Q-Chem Program Features

4.0 Features at a Glance

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; Valence Space Models for Strong Correlation

Excited State Methods: Supported Calculation Types; CIS Methods; Time-Dependent DFT; Wavefunction-Based Correlated Excited State Methods; Attachment-Detachment Analysis

Properties Analysis: Automated Geometry and Transition Structure Optimization; Vibrational Spectroscopy; NMR Shielding Tensors; Analysis of Electronic Structures; Solvation Modeling; Relativistic Energy Corrections; Diagonal Adiabatic Correction; Intermolecular Interaction Analysis; Electron Transfer Analysis; Distributed Multipole Analysis; Other Analytical Tools

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

QM/MM: Interface to CHARMM; ONIOM

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-GGA Functionals
- B3LYP, B3PW91, B3LYP5
  (using the VWN5 functional)
- User-definable hybrid functionals
Meta GGA Functionals
- M06-L
- PK06, BR89, B94
- TPSS
Hybrid Meta GGA and Hyper-GGA Functionals
- BMK
- MPW1B95, MPWB1K, PW6B95, PWB6K, M05, M05-2X, M06, M06-2X, M06-HF, M08, M11
- B3tLap
- BR89BR94hyb
- TPSSh
- RI-B05 for nondynamic correlation
Double-Hybrid Functionals
Long-range corrected (LRC) functionals
- Long-range corrections from Herbert group
- Baer-Neuhauser-Livshits (BNL) functional
- wB97X and wB97X-D functionals
Dispersion corrections to DFT
- Becke and Johnson’s XDM model
- vdw-DF-04 of Langreth, Lundqvist and co-workers’
- VV09
- -D2 and -D3 of Grimme's
- ωB97X-D
Constrained DFT

Calculation of reactions with configuration interactions of charge-constrained states with constrained DFT

User-Definable Linear Combination of Functionals
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.

Near-edge X-ray absorption with short-range corrected DFT

Linear Scaling Methods

Fast numerical integration of exchange-correlation with mrXC (multiresolution exchange-correlation)

Treats the smooth and compact parts of the electron density separately
Highly efficient, no errors

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

Resolution-Identity

Faster DFT and HF calculations with atomic resolution of the identity (ART) algorithms

Dual Basis

Fast calculation with one iteration only with the large basis basis
Accurate in relative energy
Applicable to DFT and MP2

Linear Scaling Grid Based Integration for Exchange-Correlation Functional Evaluation

Efficient computation of the exchange-correlation part of the dual basis DFT
Fast DFT calculation with ‘triple jumps’ between different sizes of basis set and grid and different levels of functional

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
Relaxed constraint algorithm (RCA) for converging SCF
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
Dual-basis RIMP2 methods
Opposite-spin MP2 methods
- Scaled opposite-spin MP2 method (SOS-MP2)
- Modified opposite-spin MP2 method (MOS-MP2)
- Optimized-orbitals opposite-spin MP2 method (O2)

Coupled-Cluster Methods

Significantly enhanced coupled-cluster code rewritten for better performance and multicore systems for many modules in 4.0
Singles and Doubles (CCSD)
- Energies and gradients are available.
- Frequenies available via finite differences of forces.
- RI implementation is available (energies only)
EOM-XX-CCSD

XX = EE, EA, IP, SF (energies and gradients) DIP, 2SF (energies)
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
- (dT) and (dF) corrections for CCSD, EOM-SF-CCSD, and EOM-IP-CCSD.
Extensive use of molecular point group and spin 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
Frozen Core Approximations, including frozen natural orbitals, available to increase treatable system size
Interface with EFP is avaliable for treating the effect of the environment
Dyson orbitals are available

Valence Space Models for Strong Corrrelation

Optimized Orbital Coupled-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
Perfect Quadruples and Perfect Hextuples methods
Coupled Cluster Valence Bond (CCVB) and related methods for multiple bond breaking

