Ryan P. Steele

The initial and final states of electron and energy transfer processes: diabatization as motivated by system-solvent interactions.

For a system which undergoes electron or energy transfer in a polar solvent, we define the diabatic states to be the initial and final states of the system, before and after the nonequilibrium transfer process. We consider two models for the system-solvent interactions: A solvent which is linearly polarized in space and a solvent which responds linearly to the system. From these models, we derive two new schemes for obtaining diabatic states from ab initio calculations of the isolated system in the absence of solvent. These algorithms resemble standard approaches for orbital localization, namely, the Boys and Edmiston-Ruedenberg (ER) formalisms. We show that Boys localization is appropriate for describing electron transfer [Subotnik et al., J. Chem. Phys. 129, 244101 (2008)] while ER describes both electron and energy transfer. Neither the Boys nor the ER methods require definitions of donor or acceptor fragments and both are computationally inexpensive. We investigate one chemical example, the case of oligomethylphenyl-3, and we provide attachment/detachment plots whereby the ER diabatic states are seen to have localized electron-hole pairs.

An Improved Algorithm for Analytical Gradient Evaluation in Resolution-of-the-Identity Second-Order Møller-Plesset Perturbation Theory: Application to Alanine Tetrapeptide Conformational Analysis

We present a new algorithm for analytical gradient evaluation in resolution‐of‐the‐identity second‐order Møller‐Plesset perturbation theory (RI‐MP2) and thoroughly assess its computational performance and chemical accuracy. This algorithm addresses the potential I/O bottlenecks associated with disk‐based storage and access of the RI‐MP2 t‐amplitudes by utilizing a semi‐direct batching approach and yields computational speed‐ups of approximately 2–3 over the best conventional MP2 analytical gradient algorithms. In addition, we attempt to provide a straightforward guide to performing reliable and cost‐efficient geometry optimizations at the RI‐MP2 level of theory. By computing relative atomization energies for the G3/99 set and optimizing a test set of 136 equilibrium molecular structures, we demonstrate that satisfactory relative accuracy and significant computational savings can be obtained using Pople‐style atomic orbital basis sets with the existing auxiliary basis expansions for RI‐MP2 computations. We also show that RI‐MP2 geometry optimizations reproduce molecular equilibrium structures with no significant deviations (>0.1 pm) from the predictions of conventional MP2 theory. As a chemical application, we computed the extended‐globular conformational energy gap in alanine tetrapeptide at the extrapolated RI‐MP2/cc‐pV(TQ)Z level as 2.884, 4.414, and 4.994 kcal/mol for structures optimized using the HF, DFT (B3LYP), and RI‐MP2 methodologies and the cc‐pVTZ basis set, respectively. These marked energetic discrepancies originate from differential intramolecular hydrogen bonding present in the globular conformation optimized at these levels of theory and clearly demonstrate the importance of long‐range correlation effects in polypeptide conformational analysis.

Potential Energy Curves for Cation-π Interactions: Off-Axis Configurations Are Also Attractive

Accurate potential energy surfaces for benzene.M complexes (M = Li+, Na+, K+, and NH4+) are obtained using coupled-cluster theory through perturbative triple excitations, CCSD(T). Our computations show that off-axis cation-pi interactions, where the cation is not directly above the aromatic ring, can be favorable and may influence molecular recognition. Even perpendicular, side-on interactions retain 18-32% of their pi-face interaction energy in the gas phase, making their bond strengths comparable to hydrogen bonds in the gas phase. Solvent effects have been explored for each complex using the polarizable continuum model.

Dual-basis second-order Møller-Plesset perturbation theory: A reduced-cost reference for correlation calculations

The resolution-of-the-identity (RI) approximation has placed the onus of the cost of a second-order Moller-Plesset (MP2) calculation on the underlying self-consistent field (SCF) calculation for many moderately sized molecules. A dual-basis approach to the SCF calculation, based on previous methods demonstrated for density functional theory, is combined with RI-MP2 calculations, and small basis subsets for cc-pVTZ, cc-pVQZ, and 6-311++G(3df,3pd) are presented. These subsets provide time savings of greater than 90%, with negligible errors in absolute and relative energies, compared to the associated full-basis counterpart. The method is tested with a series of rotational barriers, relative conformational energies of alanine tetrapeptides, as well as the full G3/99 molecular set. RI-MP2 calculations on alanine octapeptides (40 heavy atoms, 3460 basis functions), using cc-pVQZ, are presented. Results improve upon previous methods that diagonalize the virtual space separately.

How the Shape of an H-Bonded Network Controls Proton-Coupled Water Activation in HONO Formation

Its the Network Numerous reactions of small molecules and ions in the atmosphere take place in the confines of watery aerosols. Relph et al. (p. 308; see the Perspective by Siefermann and Abel) explored the specific influence of a water clusters geometry on the transformation of solvated nitrosonium (NO+) to nitrous acid (HONO). The reaction involves (O)N–O(H) bond formation with one water molecule, concomitant with proton transfer to additional, surrounding water molecules. Vibrational spectroscopy and theoretical simulations suggest that certain arrangements of the surrounding water network are much more effective than others in accommodating this charge transfer, and thus facilitating the reaction. Vibrational spectroscopy uncovers the role of a surrounding water network in the mediating reaction of a solvated ion. Many chemical reactions in atmospheric aerosols and bulk aqueous environments are influenced by the surrounding solvation shell, but the precise molecular interactions underlying such effects have rarely been elucidated. We exploited recent advances in isomer-specific cluster vibrational spectroscopy to explore the fundamental relation between the hydrogen (H)–bonding arrangement of a set of ion-solvating water molecules and the chemical activity of this ensemble. We find that the extent to which the nitrosonium ion (NO+)and water form nitrous acid (HONO) and a hydrated proton cluster in the critical trihydrate depends sensitively on the geometrical arrangement of the water molecules in the network. Theoretical analysis of these data details the role of the water network in promoting charge delocalization.

