Q-Chem Program Features

Ground State Self-Consistent Field Methods: Hartree-Fock Methods; Density Functional Theory; Linear Scaling Methods; AOINTS Package for Two Electron Integrals; SCF Improvements; Hartree-Fock-Wigner Method

Wave Function Based Treatments of Electron Correlation: Møller-Plesset Perturbation Theory; Local MP2 Methods; Coupled Cluster Methods; Optimized Orbital Coupled-Cluster Methods

Excited State Methods: Supported Calculation Types; CIS Methods; Time-Dependent DFT; Coupled-Cluster Excited State Methods; Attachment-Detachment Analysis

Properties Analysis: Automated Geometry and Transition Structure Optimization; Vibrational Spectroscopy; NMR Shielding Tensors; Natural Bond Orbital Analysis; Stewart Atoms; Momentum Densities; Intracules; Atoms in Molecules; Solvation Modeling; Relativistic Energy Corrections; Diagonal Adiabatic Correction

Basis Sets: Gaussian Basis Sets; Pseudopotential Basis Sets; Correction for Basis Set Superposition Error

QM/MM: Interface to CHARMM; ONIUM

For a complete list of features please see Q-Chem User's Guide

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

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)
  - Handy and Cohen's OPTX (HC_OPTX)
Hybrid HF-DFT Functionals
- B3LYP, B3PW91, B3LYP5
  (using the VWN5 functional)
- User-definable hybrid functionals
Meta GGA Functionals
- BMK
- M05 and M06
Numerical-Grid Based Numerical Quadrature Schemes
- The SG-0 standard grid
  - This grid is derived from a MultiExp-Lebedev-(23,170), (i.e. 23 radial points and 170 angular points per radial point). This grid was pruned whilst ensuring the error in the computed exchange energies for the atoms and a selection of small molecules was less than 10 microhartree from that computed using a very large grid.
- The SG-1 standard grid
  - This grid is derived from a Euler-Maclaurin-Lebedev-(50,194) grid (i.e., 50 radial points, and 194 angular points per radial point).
    This grid has been found to give numerical integration errors of the order of 0.2 kcal/mol for medium-sized molecules, including particularly demanding test cases such as isomerization energies
    of alkanes.
- Lebedev and Gauss-Legendre Angular Quadrature Schemes
  - Lebedev Spheres avaiable for up to 5294 angular points.
- Incremental Density Function Theory
  - Improves efficiency of DFT calculations by greater amounts as convergence is reached by use of the difference denisty and Fock matrices.
Analytical First Derivatives for Geometry Optimizations
Analytical Second Derivatives for Harmonic Frequency Analysis
- Inclusion of the first and second derivatives
  of the Becke Weighting Functions for
  greater accuracy.

Linear Scaling Methods

Fourier Transform Coulomb Method (FTC)
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 HF-exchange method (LinK)
- Linear scaling exchange energies and gradients for cases with sparse density matrices
Linear Scaling Grid Based Integration for Exchange-Correlation Functional Evaluation
Linear Scaling NMR Chemical Shifts

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

SCF Improvements

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
Stability Analysis for SCF Wavefunctions
- Tests for a complex solution to the SCF equations to ensure the quality of energy minima.
- Available for restricted and unrestriced HF or DFT wavefunctions.
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

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
Local MP2 Methods
- Drastically reduces cost through physically motivated truncations 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 standard 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
RI-MP2 Methods
- Up to 10 times faster for MP2 and Local MP2

Coupled-Cluster Methods

Singles and Doubles (CCSD)
- Energies available.
- Gradients available via finite differences of energies.
EOM-XX-CCSD

XX = EE, EA, IP, SF
Robust treatment of radicals, bond-breaking and symmetry- breaking problems

Non-Iterative Corrections to the Coupled Cluster Energies
- (T) Triples Corrections (CCSD(T)) for CC energies
- (2) Triples and Quadruples Corrections (CCSD(2)) for CC energies
Extensive use of molecular point group symmetry to improve efficiency.
Quadratic Coupled-Cluster Doubles
- Improved behavior of the coupled-cluster wavefunction for such trouble cases as homolytic bond dissociation
QCISD, QCISD(T) and QCISD(2) energies available
Direct Inversion of the Iterative Subspace (DIIS) convergence acceleration
Frozen Core Approximations available to increase treatable system size.

