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$DFT group (relevant if DFTTYP is chosen)
(relevant if SCFTYP=RHF,UHF,ROHF)
Note that if DFTTYP=NONE, an ab initio calculation will
be performed, rather than density functional theory.
This group permits the use of various one electron
(usually empirical) operators instead of the true many
electron Hamiltonian. Two programs are provided, METHOD=
GRID or GRIDFREE. The programs have different functionals
available, and so the keyword DFTTYP (which is entered in
$CONTRL) and other associated inputs are documented
separately below. Every functional that has the same name
in both lists is an identical functional, but each METHOD
has a few functionals that are missing in the other.
The grid free implementation is based on the use of the
resolution of the identity to simplify integrals so that
they may be analytically evaluated, without using grid
quadratures. The grid free DFT computations in their
present form have various numerical errors, primarily in
the gradient vectors. Please do not use the grid-free DFT
program without reading the discussion in the 'Further
References' section regarding the gradient accuracy.
The grid based DFT uses a typical grid quadrature to
compute integrals over the rather complicated functionals,
using two possible angular grid types.
Achieving a self-consistent field with DFT is rather
more difficult than for normal HF, so DIIS is the default
converger.
Both DFT programs will run in parallel. See the two
lists below for possible functionals in the two programs.
See also the $TDDFT input group for excited states.
METHOD = selects grid based DFT or grid free DFT.
= GRID Grid based DFT (default)
= GRIDFREE Grid free DFT
DFTTYP is given in $CONTRL, not here in $DFT! Possible
values for the grid-based program are listed first,
----- options for METHOD=GRID -----
DFTTYP = NONE means ab initio computation (default)
Many choices are given below, perhaps the most sensible are
local DFT: SVWN
pure DFT GGA: BLYP, PW91, B97-D, PBE/PBEsol
hybrid DFT GGA: B3LYP, X3LYP, PBE0
pure DFT meta-GGA: revTPSS
hybrid DFT meta-GGA: TPSSh, M06
but of course, everyone has their own favorite!
pure exchange functionals:
= SLATER Slater exchange
= BECKE Becke 1988 exchange
= GILL Gill 1996 exchange
= OPTX Handy-Cohen exchange
= PW91X Perdew-Wang 1991 exchange
= PBEX Perdew-Burke-Ernzerhof exchange
These will be used with no correlation functional at all.
pure correlation functionals:
= VWN Vosko-Wilk-Nusair correlation, using
their electron gas formula 5 (aka VWN5)
= VWN3 Vosko-Wilk-Nusair correlation, using
their electron gas formula 3
= VWN1RPA Vosko-Wilke-Nusair correlation, using
their e- gas formula 1, with RPA params.
= PZ81 Perdew-Zener 1981 correlation
= P86 Perdew 1986 correlation
= LYP Lee-Yang-Parr correlation
= PW91C Perdew-Wang 1991 correlation
= PBEC Perdew-Burke-Ernzerhof correlation
= OP One-parameter Progressive correlation
These will be used with 100% HF exchange, if chosen.
combinations (partial list):
= SVWN SLATER exchange + VWN5 correlation
Called LDA/LSDA in physics for RHF/UHF.
= SVWN1RPA Slater exchange + VWN1RPA correlation
= BLYP BECKE exchange + LYP correlation
= BOP BECKE exchange + OP correlation
= BP86 BECKE exchange + P86 correlation
= GVWN GILL exchange + VWN5 correlation
= GPW91 GILL exchange + PW91 correlation
= PBEVWN PBE exchange + VWN5 correlation
= PBEOP PBE exchange + OP correlation
= OLYP OPTX exchange + LYP correlation
= PW91 means PW91 exchange + PW91 correlation
= PBE means PBE exchange + PBE correlation
There's a nearly infinite set of pairings (well, 6*9), so
we show only enough to give you the idea. In other words,
pairs are formed by abbreviating the exchange functionals
SLATER=S, BECKE=B, GILL=G, OPTX=O, PW91X=PW91, PBEX=PBE
and matching them with any correlation functional, of which
only two are abbreviated when used in combinations,
PW91C==>PW91, PBEC==>PBE
The pairings shown above only scratch the surface, but
clearly, many possibilities, such as PW91PBE, are nonsense!
pure DFT GGA functionals:
= EDF1 empirical density functional #1, which is
a modified BLYP from Adamson/Gill/Pople.