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
- Analytic gradient available with CIS, TDDFT and EOM-CCSD
Excited state vibrational analysis
- Available for UCIS, RCIS and TDDFT
Collinear and Non-Collinear 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) and SOS-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) and RI-CIS(D0) methods 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
Nuclear gradients of excited states with TDDFT
Direct coupling of charged states for the study of charge transfer reactions
Analytical excited-state Hessian in TDDFT within Tamm-Dancoff approximation
Improved TDDFT prediction with implementation of asymptotically corrected exchange-correlation potential (TDDFT/TDA with LB94)
Obtaining an excited state self-consistently with MOM (maximum overlap method)
Overlap analysis of the charge transfer in a excited state with TDDFT (Nick Besley, Section 6.3.2).
Localizing diabatic states with Boys or Edmiston-Ruedenberg localization scheme for charge or energy transfer
Implementation of non-collinear formulation extends SF-TDDFT to a broader set of functionals and improves its accuracy

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Wavefunction-Based Correlated 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.
Excited State Property Calculations
- Transition dipoles and getometry
Potential energy surface crossing minimization with EOM-CCSD
Correlated excited states with the perturbation-theory based, size consistent ADC scheme of second order
Restricted active space spin- flip method for multireference ground states and multi-electron excited states

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
Intrinsic Reaction Coordinates (IRC) following
- Connect equilibrium geometries and transistion states along reaction paths.
- Ab initio dynamics with extrapolated z-vector techniques for MP2 and/or dual-basis methods
- Improved robustness with Version 4.0
Freezing and Growing String Methods for efficient automatic reaction path finding

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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

Partial hessian analysis

Exact, quantum mechanical treatment of nuclear motions at equilibrium with path integral methods.

Calculation of local vibrational modes of interest with partial Hessian vibrational analysis.

Quasiclassical ab initio molecular dynamics.

NOB 5.0, a sophisticated approach to population analysis
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.

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
Analytical Wigner Intracule

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

Hirshfeld population analysis

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Solvation Modeling

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
SM8 solvation model
Smooth solvation energy surface with switching/Gaussian polarizable continuum medium PCM) solvation models for QM and QM/MM calculations.
The original COSMO solvation model by Klamt and Schüürmann with DFT energy and gradient.

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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

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Intermolecular Interaction Analysis

SCF with absolutely localized molecular orbitals for molecular interactions (SCF-MI)
Roothaan-step (RS) correction following SCF-MI
Energy decomposition analysis (EDA)
Complementary occupied-virtual pair (COVP) analysis for charge transfer
Automated basis-set superposition error (BSSE) calculation

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Other Analytical tools

Analysis of metal oxidation states via localized orbital bonding analysis
Visualization of noncovalent bonding using Johnson and Yang’s algorithm
ESP on a grid for transition density

strong>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 Ahlrichs double and triple zeta basis sets are also available
G3Large basis set for transition metals
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.

YinYang Atom model without linked atoms
ONIOM model implemented
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

Single-point energy, geometry optimization, and hessian analysis with QM/MM
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. 28, 1485, 2007. 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)

Effective fragment orbital (EFP) approach for accurate and fast energy computation for large systems including polarizable explicit solvation for ground and excited states using DFT/TDDFT, CCSD/EOM-CCSD, as well as CIS and CIS(D); library of effective fragments for common solvents; energy gradient for EFP-EFP systems

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Support for Modern Computing Platforms

Multicore systems with shared-memory parallel DFT/HF
Accelerating RI-MP2 calculation with GPU (graphic processing unit)

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Graphic User Interface

Integrated with Spartan
Support of new IQmol, a free GUI designed by Andrew Gilbert at Australian National University. For more information on IQmol, visit www.iqmol.org
Support of other third-party GUI's: Avogadro, WebMO, MolDen, JMol

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More details on the new features of Q-Chem 4.0 can be found in the 4.0 User's Guide.

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