Molecular Physics, Vol. 103, No. 6–8, 20 March–20 April 2005, 719–747 The GAMESS-UK electronic structure package: algorithms, developments and applications MARTYN F. GUESTy*, IAN J. BUSHy, HUUB J. J. VAN DAMy, PAUL SHERWOODy, JENS M. H. THOMASy, JOOP H. VAN LENTHEz, REMCO W. A. HAVENITHz and JOHN KENDRICK} yComputational Science and Engineering Department, CLRC Daresbury Laboratory, Daresbury, Warrington, Cheshire WA4 4AD, UK zTheoretical Chemistry Group, Debye Institute, Utrecht University, Utrecht, The Netherlands }QMolecular Ltd, 13 Castle Close, Middleton St George, Darlington DL2 1DE, UK A description of the ab initio quantum chemistry package GAMESS-UK is presented. The package offers a wide range of quantum mechanical wavefunctions, capable of treating systems ranging from closed-shell molecules through to the species involved in complex reaction mechanisms. The availability of a wide variety of correlation methods provides the necessary functionality to tackle a number of chemically important tasks, ranging from geometry optimization and transition-state location to the treatment of solvation effects and the prediction of excited state spectra. With the availability of relativistic ECPs and the development of ZORA, such calculations may be performed on the entire Periodic Table, including the lanthanides. Emphasis is given to the DFT module, which has been extensively developed in recent years, and a number of other, novel features of the program. The parallelization strategy used in the program is outlined, and detailed speedup results are given. Applications of the code in the areas of enzyme and zeolite catalysis and in spectroscopy are described. 1. Introduction quantum chemistry, as well as key contributor to the improvement of functionals for chemical problems and The UK version of GAMESS (Generalised Atomic and the techniques for its efficient implementation. His Molecular Electronic Structure System) [1] has been influence was key to the decision to set up a CCP1 under development for nearly a quarter of a century and flagship project in this area, and the results of this this volume, in celebration of the contribution of project are now maintained and distributed as part of Nicholas Handy, presents an ideal opportunity to GAMESS-UK, as well as being available for use in describe the current status of the program. The code other projects. The DFT module in GAMESS-UK has represents the principal piece of software developed and been available since version 6.0 of the code, and is maintained under the auspices of Collaborative described in some detail in section 3 of this paper. Computational Project No. 1 (CCP1). Nicholas Handy The article is organized as follows. An overview of the has, over this period, played a leading role in many program is given in section 2, tracing the development of aspects of this project, and we, the GAMESS-UK the code and outlining the possible wavefunctions that developers, owe a sincere debt of thanks to Nicholas for GAMESS-UK can calculate and the types of runs that the support he has given to the concept of a freely can be performed. Section 3 describes the GAMESS- available, centrally supported UK-based quantum UK implementation of DFT. Section 4 focuses on the chemistry code. Many parts of the program, specifically implementation aspects for a number of the more in the areas of perturbation theory for electron popular, and the more novel, features available within correlation and analytic derivatives, can be traced to the code. These include the modules for (i) Geometry developments in the Cambridge group. More recently, Optimization, (ii) the treatment of Relativistic Effects Nicholas has been the leading UK proponent of Density and ZORA, (iii) Valence Bond, (iv) MRDCI, (v) RPA Functional Theory (DFT) in the field of molecular and MCLR treatments of Excited States, (vi) QM/ MM and the treatment of Large Systems and, finally, our recent work on graphical interfaces, also performed * Corresponding author. e-mail: [email protected] within the CCP1 programme. Details of the parallel Molecular Physics ISSN 0026–8976 print/ISSN 1362–3028 online # 2005 Taylor & Francis Group Ltd http://www.tandf.co.uk/journals DOI: 10.1080/00268970512331340592 720 M. F. Guest et al. implementation of GAMESS-UK and the associated both CCSD [17, 18] and CCSD(T) [19, 20] coupled- performance attributes are given in section 5, while cluster calculations, although the latter remain limited section 6 considers the applications of the code in a to closed-shell systems [21]. A size-consistent variant of number of areas, including enzyme and zeolite catalysis multi-reference MP2 theory, popularized in its CASPT2 and spectroscopy. form by Roos et al. [22], is also available [23]. With no restriction