website
Isborn, C. M., Tang, C., Martini, A., Johnson, E. R., Otero-De-La-Roza, A., & Tung, V. C. (2013). Carbon nanotube chirality determines efficiency of electron transfer to fullerene in all-carbon photovoltaics. Journal of Physical Chemistry Letters, 4, 2914–2918. Abstract
Nanocarbon-based photovoltaics offer a promising new architecture for the next generation of solar cells. We demonstrate that a key factor determining the efficiency of single-walled carbon nanotube (SWCNT)/fullerene devices is the chirality of the SWCNT. This is shown via current density vs voltage measurements of nanocarbon devices prepared with (9,7), (7,6) and (6,5) SWCNTs, as well as density-functional theory (DFT) density of states calculations of C60 adsorbed onto the corresponding SWCNTs. The trends in efficiency are rationalized in terms of the relative energies of the fullerene and SWCNT conduction band energy levels.
Isborn, C. M., Mar, B. D., Curchod, B. F. E., Tavernelli, I., & Mart\'ınez, T. J. (2013). The charge transfer problem in density functional theory calculations of aqueously solvated molecules.. The Journal of Physical Chemistry B, 117, 12189–201. Website Abstract
Recent advances in algorithms and computational hardware have enabled the calculation of excited states with time-dependent density functional theory (TDDFT) for large systems of O(1000) atoms. Unfortunately, the aqueous charge transfer problem in TDDFT (whereby many spuriously low-lying charge transfer excited states are predicted) seems to become more severe as the system size is increased. In this work, we concentrate on the common case where a chromophore is embedded in aqueous solvent. We examine the role of exchange-correlation functionals, basis set effects, ground state geometries, and the treatment of the external environment in order to assess the root cause of this problem. We conclude that the problem rests largely on water molecules at the boundary of a finite cluster model, i.e., "edge waters." We also demonstrate how the TDDFT problem can be related directly to ground state problems. These findings demand caution in the commonly employed strategy that rests on "snapshot" cutout geometries taken from ground state dynamics with molecular mechanics. We also find that the problem is largely ameliorated when the range-separated hybrid functional LC-$ømega$PBEh is used.
Isborn, C. M., Götz, A. W., a. Clark, M., Walker, R. C., & Martinez, T. J. (2012). Electronic absorption spectra from MM and ab initio QM/MM molecular dynamics: Environmental effects on the absorption spectrum of photoactive yellow protein. Journal of Chemical Theory and Computation, 8, 5092–5106. Abstract
We describe a new interface of the GPU parallelized TeraChem electronic structure package and the Amber molecular dynamics package for quantum mechanical (QM) and mixed QM and molecular mechanical (MM) molecular dynamics simulations. This QM/MM interface is used for computation of the absorption spectra of the photoactive yellow protein (PYP) chromophore in vacuum, aqueous solution, and protein environments. The computed excitation energies of PYP require a very large QM region (hundreds of atoms) covalently bonded to the chromophore in order to achieve agreement with calculations that treat the entire protein quantum mechanically. We also show that 40 or more surrounding water molecules must be included in the QM region in order to obtain converged excitation energies of the solvated PYP chromophore. These results indicate that large QM regions (with hundreds of atoms) are a necessity in QM/MM calculations.
Isborn, C. M., Luehr, N., Ufimtsev, I. S., & Martinez, T. J. (2011). Excited-state electronic structure with configuration interaction singles and Tamm-Dancoff time-dependent density functional theory on graphical processing units. Journal of Chemical Theory and Computation, 7, 1814–1823. Abstract
Excited-state calculations are implemented in a development version of the GPU-based TeraChem software package using the configuration interaction singles (CIS) and adiabatic linear response Tamm–Dancoff time-dependent density functional theory (TDA-TDDFT) methods. The speedup of the CIS and TDDFT methods using GPU-based electron repulsion integrals and density functional quadrature integration allows full ab initio excited-state calculations on molecules of unprecedented size. CIS/6-31G and TD-BLYP/6-31G benchmark timings are presented for a range of systems, including four generations of oligothiophene dendrimers, photoactive yellow protein (PYP), and the PYP chromophore solvated with 900 quantum mechanical water molecules. The effects of double and single precision integration are discussed, and mixed precision GPU integration is shown to give extremely good numerical accuracy for both CIS and TDDFT excitation energies (excitation energies within 0.0005 eV of extended double precision CPU results).
Ding, F., Liang, W., Chapman, C. T., Isborn, C. M., & Li, X. (2011). On the gauge invariance of nonperturbative electronic dynamics using the time-dependent Hartree-Fock and time-dependent Kohn-Sham. Journal of Chemical Physics, 135, 164101. Abstract
Nonperturbative electronic dynamics using the time-dependent Hartree-Fock (TDHF) and time-dependent Kohn-Sham (TDKS) theories with the adiabatic approximation is a powerful tool in obtaining insights into the interaction between a many-electron system and an external electromagnetic field. In practical applications of TDHF/TDKS using a truncated basis set, the electronic dynamics and molecular properties become gauge-dependent. Numerical simulations are carried out in the length gauge and velocity gauge to verify the extent of gauge-dependence using incomplete basis sets. Electronic dynamics of two many-electron systems, a helium atom and a carbon monoxide molecule in high-intensity linearly polarized radiation fields are performed using the TDHF and TDKS with two selected adiabatic exchange-correlation (xc) functionals. The time evolution of the expectation values of the dipole moment and harmonic spectra are calculated in the two gauges, and the basis set dependence on the gauge-invariance of these properties is investigated.
