SPARTAN 5.1 User's Guide: Chapter 1

Spartan 5.1 User's Guide

Chapter 1: Introduction

This section first outlines the goals which have guided, and continue to guide, the development of Spartan. Following this is a brief discussion of Spartan's architecture, in particular, the connectivity of its graphics and compute components, and how this architecture relates to the intended use of the program. Spartan's present capabilities and limitations are then enumerated. A listing of hardware and operating systems on which Spartan's modules are available is provided.

Section 1.1: Spartan

Calculations, in particular molecular mechanics calculations¹ and quantum chemical calculations,^2-4 play a multiple role in modern-day computational chemistry. Traditionally, they have served to supply information about the structures, relative stabilities and other properties of isolated molecules. Because of their inherent simplicity, molecular mechanics calculations on complex molecules may even be performed on personal computers and, probably because of this, have spread widely throughout the chemical community. Quantum chemical calculations, even semi-empirical molecular orbital calculations, but especially ab initio molecular orbital calculations and density functional calculations, are much more time demanding. Only recently, with the availability of fast workstations and efficient graphics-based programs, have these methods begun to be widely applied.

Quantum chemical methods have also been called on to furnish information about the mechanisms and product distributions of chemical reactions, either directly by calculations on transition states, or indirectly by modeling the steric and electronic demands of the reactants. Quantitative quantum chemical calculations, leading to information about reaction mechanisms, will become more common with increasing knowledge about the geometries of transition states, while qualitative models will still be needed for systems too large to be subjected to the more rigorous treatments.

Quantum chemical calculations are also able to supply information needed as input for other techniques, for example, atomic charges for QSAR analyses. Ab initio Hartree-Fock and correlated molecular orbital calculations, and density functional calculations, in particular, are also able to provide accurate intra and intermolecular potentials. This kind of information is required both by molecular mechanics and by molecular dynamics techniques used to describe a wide variety of phenomena, ranging from interactions between an enzyme and a drug to the physical properties of polymeric materials. All of these tasks are too complex now to be treated using quantum chemical models, even semi-empirical models. Non-empirical quantum chemical methods may also provide the best means of parameterizing next-generation, semi-empirical molecular orbital models, extending the range of application of quantum chemical techniques beyond that currently practical using ab initio and/or density functional methods.

The expanding role of molecular mechanics and quantum chemical calculations in chemistry and biochemistry and closely related fields, together with truly explosive developments in computer hardware and software technologies and with the rapidly changing makeup of the user community, prompted the development of Spartan, a program embracing molecular mechanics as well as ab initio and semi-empirical molecular orbital and density functional methods. Spartan is intended to provide a convenient environment to carry out individual molecular mechanics calculations, as well as semi-empirical and ab initio Hartree-Fock and correlated molecular orbital calculations and density functional calculations on diverse molecular systems. It also serves to facilitate processing of large numbers of closely-related calculations as might be required to map a conformational energy profile, to screen a set of compounds for a particular property or structural characteristic, or to parameterize a potential function for later use in a molecular mechanics or molecular dynamics calculation. Spartan is intended to be utilized by chemists, primarily experimental chemists, who may have little or no background in molecular mechanics or quantum chemical methods, but who want to use calculations much in the same way as experimental techniques such as NMR spectroscopy. With this in mind, particular attention has been paid to the interface linking Spartan to the user. Modern computer graphics techniques have been extensively employed, not only to greatly reduce the drudgery and possibility of error associated with the construction of program input, but also to guide the interpretation of program output.

Section 1.2: Spartan's Architecture

Spartan presently comprises seven independent program modules: a graphical user interface and ab initio, density functional, semi-empirical, mechanics, properties and graphics modules. Different modules may reside on the same or on different computers, and communicate with each other via the transfer of files without user intervention. In addition, Spartan's graphical user interface may also provide input for, execute and retrieve output from the Gaussian 94 electronic structure program,5 thereby extending its capability in a completely transparent manner.

The figure below illustrates the interconnectivity of Spartan's modules.