to CAS wavefunctions, the module also provides MR-MP3 capabilities. One of the more recent 2. Overview of the program developments includes an implementation of the semi- direct table-driven MRDCI module [24, 25], providing The program is derived from the original GAMESS for more extensive capabilities in the treatment of code, obtained from Michel Dupuis in 1981 (then at electronic spectra and related phenomena. the National Resource for Computational Chemistry, The treatment of both excited and ionized states has NRCC), and has been extensively modified and long been a major requirement from users of the code. enhanced over the past two decades. The key driver in In addition to the MRD-CI treatments above, calcula- our adopting the code lay in the availability of gradient tions of electronic transition energies and corresponding capabilities, absent in the ATMOL suite of programs [2] oscillator strengths may be performed using either the that had been the main electronic structure code Random Phase Approximation (RPA) method or the supported under CCP1. Note that these developments Multiconfigurational Linear Response (MCLR) proce- have been conducted independently of the impressive dure [26]. The RPA calculations may be performed programme of extensions to the GAMESS code itself, either within the conventional approach where the conducted under the leadership of Mark Gordon and two-electron integrals are transformed or with a ‘direct’ Mike Schmidt at Iowa State University [3]. implementation. The direct calculation of molecular When first acquired, the code was essentially limited valence ionization energies may be performed through to HF/gradient functionality allowing for basis sets Green’s function techniques, using either the outer- involving s, p and d Cartesian Gaussian orbitals, with valence Green’s function (OVGF) [27] or the two- open- and closed-shell SCF treatments available within particle-hole Tamm–Dancoff method (2ph-TDA) [28]. both the RHF and UHF framework. Generalized While employing effectively the same integral and valence bond [4] treatments were also supported. The gradient technology, the program has been extended to program utilized Rotation [5] techniques to evaluate evaluate repulsion and the associated gradient integrals repulsion integrals over s and p Gaussians, and the Rys over f and g Gaussians. The original limitation to Polynomial [6] for integrals involving d Gaussians. SCF cartesian basis sets is lifted through the provision of convergence controls were provided through a hybrid spherical harmonic basis sets for all options within the scheme of level shifters and damping factors. The programme. SCF controls now use a hybrid scheme of analytic energy gradient was available for the above level shifters and the DIIS method [29, 30]. In addition, wavefunctions, with gradients for s and p Gaussians complete active space SCF [22, 31, 32] and more general evaluated using the algorithm due to Schlegel [7], MCSCF [33], and Møller Plesset (MP2 and MP3) [34, while gradients involving d Gaussians utilized the Rys 35] calculations may now be performed. Geometry Polynomial Method [8]. Force constants were evaluated optimization is conducted using a quasi-Newton rank- by numerical differentiation. Ab initio core potentials two update method, while transition state location is were provided in a semi-local [9–11] formalism for available through either a synchronous transit [36], trust performing valence-only molecular orbital treatments. region [37] or ‘hill-walking’ [38, 39] method. Force Many of the initial developments around the code constants may be evaluated analytically [40, 41], while focused on enriching the range of available post- coupled Hartree–Fock (CHF) calculations provide for a Hartree–Fock capabilities, with functionality originally range of molecular properties, including polarizabilities developed within the ATMOL suite of programmes and molecular hyperpolarizabilities [42] and, through integrated into the code. Thus conventional CI treat- the calculation of dipole moment and polarizability ments using the table-driven selection algorithms within derivatives, the computation of infra-red and Raman the framework of MR-DCI calculations [12–14] allowed intensities [43]. for the treatment of electronic spectra and related Many new ab initio core potentials have been phenomena, while large-scale CI calculations of both incorporated into the code which now includes both ground and first few excited states were provided by the semi-local and non-local [44] formalisms for Direct-CI [15] module. valence-only molecular orbital treatments. These initial correlation treatments have since been A wide variety of wavefunction analysis methods are extended through the incorporation of Full-CI