Bing, Y., Selassie, D., Paradise, R. H., Isborn, C., Kramer, N., Sadilek, M., Kaminsky, W., et al. (2010). {Circular dichroism tensor of a triarylmethyl propeller in sodium chlorate crystals}. Journal of the American Chemical Society, 132, 7454–7465. Abstract
In 1919, Perucca reported anomalous optical rotatory dispersion from chiral NaClO(3) crystals that were colored by having been grown from a solution containing an equilibrium racemic mixture of a triarylmethane dye (Perucca, E. Nuovo Cimento 1919, 18, 112-154). Perucca's chiroptical observations are apparently consistent with a resolution of the propeller-shaped dye molecules by NaClO(3) crystals. This implies that Perucca achieved the first enantioselective adsorption of a racemic mixture on an inorganic crystal, providing evidence of the resolution of a triarylmethyl propeller compound lacking bulky ortho substituents. Following the earlier report, NaClO(3) crystals dyed with aniline blue are described herein. The rich linear optical properties of (001), (110), and (111) sections of these mixed crystals are described via their absorbance spectra in polarized light as well as images related to linear dichroism, linear birefringence, circular dichroism, and anomalous circular extinction. The linear dichroism fixes the transition electric dipole moments in the aromatic plane with respect to the growth faces of the NaClO(3) cubes. Likewise, circular dichroism measurements of four orientations of aniline blue in NaClO(3) fix a bisignate tensor with respect to the crystal growth faces. Electronic transition moments and circular dichroism tensors were computed ab initio for aniline blue. These calculations, in conjunction with the crystal-optical properties, establish a consistent mixed-crystal model. The nature of the circular extinction depends upon the crystallographic direction along which the crystals are examined. Along 100, the crystals evidence circular dichroism. Along 110, the crystals evidence mainly anomalous circular extinction. These two properties, while measured by the differential transmission of left and right circularly polarized light, are easily distinguished in their transformation properties with respect to reorientations of the sample plates. Circular dichroism is symmetric with respect to the wave vector, whereas anomalous circular extinction is antisymmetric. Analysis of Perucca's raw data reveals that he was observing a convolution of linear and circular optical properties. The relatively large circular dichroism should in principle establish the absolute configuration of the propeller-shaped molecules associated with d- or l-NaClO(3) crystals. However, this determination was not as straightforward as it appeared at the outset. In the solid state, unlike in solution, a strong chiroptical response is not in and of itself evidence of enantiomeric resolution. It is shown how it is possible to have a poor resolution-even an equal population of P and M propellers-within a given chiral NaClO(3) crystal and still have a large circular dichroism.
Fischer, S. A., Madrid, A. B., Isborn, C. M., & Prezhdo, O. V. (2010). {Multiple exciton generation in small Si clusters: A high-level, ab initio study}. Journal of Physical Chemistry Letters, 1, 232–237. Abstract
The electron hole excitonic nature of high energy states is investigated in neutral and charged Si clusters, motivated by the multiple exciton generation (MEG) process that is highly debated in photovoltaic literature, Silicon forms the basis for-much of the photovoltaic industry, and our high-level, first principles calculations show that at 2-3 times the lowest excitation energy, the majority of optically excited states in neutral Si, and Si 10 take on multiple exciton (ME) character. The transition from single excitons (SEs) to MEs is not as sharp in Si as in PbSe clusters, but it is much more pronounced than in CdSe. The closer similarity of Si to PbSe than CdSe is unexpected, since Si clusters are less symmetric than PbSe clusters. Charging suppresses MEG in Si clusters; however, the suppression is less pronounced than in PbSe. A strong ME signal is seen already at 5 X E(g) upon charging. The low ME thresholds and nearly complete switch from SEs to MEs create a good possibility for efficient MEG in neutral Si nanoclusters and reveal hope that reasonable quantum yields can still be obtained despite charging.
Liang, W., Isborn, C. M., Lindsay, A., Li, X., Smith, S. M., & Levis, R. J. (2010). {Time-dependent density functional theory calculations of ehrenfest dynamics of laser controlled dissociation of NO+: Pulse length and sequential multiple single-photon processes}. Journal of Physical Chemistry A, 114, 6201–6206. Abstract
Intense laser field controlled dissociation reactions of the nitric oxide cation (NO(+)) are studied by ab initio Ehrenfest dynamics with time-dependent density functional theory. Intense electric fields with five different pulse lengths are compared, combined with potential energy surface and density of state analysis, to reveal the effect of pulse length on the control mechanism. Controllable dissociative charge states are observed, and the correlation between the laser pulse length and the probability of sequential multiple single-photon processes is presented. This work introduces a concept of using laser pulse length to control the sequential multiple single-photon process.