Efficient anharmonic vibrational spectroscopy for large molecules using local-mode coordinates

This article presents a general computational approach for efficient simulations of anharmonic vibrational spectra in chemical systems. An automated local-mode vibrational approach is presented, which borrows techniques from localized molecular orbitals in electronic structure theory. This approach generates spatially localized vibrational modes, in contrast to the delocalization exhibited by canonical normal modes. The method is rigorously tested across a series of chemical systems, ranging from small molecules to large water clusters and a protonated dipeptide. It is interfaced with exact, grid-based approaches, as well as vibrational self-consistent field methods. Most significantly, this new set of reference coordinates exhibits a well-behaved spatial decay of mode couplings, which allows for a systematic, a priori truncation of mode couplings and increased computational efficiency. Convergence can typically be reached by including modes within only about 4 Å. The local nature of this truncation suggests particular promise for the ab initio simulation of anharmonic vibrational motion in large systems, where connection to experimental spectra is currently most challenging.

Non-Covalent Interactions with Dual-Basis Methods: Pairings for Augmented Basis Sets

Basis set pairings for dual-basis calculations are presented for the aug-cc-pVXZ (X = D, T, Q) series of basis sets. Fidelity with single-basis results is assessed at the second-order Møller-Plesset perturbation theory (MP2) level within the resolution-of-the-identity (RI) approximation, using the S22 set of noncovalent interactions and a series of electron affinities from the G3 set. Root-mean-squared errors for the S22 set are 0.019 kcal mol(-1) or lower, with a maximum deviation of 0.44%, and errors in nuclear structures are 0.09% or lower. Cost savings of 60-93% (RI-MP2 energies) and 50-88% (RI-MP2 gradients) are demonstrated. Spin-component-scaled MP2 [SCS(MI)-MP2] scaling parameters are provided for the aug-cc-pVXZ series, and dual-basis results are shown to be consistent without reoptimization of the single-basis parameters. Explicit handling of linear dependence in the basis set projection scheme is also provided. These dual-basis pairings will be helpful for accelerating accurate Hartree-Fock, density functional theory (DFT), MP2 and scaled MP2, and so-called doubly hybrid DFT calculations of intermolecular interactions (and other systems), where augmented basis sets are physically important.

The analytical gradient of dual-basis resolution-of-the-identity second-order Møller–Plesset perturbation theory

In this work, we present the analytical gradient of dual-basis second-order Møller–Plesset perturbation theory within the resolution-of-the-identity approximation (DB-RI-MP2). Interestingly, analytical DB-RI-MP2 gradient theory involves significant changes to both the theory and computation of the coupled-perturbed self-consistent field equations (CPSCF). From a theoretical point of view, the number of orbital responses required in DB-RI-MP2 analytical gradient theory has been reduced to the product of the number of occupied and virtual orbitals determined by the rank of the small atomic orbital (AO) basis. From a computational point of view, the DB-CPSCF equations can be solved within this smaller space at a fraction of the computational cost. Additional computational savings can be obtained during the digestion of the four-centered AO integral derivatives and the efficient underlying DB-SCF procedure, which lead to a significant overall reduction in the computational cost necessary for treating molecular systems containing less than 100 atoms. Based on stringent chemical tests and a detailed computational timings analysis, it was found that DB-RI-MP2 reproduces molecular equilibrium structures with an accuracy that approximates RI-MP2 using the target AO basis but at a dramatically reduced cost, thereby enabling more routine use of large AO basis sets during geometry optimizations at the MP2 level of theory.

Structural Progression in Clusters of Ionized Water, (H2O)n=1–5+

Ionized water clusters serve as a model of water-splitting chemistry for energetic purposes, as well as postradiolytic events in condensed-phase systems. Structures, properties, and relative energies are presented for oxidized water clusters, (H2O)n=1-5(+), using equation-of-motion coupled-cluster theory approaches. In small clusters, an ion-radical contact pair OH···H3O+ is known to form upon ionization. The transition from n = 4 to n = 5 molecules in the cluster, however, is found to demarcate a size regime in which a propensity for the ion and radical to separate exists. This trend is consistent with recent experimental vibrational analyses. Decomposition of the cluster energetics reveals that preferential solvation of the hydronium cation by water serves as the dominant driving force for this pair separation, which should persist in larger clusters and bulk water ionization.

Dual-basis self-consistent field methods: 6-31G* calculations with a minimal 6-4G primary basis

The feasibility of the strongest possible dual-basis approximation to polarized valence double zeta Hartree–Fock and density functional theory calculations is explored. Specifically, to approximate 6-31G* and 6-31 + G* calculations, a minimal 6-4G basis is constructed from 6-31G exponents. The self-consistent field calculation is performed in this minimal basis, followed by a single diagonalization step in the target basis. Statistical errors in atomization energies, molecular structures, and harmonic frequencies approach those of the target basis for HF, B3LYP and EDF1, and are far superior to calculations that do not include polarization functions. Speedups of approximately 5–10 are obtained for the energy, with speedups of 2–3 for the gradient, using existing algorithms, with significant potential for future improvements.