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.

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 İMD\ 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 İMD\ and AI-PIMD simulations to enzymes.

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.

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.

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 İMD\ 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 İMD\ and AI-PIMD simulations to enzymes.

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.

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.