
Ground
State SelfConsistent Field Methods 
HartreeFock Theory
 Restricted, Unrestricted, and Restricted
OpenShell Formulations
 Analytical First Derivatives for
Geometry Optimizations
 Analytical Second Derivatives for
Harmonic Frequency Analysis

Density Functional Theory
 Local Functionals and GradientCorrected
Functionals
 Exchange Functionals
 Slater
 Becke '88 (B)
 GGA91 (Perdew '91, PW91)
 Gill '96
 Gilbert and Gill '99 (GG99)
 Correlation Functionals
 VWN (#5 parameterization)
 LeeYangParr (LYP), LYP(EDF1
parameterization)
 PerdewZunger '81 (PZ81)
 Perdew '86 (P86)
 Wigner
 GGA91 (Perdew '91, PW91)
 EDF1 and Becke(EDF1) exchangecorrelation
functionals
 Userdefinable exchangecorrelation
functionals
 Hybrid HFDFT Functionals
 B3LYP, B3PW91, B3LYP5 (using the
VWN5 functional)
 Userdefinable hybrid functionals
 NumericalGrid Based Numerical Quadrature
Schemes
 The SG1 standard grid
 Lebedev and GaussLegendre Angular
Quadrature Schemes
 Analytical First Derivatives for
Geometry Optimizations
 Analytical Second Derivatives for
Harmonic Frequency Analysis

Linear Scaling Methods
 Continuous Fast Multipole Method
(CFMM)
 Fastest ab initio implementation
of multipolebased methods
 Linearcost calculation of electronic
Coulomb interactions
 Finds exact Coulomb energy;
no approximations are made
 Efficiently calculates energy
and gradient
 LinearScaling K method
 Linear scaling exchange energies
and gradients for cases with sparse density matrices
 Linear Scaling Grid Based Integration
for ExchangeCorrelation Functional Evaluation

QChem's AOINTS Package
for Two Electron Integrals
 Incorporates the latest advances
in high performance integrals technology
 COLD PRISM
 The most efficient method available
for evaluation of twoelectron Gaussian integrals
 Algorithms choose the optimum method
for each integral given the angular momentum and degree of
contraction
 Analytical solution of integrals
over pseudopotential operators
 J Matrix engine
 Direct computation of Coulomb matrix
elements approximately 10 times faster than explicit integral
evaluation.

SCF Improvement Features
 Automated optimal hybrid of incore
and direct SCF methods
 Direct Inversion in the Iterative
Subspace (DIIS)
 Drastically reduces the number of
iterations necessary to converge the SCF
 Initial Guessing Schemes
 Improves the initial starting point
for the SCF procedure
 Superposing spherical averaged atomic
densities (SAD)
 Generalized WolfsbergHelmholtz
(GWH)
 Projection from smaller basis sets
 Core Hamiltonian Guessing
 Maximum Overlap Method (MOM)
 Prevents oscillation of the occupations
at each iteration that can hinder convergence
 Scales cubic with the number of
orbitals
 Direct Minimization of the Fock Matrix
 Follows the energy gradients to
minimize the SCF energy providing a useful alternative to
DIIS
 Intermediate molecularoptimized
minimal basis of polarized atomic orbitals (PAOs)
 Set of orbitals defined by a atomblocked
linear transformation from the fixed atomic orbital basis
 Potential computational advantages
for local MP2 compuations
 Analytical gradients and secondorder
corrections to the energy available

Wave
Function Based Treatments of Electron Correlation 
MøllerPlesset Theory
 SecondOrder MøllerPlesset Theory
(MP2)
 Restricted, Unrestricted, and Restriced
OpenShell Formulations Available
 Energy via direct and semidirect
methods
 Analytical gradient via efficient
semidirect method available for restricted and unrestricted
formalisms
 Proper treatment of frozen orbitals
in analytical gradient
 Energy via MP3, MP4 and MP4SDQ methods
also available

Local MP2 Methods
 Drastically reduces cost through
physically motivated tructions of the full MP2 energy expression
 Reduces the scaling of the computation
with molecular size
 Capable of performing MP2 computations
on molecules roughly twice the size as capable with MP2 without
significant loss of accuracy!
 Utilizes extrapolated PAO's (EPAO's)
for local correlation
 Available methods are the TRIM (triatomics
in molecules) and DIM (diatomics in molecules) techniques
 Yields contiuous potential energy
surfaces
 TRIM recovers around 99.7% of the
full MP2 energy
 DIM recovers around 95% of the full
MP2 energy

CoupledCluster Methods
 CCD, CCSD, and CCSD(T), and CCSD(2)
 QCISD, QCISD(T) and QCISD(2) energies
available

Optimized Orbital CoupledCluster
Methods
 Optimized Orbital CoupleCluster
Doubles (OD)
 Helpful in avoiding artifactual
symmetry breaking problems
 The meanfield reference orbitals
are optimized to minimize the total energy
 Alternative approach to Brueckner
coupledcluster
 OD, OD(T), and OD(2) energies and
gradients available
 Valence Optimized Orbital CoupledCluster
Doubles (VOD)
 Coupledcluster approximation of
the traditional CASSCF method.
 A truncated OD wave function is
utilized within a valence active space
 Requires far less disk space and
scales better with system size than CASSCF so that larger
systems can be treated
 VOD, VOD(T), and VOD(2) energies
and gradients available

