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Ground
State Self-Consistent Field Methods |
Hartree-Fock Theory
- Restricted, Unrestricted, and Restricted
Open-Shell Formulations
- Analytical First Derivatives for
Geometry Optimizations
- Analytical Second Derivatives for
Harmonic Frequency Analysis
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Density Functional Theory
- Local Functionals and Gradient-Corrected
Functionals
- Exchange Functionals
- Slater
- Becke '88 (B)
- GGA91 (Perdew '91, PW91)
- Gill '96
- Gilbert and Gill '99 (GG99)
- Correlation Functionals
- VWN (#5 parameterization)
- Lee-Yang-Parr (LYP), LYP(EDF1
parameterization)
- Perdew-Zunger '81 (PZ81)
- Perdew '86 (P86)
- Wigner
- GGA91 (Perdew '91, PW91)
- EDF1 and Becke(EDF1) exchange-correlation
functionals
- User-definable exchange-correlation
functionals
- Hybrid HF-DFT Functionals
- B3LYP, B3PW91, B3LYP5 (using the
VWN5 functional)
- User-definable hybrid functionals
- Numerical-Grid Based Numerical Quadrature
Schemes
- The SG-1 standard grid
- Lebedev and Gauss-Legendre Angular
Quadrature Schemes
- Analytical First Derivatives for
Geometry Optimizations
- Analytical Second Derivatives for
Harmonic Frequency Analysis
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Linear Scaling Methods
- Continuous Fast Multipole Method
(CFMM)
- Fastest ab initio implementation
of multipole-based methods
- Linear-cost calculation of electronic
Coulomb interactions
- Finds exact Coulomb energy;
no approximations are made
- Efficiently calculates energy
and gradient
- Linear-Scaling K method
- Linear scaling exchange energies
and gradients for cases with sparse density matrices
- Linear Scaling Grid Based Integration
for Exchange-Correlation Functional Evaluation
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Q-Chem'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 two-electron 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.
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SCF Improvement Features
- Automated optimal hybrid of in-core
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 Wolfsberg-Helmholtz
(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 molecular-optimized
minimal basis of polarized atomic orbitals (PAOs)
- Set of orbitals defined by a atom-blocked
linear transformation from the fixed atomic orbital basis
- Potential computational advantages
for local MP2 compuations
- Analytical gradients and second-order
corrections to the energy available
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Wave
Function Based Treatments of Electron Correlation |
Møller-Plesset Theory
- Second-Order Møller-Plesset Theory
(MP2)
- Restricted, Unrestricted, and Restriced
Open-Shell Formulations Available
- Energy via direct and semi-direct
methods
- Analytical gradient via efficient
semi-direct method available for restricted and unrestricted
formalisms
- Proper treatment of frozen orbitals
in analytical gradient
- Energy via MP3, MP4 and MP4SDQ methods
also available
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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
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Coupled-Cluster Methods
- CCD, CCSD, and CCSD(T), and CCSD(2)
- QCISD, QCISD(T) and QCISD(2) energies
available
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Optimized Orbital Coupled-Cluster
Methods
- Optimized Orbital Couple-Cluster
Doubles (OD)
- Helpful in avoiding artifactual
symmetry breaking problems
- The mean-field reference orbitals
are optimized to minimize the total energy
- Alternative approach to Brueckner
coupled-cluster
- OD, OD(T), and OD(2) energies and
gradients available
- Valence Optimized Orbital Coupled-Cluster
Doubles (VOD)
- Coupled-cluster 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
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Excited
State Methods |
CIS Methods
- Excited states are computed starting
from a Hartree-Fock wavefunction
- Provides qualitatively correct descriptions
of single-electron excited states
- Geometries and frequencies comparable
to ground-state Hartree-Fock results
- Efficient, direct algorithm for computing
closed- and open- shell energies, analytical gradients and second
derivatives
- CIS (XCIS) Method available
- Comparible results to the closed-shell
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)
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Time-Dependent DFT (TD-DFT)
- Excited state energies computed from
a ground state Kohn-Sham wavefunction
- For low-lying valence excited states,
TD-DFT 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 low-lying valence excited states of radicals
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Coupled-Cluster Based Excited
State Methods
- OOD method
- Essentially identical numerical
performance to CCSD excited state energies
- Higher accuracy than TD-DFT, but
more computationally expensive
- Equation of Motion VOOD method
- Similar to EOM-CCSD cast into the
VOOD scheme
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Attachment-Detachment Analysis
for Excited States
- A unique tool for visualizing electronic
transtions
- Utilizes the difference density
matrix between the ground exctied state to create a one-electron
picture of electronic transitions
- Useful in classifying the character
electronic transistion as valence, Rydberg, mixed, or charge-transfer.
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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 out-of-plane bend constraints
- Freezes atoms in Cartesian coordinates
- Desired constraints do not need
to be imposed in starting structure
- Optimizes in Cartesian, Z-Matrix
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
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Vibrational Spectra
- Automated with both analytical and
numerical second-derivatives
- Infrared and Raman intensities
- Outputs standard statistical thermodynamic
information
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Natural Bond Orbital Analysis
- A sophistocated approach to population
analysis
- Q-Chem provided with NBO version
4.0
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Stewart Atoms
- Recovers the atomic identity from
a molecular density
- Provides a simplified representation
of the electronic density
- Q-Chem utilizes the resolution of
the identity (RI) for computaion of these values.
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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
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Intracules
- Q-Chem 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
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Solvation Modelling
- Include solvation effects in ab-initio
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
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Relativistic Energy Corrections
- Additive correction to the Hartree-Fock
energy is computed atomatically everytime a frequency calculation
is requested
- Needed for an accurate description
of heavy-atoms
- Approximately accounts for the increase
of electron mass as the electron approaches the speed of light
- Based on Dirac-Fock theory
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Diagonal Adiabatic Correction
- Computes the Born-Oppenheimer diagonal correction in order
account a breakdown in the seperation of nuclear and electronic
motion
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Basis
Sets |
Gaussian Basis Sets
- Standard Pople Basis Sets
- 3-21G (H-Cs), 4-31G (H-Cl), 6-31G
(H-Kr), and 6-311G (H-Kr)
- polarization and diffuse function
extensions
- Dunning's systematic sequence of
correlation consistent basis sets
- Obtained from the Pacific
Northwest Basis Set Database
- cc-pVDZ, cc-pVTZ, cc-pVQZ, cc-pV5Z
for H-Ar
- augmented versions of these sets
for H-Ar
- core-valence effects included through
the cc-pCVXZ basis set for B-Ne
- DZ and TZ basis sets also available
The modern Ahlrich's double and triple
zeta basis sets are also available
- User-specified basis sets supported
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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 Hay-Wadt minimal basis
- The Hay-Wadt valence double zeta
basis
- lanl2dz (mimic of Gaussian's lanl2dz)
- Stevens-Bausch-Krauss-Jaisen-Cundari-21G
- CRENBL-Christiansen et al.
shape consistent large orbital,small core
- CRENBS-Christiansen et al.
shape consistent small basis large core
- Stuggart relativistic large core
- Stuggart relativistic small core
- User-defined pseudopotential basis
sets supported
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