Andrew T. B. Gilbert

Q-Chem 2.0: A High-Performance Ab Initio Electronic Structure Program Package

Q‐Chem 2.0 is a new release of an electronic structure program package, capable of performing first principles calculations on the ground and excited states of molecules using both density functional theory and wave function‐based methods. A review of the technical features contained within Q‐Chem 2.0 is presented. This article contains brief descriptive discussions of the key physical features of all new algorithms and theoretical models, together with sample calculations that illustrate their performance.

Self-Consistent Field Calculations of Excited States Using the Maximum Overlap Method (MOM) †

We present a simple algorithm, which we call the maximum overlap method (MOM), for finding excited-state solutions to self-consistent field (SCF) equations. Instead of using the aufbau principle, the algorithm maximizes the overlap between the occupied orbitals on successive SCF iterations. This prevents variational collapse to the ground state and guides the SCF process toward the nearest, rather than the lowest energy, solution. The resulting excited-state solutions can be treated in the same way as the ground-state solution and, in particular, derivatives of excited-state energies can be computed using ground-state code. We assess the performance of our method by applying it to a variety of excited-state problems including the calculation of excitation energies, charge-transfer states, and excited-state properties.

Interfacing Q-Chem and CHARMM to perform QM/MM reaction path calculations†

A hybrid quantum mechanical/molecular mechanical (QM/MM) potential energy function with Hartree‐Fock, density functional theory (DFT), and post‐HF (RIMP2, MP2, CCSD) capability has been implemented in the CHARMM and Q‐Chem software packages. In addition, we have modified CHARMM and Q‐Chem to take advantage of the newly introduced replica path and the nudged elastic band methods, which are powerful techniques for studying reaction pathways in a highly parallel (i.e., parallel/parallel) fashion, with each pathway point being distributed to a different node of a large cluster. To test our implementation, a series of systems were studied and comparisons were made to both full QM calculations and previous QM/MM studies and experiments. For instance, the differences between HF, DFT, MP2, and CCSD QM/MM calculations of H2O···H2O, H2O···Na+, and H2O···Cl− complexes have been explored. Furthermore, the recently implemented polarizable Drude water model was used to make comparisons to the popular TIP3P and TIP4P water models for doing QM/MM calculations. We have also computed the energetic profile of the chorismate mutase catalyzed Claisen rearrangement at various QM/MM levels of theory and have compared the results with previous studies. Our best estimate for the activation energy is 8.20 kcal/mol and for the reaction energy is −23.1 kcal/mol, both calculated at the MP2/6‐31+G(d)//MP2/6‐31+G(d)/C22 level of theory.

Self-consistent-field calculations of core excited states

The accuracy of core excitation energies and core electron binding energies computed within a Delta self-consistent-field framework is assessed. The variational collapse of the core excited state is prevented by maintaining a singly occupied core orbital using an overlap criterion called the maximum overlap method. When applied to a wide range of small organic molecules, the resulting core excitation energies are not systematically underestimated as observed in time-dependent density functional theory and agree well with experiment. The accuracy of this approach for core excited states is illustrated by the calculation of the pre-edge features in x-ray absorption spectra of plastocyanin, which shows that accurate results can be achieved with Delta self-consistent-field calculations when used in conjunction with uncontracted basis functions.

The role of exchange in systematic DFT errors for some organic reactions

Serious (up to 87 kJ mol(-1)) systematic DFT errors in a series of isodesmic reactions are found to be due to the DFT exchange component, and can be largely corrected by substitution of the DFT exchange energy with the Fock exchange energy.

Effective fragment potential method in Q‐CHEM: A guide for users and developers

A detailed description of the implementation of the effective fragment potential (EFP) method in the Q‐CHEM electronic structure package is presented. The Q‐CHEM implementation interfaces EFP with standard quantum mechanical (QM) methods such as Hartree–Fock, density functional theory, perturbation theory, and coupled‐cluster methods, as well as with methods for electronically excited and open‐shell species, for example, configuration interaction, time‐dependent density functional theory, and equation‐of‐motion coupled‐cluster models. In addition to the QM/EFP functionality, a “fragment‐only” feature is also available (when the system is described by effective fragments only). To aid further developments of the EFP methodology, a detailed description of the C++ classes and EFP modules workflow is presented. The EFP input structure and EFP job options are described. To assist setting up and performing EFP calculations, a collection of Perl service scripts is provided. The precomputed EFP parameters for standard fragments such as common solvents are stored in Q‐CHEMs auxiliary library; they can be easily invoked, similar to specifying standard basis sets. The instructions for generating user‐defined EFP parameters are given. Fragments positions can be specified by their center of mass coordinates and Euler angles. The interface with the IQMOL and WEBMO software is also described.

Performance of Density Functional Theory Procedures for the Calculation of Proton-Exchange Barriers: Unusual Behavior of M06-Type Functionals

We have examined the performance of a variety of density functional theory procedures for the calculation of complexation energies and proton-exchange barriers, with a focus on the Minnesota-class of functionals that are generally highly robust and generally show good accuracy. A curious observation is that M05-type and M06-type methods show an atypical decrease in calculated barriers with increasing proportion of Hartree-Fock exchange. To obtain a clearer picture of the performance of the underlying components of M05-type and M06-type functionals, we have investigated the combination of MPW-type and PBE-type exchange and B95-type and PBE-type correlation procedures. We find that, for the extensive E3 test set, the general performance of the various hybrid-DFT procedures improves in the following order: PBE1-B95 → PBE1-PBE → MPW1-PBE → PW6-B95. As M05-type and M06-type procedures are related to PBE1-B95, it would be of interest to formulate and examine the general performance of an alternative Minnesota DFT method related to PW6-B95.

Approaching the Hartree-Fock limit by perturbative methods

We describe perturbative methods for improving finite-basis Hartree-Fock calculations toward the complete-basis limit. The best method appears to offer quadratic error reduction and preliminary numerical applications demonstrate that remarkably accurate Hartree-Fock energies can be obtained.

An optimal point-charge model for molecular electrostatic potentials

Motivated by the Legendre expansion of the electrostatic potential (ESP), we propose a method for obtaining atomic point-charges for a molecule based on reproducing the low-order multipole moments of the system. The resulting multipole-derived charges (MDCs) are well defined, do not require sampling of the ESP at grid points around the molecule and provide excellent reproduction of the electrostatic potential. No constraints are placed on the magnitude of the atomic charges.

Density functional triple jumping

We propose a density functional perturbative scheme to approximate the energy of a high-level DFT calculation at a significantly reduced cost. Our approach involves performing a primary SCF calculation using a crude functional, basis set and quadrature grid, followed by a single step using a more sophisticated secondary functional, basis and grid. Unlike the earlier dual-level DFT approach of Nakajima and Hirao, we use Roothaan diagonalization instead of perturbation theory to incorporate the effects of the secondary basis set. We show that energies at the popular B3LYP/6-311+G(3df,2p)/(75,302) level can be accurately estimated from primary calculations at the relatively economical BLYP/6-31G(d)/SG-0 level.