Spartan provides tight interconnectivity between compute and graphical components. Without leaving the graphical interface, the user can build a complex molecular structure and refine its geometry using molecular mechanics, then specify a task, e.g., geometry optimization, and level of quantum chemical calculation, e.g., AM1 semi-empirical. Following this, the user can designate any graphical surfaces, e.g., a surface of constant total electron density, and/or any graphical volumes from which isosurfaces and/or 2D slices can later be constructed, e.g., a volume of points corresponding to the electrostatic potential, for later display, specify properties of interest, e.g., charges based on fits to electrostatic potentials, and then submit the calculation either to the local workstation or to a server somewhere on the network. Once the calculation has completed, the user can view and/or print text and/or graphical output. Requests for additional molecular mechanics or quantum chemical calculations and/or additional graphical and property output may be made following completion. Spartan keeps track of what has already been done and will not repeat calculations unnecessarily. While one (or more) job is running, input for another job can be constructed or output corresponding to yet another examined. These jobs may be derivative, i.e., based on information resulting from earlier jobs, or completely independent. In short, the graphical user interface is a window into Spartan, allowing convenient access to its many features.

Spartan's architecture makes a clear separation between tasks and methods. Tasks indicate what is to be done, e.g., perform a geometry optimization or search conformation space, while methods dictate how the tasks are to be done, e.g., use MMFF molecular mechanics or the PM3 semi-empirical method. Both tasks and methods are specified in the graphical user interface, while the actual calculations are performed in the outlying modules. In principle, any task can be handled by any method and, while practical considerations may prove limiting in some cases, e.g., full conformation searches using high-level ab initio or correlated techniques are probably impractical at present, the notion that tasks and methods are independent is fundamental in the design of Spartan. Technology developments will continue to push the limits of what is practical.

SPARTAN's graphical user interface provides a number of functions, among them:

construction and editing of molecular structures,
preparation of input designating the quantum chemical or molecular mechanics calculation to be performed by the ab initio, density functional, semi-empirical or mechanics modules; the preparation of input for Gaussian 94,
preparation of input designating molecular properties to be calculated using the properties module,
preparation of input designating graphical surfaces and/or volumes to be calculated by the graphics module for later display,
display of text output resulting from molecular mechanics and quantum chemical calculations; special dialogs are available for the energy, dipole moment, HOMO and LUMO energies and atomic charges,
display and manipulation of structures resulting from molecular mechanics calculations and quantum chemical calculations; geometrical parameters, volume and surface area and symmetry are available,
display of isosurfaces (with or without mapped properties) from surface data, and construction and display of 2D slices and isosurfaces (with or without mapped properties) from volume data, either for single molecules or as differences between molecules which have previously been aligned; a special dialog is available for determining volume and surface area of a graphical object and for "reading" the value of a slice or of a property mapped onto an isosurface,
animation of normal modes of vibration, or motion along other geometrical coordinates, e.g., torsional motion; both geometrical structures and any graphical displays may be animated,
setting up coordinate sequences used, for example, to progress from reactant to product through a transition state,
setting up collections of molecules, either a result of previously completed tasks, e.g., conformation searching, or user defined,
statistical analyses and graphing of information on collections of molecules,
aligning molecules based on geometrical structure,
"export" and "import" of structures and other data to and from other programs,
printing of graphical displays, and
display of the dipole moment vector.

Spartan's ab initio, density functional and semi-empirical modules each serve five primary functions:

calculation of the energy (heat of formation for the semi-empirical module) and wavefunction corresponding to a single geometry,
calculation of equilibrium geometry,
calculation of transition-state geometry,
calculation of the Hessian (matrix of second derivatives) and subsequent evaluation of normal-mode vibrational frequencies and thermodynamic properties, and
searching conformation space.

Spartan's mechanics module serves four primary functions:

calculation of the strain energy corresponding to a single geometry,
calculation of equilibrium geometry,
calculation of the Hessian and evaluation of normal-mode vibrational frequencies and thermodynamic properties, and
searching conformation space.

