Calculations, in particular molecular mechanics
calculations^{1} and quantum chemical
calculations,^{24} play a multiple role in modernday 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
semiempirical 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
graphicsbased 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 HartreeFock 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 semiempirical
models. Nonempirical quantum chemical methods may also provide the best means
of parameterizing nextgeneration, semiempirical 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 semiempirical molecular orbital and density functional
methods. Spartan is intended to provide a convenient environment to carry out
individual molecular mechanics calculations, as well as semiempirical and
ab initio HartreeFock and correlated molecular orbital calculations and density
functional calculations on diverse molecular
systems. It also serves to facilitate processing of large numbers of closelyrelated 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,
semiempirical, 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 semiempirical. 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 semiempirical
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 highlevel
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, semiempirical 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 semiempirical modules each serve five primary functions:
 calculation of the energy (heat of formation for the
semiempirical module) and wavefunction corresponding to a single geometry,
 calculation of equilibrium geometry,
 calculation of transitionstate geometry,
 calculation of the Hessian (matrix of second derivatives) and
subsequent evaluation of normalmode 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 normalmode
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 semiempirical
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, semiempirical 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
transitionstate geometries and of normalmode 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 HartreeFock and
MP2 correlated models,^{3,6} for both closedshell and openshell systems (UHF
and UMP2 methods only). Internally stored basis sets include
STO3G, 321G, 631G and 6311G, 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 dtype Gaussians, is permitted.
Spartan's ab initio module provides both inmemory and direct techniques.
In memory techniques are very fast but are limited in their range of
application. HartreeFock calculations for closedshell 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. Inmemory, closedshell MP2 calculations are limited to
approximately 75 and 90 basis functions for 64 and 128 mbytes of memory,
respectively. Memory requirements for openshell molecules are greater.
Direct HartreeFock and MP2 methods incur significant additional
computation cost, but may be extended to much larger systems with quite low
memory demands. HartreeFock calculations involving 300550 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 150200 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 transitionstate geometries and normalmode
vibrational frequencies. At the present time it supports local density calculations using
the SVWN functional,^{4} and nonlocal density functional calculations using
the BP86^{4,8} functional. Two different implementations of the latter have
been provided, one in which nonlocal corrections are introduced in a
selfconsistent 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 631G, 631G* and 631G**
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
dtype functions on heavy (nonhydrogen) atoms is perhaps the simplest
basis set which could be expected to reliable results. DN**, which includes as well
ptype 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 300550 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: SemiEmpirical Module
Spartan's semiempirical module provides for the calculation of heats
of formation, equilibrium and transitionstate geometries and
normalmode vibrational frequencies, as well as for searching of conformation space of
both acyclic and cyclic molecules. The MNDO,^{9}
AM1^{10} and
PM3^{11} models are supported,
as is the MNDO/d method of
Thiel.^{12}
Also available is a semiempirical 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 dtype as well as s and ptype valence atomic orbitals. It is
distinct from previous semiempirical 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 nontransition
metals.
Any of these semiempirical 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
water^{14} 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 semiempirical 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 semiempirical
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 normalmode vibrational frequencies, as well
as for searching of conformation space for both cyclic and acyclic
molecules. The SYBYL force field^{17}
from Tripos, Inc., and the recently
introduced MMFF94^{18} 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
orbital^{20} and based on fits to molecular
electrostatic potentials^{21}), normalmode analysis and evaluation of thermodynamic
quantities (enthalpy, entropy and free energy), and calculation of the dipole
moment. These functions apply to semiempirical, 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
semiempirical, 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 
HPUX 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 semiempirical 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, SpringerVerlag, 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 higherorder MøllerPlesset 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 closedshell 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).