Excited
State Methods 
CIS Methods
 Excited states are computed starting
from a HartreeFock wavefunction
 Provides qualitatively correct descriptions
of singleelectron excited states
 Geometries and frequencies comparable
to groundstate HartreeFock results
 Efficient, direct algorithm for computing
closed and open shell energies, analytical gradients and second
derivatives
 CIS (XCIS) Method available
 Comparible results to the closedshell
CIS method for doublet and quartet states
 CIS(D) perturbative doubles correction
available
 Reduces the errors in CIS by a factor
of two or more (to roughly that of MP2)

TimeDependent DFT (TDDFT)
 Excited state energies computed from
a ground state KohnSham wavefunction
 For lowlying valence excited states,
TDDFT provides a marked improvement over CIS, at about the same
cost
 Provides an implicit representation
of correlation effects in excited states
 Provides marked improvement over
CIS for lowlying valence excited states of radicals

CoupledCluster Based Excited
State Methods
 OOD method
 Essentially identical numerical
performance to CCSD excited state energies
 Higher accuracy than TDDFT, but
more computationally expensive
 Equation of Motion VOOD method
 Similar to EOMCCSD cast into the
VOOD scheme

AttachmentDetachment Analysis
for Excited States
 A unique tool for visualizing electronic
transtions
 Utilizes the difference density
matrix between the ground exctied state to create a oneelectron
picture of electronic transitions
 Useful in classifying the character
electronic transistion as valence, Rydberg, mixed, or chargetransfer.

Property Analysis 
Automated Geometry and Transition
Structure Optimization
 Uses Dr. Jon Baker's OPTIMIZE package
 Utilizes redundant internal coordinates
to ensure rapid convergence even without an initial force
constant matrix
 Geometry Optimization with General
Constraints
 Can impose bond angle, dihedral
angle (torsion) or outofplane bend constraints
 Freezes atoms in Cartesian coordinates
 Desired constraints do not need
to be imposed in starting structure
 Optimizes in Cartesian, ZMatrix
or delocalized internal coordinates
 Eigenvector Following (EF) algorithm
for minima and transition states
 GDIIS algorithm for minima
 Greatly speeds up convergence to
an equilibrium geometry

Vibrational Spectra
 Automated with both analytical and
numerical secondderivatives
 Infrared and Raman intensities
 Outputs standard statistical thermodynamic
information

Natural Bond Orbital Analysis
 A sophistocated approach to population
analysis
 QChem provided with NBO version
4.0

Stewart Atoms
 Recovers the atomic identity from
a molecular density
 Provides a simplified representation
of the electronic density
 QChem utilizes the resolution of
the identity (RI) for computaion of these values.

Momentum Densities
 Property that shows what momentum
an electron is most likely to possess
 Useful in comparison to Compton scattering
experiment results
 Compliment the normal electron density
in providing detailed picture of the electronic structure

Intracules
 QChem can compute these functions
that provide information can provide information about the Coulomb
and exchange energies in a molecule with respect to position and
momentum

Solvation Modelling
 Include solvation effects in abinitio
computations through the use of two models
 The simple Onsager reaction field
model
 The Langevin dipoles model
 Continuum model that realistically
treats solvation effects by adding a layer of dipoles
around the Van der Waals surface of the solute

Relativistic Energy Corrections
 Additive correction to the HartreeFock
energy is computed atomatically everytime a frequency calculation
is requested
 Needed for an accurate description
of heavyatoms
 Approximately accounts for the increase
of electron mass as the electron approaches the speed of light
 Based on DiracFock theory

Diagonal Adiabatic Correction
 Computes the BornOppenheimer diagonal correction in order
account a breakdown in the seperation of nuclear and electronic
motion

Basis
Sets 
Gaussian Basis Sets
 Standard Pople Basis Sets
 321G (HCs), 431G (HCl), 631G
(HKr), and 6311G (HKr)
 polarization and diffuse function
extensions
 Dunning's systematic sequence of
correlation consistent basis sets
 Obtained from the Pacific
Northwest Basis Set Database
 ccpVDZ, ccpVTZ, ccpVQZ, ccpV5Z
for HAr
 augmented versions of these sets
for HAr
 corevalence effects included through
the ccpCVXZ basis set for BNe
 DZ and TZ basis sets also available
The modern Ahlrich's double and triple
zeta basis sets are also available
 Userspecified basis sets supported

Pseudopotential Basis
Sets
 These sets incorporate relativistic
effects
 PRISM now supports fully analytical
treatment of intergrals over pseudopotential operators
 Standard pseudopotential sets obtained
from the Pacific
Northwest Basis Set Database
 Available sets are:
 The HayWadt minimal basis
 The HayWadt valence double zeta
basis
 lanl2dz (mimic of Gaussian's lanl2dz)
 StevensBauschKraussJaisenCundari21G
 CRENBLChristiansen et al.
shape consistent large orbital,small core
 CRENBSChristiansen et al.
shape consistent small basis large core
 Stuggart relativistic large core
 Stuggart relativistic small core
 Userdefined pseudopotential basis
sets supported