Spartan's properties module serves five primary functions:

preparation of text output,
population analyses via the Mulliken and/or natural bond orbital procedures, and charge calculations based on fitting to molecular electrostatic potentials,
calculation of normal modes of vibration,
evaluation of thermodynamic properties,
calculation of the dipole moment, and
calculation of solvation energies in water, hexadecane and octanol and evaluation of LogP.

Spartan's graphics module is responsible for the actual calculation (but not the display) of volumes and surfaces and properties mapped onto those surfaces, based on ab initio, density functional, or semi-empirical wavefunctions. These include electron and spin densities and electrostatic and polarization potentials, as well as the molecular orbitals. Difference plots may be prepared from these data in the graphical user interface.

Section 1.3: Spartan's Present Capabilities and Limitations

Below are described the present capabilities and limitations of Spartan's ab initio, density functional, semi-empirical and mechanics modules.

Section 1.3.1: Ab Initio Module

Spartan's ab initio module provides for calculation of the energy and wavefunction for a given nuclear configuration, of equilibrium or transition-state geometries and of normal-mode vibrational frequencies. It also allows for searching of conformation space both for acyclic systems as well as for molecules incorporating rings. The module is presently limited to Hartree-Fock and MP2 correlated models,^3,6 for both closed-shell and open-shell systems (UHF and UMP2 methods only). Internally stored basis sets include STO-3G, 3-21G, 6-31G and 6-311G, and extensions to include one or more sets of polarization functions and/or diffuse basis functions.⁷ Input of an arbitrary basis set, comprising s, p and d-type Gaussians, is permitted.

Spartan's ab initio module provides both in-memory and direct techniques. In- memory techniques are very fast but are limited in their range of application. Hartree-Fock calculations for closed-shell systems comprising up to approximately 90 basis functions are practical with 64 mbytes of available memory, and up to approximately 105 basis functions with 128 mbytes of memory. In-memory, closed-shell MP2 calculations are limited to approximately 75 and 90 basis functions for 64 and 128 mbytes of memory, respectively. Memory requirements for open-shell molecules are greater.

Direct Hartree-Fock and MP2 methods incur significant additional computation cost, but may be extended to much larger systems with quite low memory demands. Hartree-Fock calculations involving 300-550 basis functions are practical with even modest amounts of memory, e.g., 32 mbytes. Memory demands for direct MP2 calculations are greater; calculations on systems with 150-200 basis functions are practical.

Preset limits within Spartan's ab initio module are enumerated below.

maximum number of atoms	100
maximum number of basis functions	600

Section 1.3.2: Density Functional Module

Spartan's density functional module provides for calculation of energies, equilibrium and transition-state geometries and normal-mode vibrational frequencies. At the present time it supports local density calculations using the SVWN functional,⁴ and non-local density functional calculations using the BP86^4,8 functional. Two different implementations of the latter have been provided, one in which non-local corrections are introduced in a self-consistent manner, and the other (less expensive) in which they are introduced perturbatively. Three different numerical basis sets are available: DN, DN* and DN**. While they are roughly equivalent in "size" to the 6-31G, 6-31G* and 6-31G** Gaussian basis sets, respectively, experience suggests that they yield results closer to much larger Gaussian basis sets.1b Note, that because density functional methods are correlated methods, basis sets need to include functions of higher angular quantum number than required for description of atomic ground states. DN* which includes
d-type functions on heavy (non-hydrogen) atoms is perhaps the simplest basis set which could be expected to reliable results. DN**, which includes as well
p-type functions on hydrogen, may be required in some instances.

Spartan's density functional module does not make significant use of intermediate disk storage, and in addition makes only modest memory demands. Calculations on molecules comprising 300-550 basis functions require on the order of 32 mbytes of memory.

