## Introduction

The Jaguar *ab initio* electronic structure program has been developed over the past 20 years with the goal of treating large systems with accurate quantum chemical methods. Currently Jaguar is commercial software produced and maintained by Schrödinger Inc. A distinguishing characteristic of Jaguar is that computational efficiency for large systems has been implemented in it via the use of the pseudospectral (PS) method, a numerical approach to the calculation of the Coulomb and exchange terms, which provides particularly significant advantages for the computation of exact exchange terms.[1-9]

The focus of the present code is on density functional theory (DFT)[10] and local second-order perturbation theory (LMP2).[11, 12] The scaling with system size and prefactors in these methods are reasonable, which enables practical calculations for systems containing hundreds of atoms. The program is employed in both the biological and materials science communities for calculations on large systems, particularly in pharmaceutical applications and modeling of enzymatic reactions. Another important application of Jaguar is in force field development. As an important example, Jaguar is an intrinsic component of the Schrödinger OPLS2 package,[13] which features extensive coverage of pharmaceutically relevant chemistries via more than 10,000 torsional terms, each of which has been fitted to appropriate quantum mechanical data.

Over the past decade, our major efforts have been devoted to enhancing Jaguar performance and accuracy in DFT calculations, particularly those using hybrid functionals that require exact exchange. Three areas have seen particularly active development during the previous two decades: enhancing accuracy of DFT functionals, accelerating computational performance of the self-consistent field (SCF) algorithm by, for example, creating better initial guesses for the wave function and implementing efficient parallelization over a large number of processors, and developing methods that yield accurate results in the condensed phase. Each of these efforts is outlined briefly below and in more detail in the main body of the review. For condensed phase applications in solution, the use of continuum solvation models is critical to obtaining results that can be profitably compared with experimental data. Jaguar was one of the first quantum chemistry programs to develop an optimized continuum solvent model, based on a self-consistent reaction field solution of the Poisson–Boltzmann (PB) equation,[14-16] and we have continued to improve and test this approach for predicting a wide range of properties including solvation energies,[17, 18] pKa's,[19, 20] redox potentials,[21, 22] and other aspects of chemical processes.[23]

Development of DFT functionals is being conducted by many research groups, and at present, there is a very large number of alternatives in the literature.[24-26] Many of the popular functionals have been implemented in Jaguar. We highlight in particular the Minnesota family of density functionals, such as M06-2X,[27, 28] which have displayed substantial improvements for a wide variety of properties including heats of formation, dispersion interactions, and conformational energies. In parallel, we have developed our own novel approach to improving the results of DFT calculations, which is based on the use of empirical localized orbital correction (LOC). The theoretical foundation of the DFT-LOC approach is described in Ref. [[29] and is also briefly summarized in the present review in section Methods employing LOC. The basic idea is to associate errors in DFT energetics, particularly for the B3LYP functional, with specific electron pairs (chemical bonds and lone pairs) and singly occupied orbitals, and to assume the transferability of these errors for a specific chemical environment from one molecule to another. This approach has enabled chemical accuracy (∼1 kcal/mole average errors) to be obtained for molecules composed of second and third row atoms,[30, 31] and somewhat larger average errors of 2-3 kcal/mole for redox potentials, spin splittings, and metal-ligand bond energies in systems containing transition metal atoms.[32-34] These results compare favorably with alternative efforts to improve DFT accuracy, and therefore we decided to include several LOC-based methods in Jaguar.

Finally, achieving high performance for large systems continues to be a crucial objective in the application of *ab initio* quantum chemical methods in materials science and biology. An essential technology for biological systems involves mixed quantum mechanics/molecular mechanics (QM/MM) calculations, which enable the treatment of proteins and other biological macromolecules to be partitioned into a reactive core of 50–300 atoms surrounded by a periphery described by MM.[35, 36] For this purpose, Jaguar has been an essential component of the QM/MM package QSite.[37, 38] A second effort in this area is improvement of the parallel performance in Jaguar. This has been a challenging project, but we will describe recent results in which we have been able to scale performance up to as many as 120 computer processor cores, while retaining outstanding single node performance. Parallelization allows time to solution for an arbitrarily large system (e.g., a metal oxide cluster, such as our model for TiO_{2} nanoparticles in the Grätzel cell, discussed in section Optoelectronics and photovoltaics), to be substantially reduced; without such improvements in speed, many projects would not be feasible at all due to the high computational requirements to complete individual calculations. For performance of the Jaguar parallel code, see section Jaguar parallelization.