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), VQCCD and VOD(2) energies and gradients available

Excited State Methods

Supported Calculation Types

Vertical absorbtion spectrum
- The calculation of the excited states of the molecule at the ground state geometry, as appropriate for absorption spectroscopy.
Excited state optimization
- Available via finite differences of energies.
Excited state vibrational analysis
- Available for UCIS and RCIS only.
Spin-Flip DFT

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)
RI-CIS(D) for faster correlated excited state calculations

Excited state energies computed from a ground state Kohn-Sham wavefunction

For low-lying 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 low-lying valence excited states of radicals

Spin-flip density functional threory (SFDFT)
- Extends TDDFT to states beyond the low-lying valence states.
- Also useful for bond-breaking processes and radical and diradical systems

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Coupled-Cluster Based Excited State Methods

Equation of Motion Coupled-Cluster Singles and Doubles EOM-CCSD
- Method of computing vertical excitation energies via linear response from the ground state CC wavefunction.
Spin-Flip Excited State Methods
- Improved treatment of di- and tri-radical systems.
- Address bond-breaking problems associated with a single-determinant wavefunction.
- Available for OD and CCSD levels of theory.
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 EOM-CCSD cast into the VOOD scheme
Excited State Property Calculations
- Transition dipoles and getometry
Potential energy surface crossing minimization with EOM-CCSD

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.

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
Intrinsic Reaction Coordinates (IRC) following
- Connect equilibrium geometries and transistion states along reaction paths.

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Vibrational Spectra

Automated with both analytical and numerical second-derivatives
Infrared and Raman intensities
Outputs standard statistical thermodynamic information
Isotropic subsitution available for comparison with experiment
Anharmonic correction

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NMR Shielding Tensors

NMR chemical shifts provides a reliable comparison between the experimentally measured NMR signals and structural properties.
First and only linear-scaling NMR calculation with hundreds of atoms

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Natural Bond Orbital Analysis

A sophistocated approach to population analysis Q-Chem provided with NBO version 5.0

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 computation 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
Complement the normal electron density in providing detailed picture of the electronic structure

Intracules

These are unique 2-electron distribution functions that provide the most detailed information about the Coulomb and exchange energies in a molecule with respect to position and momentum

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Atoms in Molecules Analysis (AIMPAC)

Q-Chem can now produce output suitable for use by the AIMPAC program, which is a freely available program that performs AIM analysis.
AIMPAC is available at

http://www.chemistry.mcmaster.ca/aimpac/imagemap/imagemap.htm

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Solvation Modelling

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
SS(V)PE: a new dielectric continuum model

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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 to account for a breakdown in the adiabatic separation of nuclear and electronic motions

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
The modern Ahlrichs 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 integrals 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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Correction for Basis Set Superposition Error (BSSE)

Places basis functions on ghost atoms to correct the overestimation of binding energies.

The QM/MM interface between Q-Chem and CHARMM is distributed with the standard release version of CHARMM. More information about CHARMM can be obtained by following the links listed below.

Release schedule: http://www.charmm.org/package/logindex.shtml
License: http://www.charmm.org/info/license.shtml

For more information about using the Q-Chem/CHARMM QM/MM interface please refer to the following

Interfacing Q-Chem and CHARMM to Perform QM/MM Reaction Path Calculations. H. Lee Woodcock III, Milan Hodoscek, Andrew T.B. Gilbert, Peter M.W. Gill, Henry F. Schaefer III, and Bernard R. Brooks. J. Comp. Chem. 2006, Accepted.
http://www.charmm.org/document/Charmm/cXXbY/qchem.html (cXXbY = current release version).

For additional information please contact Dr. H. Lee Woodcock (hlwood@nih.gov)