Preset limits within Spartan's density functional module are enumerated below.

maximum number of atoms	100+
maximum number of basis functions	800

Section 1.3.3: Semi-Empirical Module

Spartan's semi-empirical module provides for the calculation of heats of formation, equilibrium and transition-state geometries and normal-mode vibrational frequencies, as well as for searching of conformation space of both acyclic and cyclic molecules. The MNDO,⁹ AM1¹⁰ and PM3¹¹ models are supported, as is the MNDO/d method of Thiel.¹²

Also available is a semi-empirical method for transition metals called PM3 (tm).13 This is related to Thiel's MNDO/d model, and describes each transition metal in terms of both d-type as well as s and p-type valence atomic orbitals. It is distinct from previous semi-empirical parameterizations available for Group IIB transition metals (Zn, Cd, Hg), in that it explicitly incorporates d functions. PM3 (tm) is intended to be used in conjunction with PM3 for non-transition metals.

Any of these semi-empirical methods may be used as the basis for singles and doubles CI, although the limits of CI calculations may be dictated by time and memory demands.

Corrections for aqueous solvation using the SM1, SM1a and SM2 models developed by Cramer and Truhlar14 may be obtained using AM1 wavefunctions. The Cramer/Truhlar SM3 model for water¹⁴ may be used with the PM3 method. Also incorporated into Spartan, are solvation models for both water and hexadecane developed by Dixon, Leonard and Hehre.¹⁵ These have been specifically parameterized for the MNDO, AM1 and PM3 methods (six parameterizations in total). They are computationally superior to the Cramer/Truhlar models as implemented in AMSOL,16 and generally produce solvation energies in better agreement with experiment.

While the memory requirements of semi-empirical molecular orbital methods are far less than those for ab initio models, they can still be significant for large molecules. The demand goes as approximately 100 times the square of the number of heavy atoms, and between 10 to 20 times the square of the number of basis functions. With 32 mbytes of memory, calculations are limited in practice to molecules comprising no more than 100 heavy atoms; 128 mbytes of available memory effectively doubles this limit.

Preset limits for Spartan's semi-empirical module are enumerated below.

maximum number of atoms (any type)

200

Section 1.3.4: Mechanics Module

Spartan's mechanics module presently provides for the calculation of equilibrium geometries, strain energies and normal-mode vibrational frequencies, as well as for searching of conformation space for both cyclic and acyclic molecules. The SYBYL force field¹⁷ from Tripos, Inc., and the recently introduced MMFF94¹⁸ are supported.

There are no preset limits for Spartan's mechanics module. Calculations on systems comprising upwards of 1,000 atoms are practical.

Section 1.3.5: Properties Module

Spartan's properties module provides text output printing, population analyses (Mulliken,¹⁹ natural bond orbital²⁰ and based on fits to molecular electrostatic potentials²¹), normal-mode analysis and evaluation of thermodynamic quantities (enthalpy, entropy and free energy), and calculation of the dipole moment. These functions apply to semi-empirical, density functional and ab initio wavefunctions from Spartan's modules, as well as to wavefunctions obtained from Gaussian 92/94/98. It also supports solvation energy calculations in water, hexadecane and in octanol and LogP calculations.

Section 1.3.6: Graphics Module

Spartan's graphics module provides data preparation associated with the display as isosurfaces, or as 2D slices of molecular orbitals, electron densities, spin densities and electrostatic and polarization potentials, as well as arbitrary sums and differences of these quantities. Graphics functions apply to semi-empirical, density functional and ab initio wavefunctions obtained from Spartan's modules as well as wavefunctions obtained from Gaussian 94.

Section 1.4: Hardware Platforms

Computers on which SPARTAN's modules are available are enumerated below.

Platform	Operating System

HP Visualize fx workstations	HP-UX 10.20 or later
DEC Alpha workstations	Digital Unix version 4.0
IBM RS/6000 workstations	AIX 3.2.5, 4.1.4
Silicon Graphics workstations	Irix 6.2, 6.3, 6.4
Fujitsu VP*
NEC SX4a*

*Graphical user interface must be run from networked workstation.

Notes

Reviews: (a) U. Burkert and N.L. Allinger, Molecular Mechanics, ACS monograph 177, American Chemical Society, Washington D.C., 1982; (b) W.J. Hehre, J. Yu and P.E. Klunzinger, A Guide to Molecular Mechanics and Molecular Orbital Calculations in Spartan, Wavefunction, Inc., Irvine, CA, 1997.
Reviews of semi-empirical methods: (a) T. Clark, A Handbook of Computational Chemistry, Wiley, New York 1986; (b) J.J.P. Stewart, J. Computer Aided Molecular Design, 4, 1 (1990). See also ref. 1b.
Review of ab initio methods: W.J. Hehre, L. Radom, P.v.R. Schleyer and J.A. Pople, Ab Initio Molecular Orbital Theory, Wiley, New York, 1986. See also ref. 1b.
Reviews of density functional theory: (a) R.O. Jones and O. Gunnarsson, Revs. Mod. Phys., 61, 689 (1989); (b) R.G. Parr and W. Yang, Density Functional Theory of Atoms and Molecules, Oxford Univ. Press, Oxford, 1989; (c) J.K. Labanowski and J.W. Andzelm, Eds., Density Functional Methods in Chemistry, Springer-Verlag, New York, 1991; (d) W.J. Hehre and L. Lou, A Guide to Density Functional Calculations in Spartan, Wavefunction, Inc., Irvine, CA, 1997.
Gaussian 92/94/98 available from Gaussian, Inc.
Additional electron correlation techniques including higher-order Møller-Plesset models and CI models are available in Gaussian 92/94/98, which may be accessed transparently from Spartan's graphical user interface. See Section 8.6.1.
For references to the basis sets supported in Spartan, see ref. 3, chapt. 4.
(a) A.D. Becke, Phys. Rev. A, 38, 3089 (1988); (b) J.P. Perdew, Phys. Rev. B, 33, 8822 (1986).
M.J.S. Dewar and W.J. Thiel, J. Am. Chem. Soc., 99, 4899 (1977).
M.J.S. Dewar, E.G. Zoebisch, E.F. Healy and J.J.P. Stewart, J. Am. Chem. Soc., 107, 3902 (1985).
J.J.P. Stewart, J. Computational Chem., 10, 209 (1989).
(a) W. Thiel and A. Voityuk, Theor. Chim. Acta., 81, 391 (1992); (b) W. Thiel and A. Voityuk, Int. J. Quantum Chem., 44, 807 (1992).
J. Yu and W.J. Hehre, J. Computational Chem., to be submitted.
(a) C.J. Cramer and D.G. Truhlar, J. Am. Chem. Soc., 113, 8305 (1991); (b) C.J. Cramer and D.G. Truhlar, Science, 256, 213 (1992); (c) C.J. Cramer and D.G. Truhlar, J. Computer Aided Molecular Design, 6, 69 (1992).
R.W. Dixon, J.M. Leonard and W.J. Hehre, Israel J. Chem., 33, 427 (1993). These solvation models are presently available only for closed-shell molecules.
C.J. Cramer and D.G. Truhlar, AMSOL, version 1.0, program no. 606, Quantum Chemistry Program Exchange, Indiana University, Bloomington, Indiana. The implementation of the SM1, SM1a, SM2 and SM3 aqueous solvation models inside of Spartan is faster than that in AMSOL, but is still slower than the implementation of the AM1aq, etc. models.
M. Clark, R.D. Cramer III and N. van Opdensch, J. Computational Chem., 10, 982 (1989).
T.A. Halgren, J. Computational Chem, 17, 490 (1996); and following papers in this issue.
R.S. Mulliken, J. Chem. Phys., 23, 1833, 1841, 2338, 2343 (1955).
(a) J.P. Foster and F. Weinhold, J. Am. Chem. Soc., 102, 7211 (1980); (b) A.E. Reed and F. Weinhold, J. Chem. Phys., 78, 4066 (1983); (c) A.E. Reed, R.B. Weinstock and F. Weinhold, ibid., 83, 735 (1985); (d) J.E. Carpenter and F. Weinhold, J. Mol. Struct. (Theochem.), 169, 41 (1988).
(a) L.E. Chirlian and M.M. Francl, J. Computational Chem., 8, 894 (1987); (b) C.M. Breneman and K.B. Wiberg, ibid., 11, 361 (1990).

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