= PW91 Perdew/Wang 1991
= PBE Perdew/Burke/Ernzerhof 1996
= revPBE PBE as revised by Zhang/Yang
= RPBE PBE as revised by Hammer/Hansen/Norskov
= PBEsol PBE as revised by Perdew et al for solids
= HCTH93 Hamprecht/Cohen/Tozer/Handy's 1998 mod
to B97, omitting HF exchange, fitting to
93 atoms and molecules
= HCTH120 later fit to 120 systems
= HCTH147 later fit to 147 systems
= HCTH407 later fit to 407 systems (best)
= SOGGA PBE revised by Zhao/Truhlar for solids
= MOHLYP metal optimized OPTX, half LYP
= B97-D Grimme's modified B97, with dispersion
correction (this forces DC=.TRUE.)
= SOGGA11 optimized with broad applicability for
chemistry, by Peverati/Zhao/Truhlar
hybrid GGA functionals:
= BHHLYP HF and BECKE exchange + LYP correlation
= B3PW91 Becke's 3 parameter exchange hybrid,
with PW91 correlation functional
= B3LYP this is a hybrid method combining five
functionals: Becke + Slater + HF exchange
(B3), with LYP + VWN5 correlation.
B3LYPV5 is a synonym for B3LYP.
= B3LYPV1R use VWN1RPA in place of VWN5, matches the
e- gas formula chosen by some programs.
= B3LYPV3 use VWN3 in place of B3LYP's VWN5
= B3P86 B3-type exchange, P86 correlation, using
VWN3 as the LDA part of the correlation.
B3P86V3 is a synonym for B3P86.
= B3P86V1R use VWN1RPA in place of VWN3
= B3P86V5 use VWN5 in place of VWN3
= B97 Becke's 1997 hybrid functional
= B97-1 Hamprecht/Cohen/Tozer/Handy's 1998
reparameterization of B97
= B97-2 Wilson/Bradley/Tozer's 2001 mod to B97
= B97-3 Keal/Tozer's 2005 mod to B97
= B97-K Boese/Martin's 2004 mod for kinetics
= B98 Schmider/Becke's 1998 mode to B97,
using their best "2c" parameters.
= PBE0 a hybrid made from PBE
= X3LYP HF+Slater+Becke88+PW91 exchange,
and LYP+VWN1RPA correlation.
= SOGGA11X a hybrid based on SOGGA11,
with 40.15% HF exchange.
Each includes some Hartree-Fock exchange, and also may use
a linear combination of many DFT parts.
range separated functionals:
These are also known as "long-range corrected functionals".
LC-BVWN, LC-BOP, LC-BLYP, or LC-BPBE are available by
selecting BVWN, BOP, BLYP, or BPBE and also setting the
flag LC=.TRUE. (see LC and also MU below). Others are
selected by their specific name, without using LC:
= CAMB3LYP coulomb attenuated B3LYP
= wB97 omega separated form of B97
= wB97X wB97 with short-range HF exchange
= wB97X-D dispersion corrected wB97X
M11 is also range-separated, but is listed below with the
other meta-GGAs.
"double hybrid" GGA:
= B2PLYP mixes BLYP, HF exchange, and MP2!
See related inputs CHF and CMP2 below.
"double hybrid" and "range separated":
= wB97X-2 intended for use with GBASIS=CCT,CCQ,CC5
= wB97X-2L intended for use with GBASIS=N311
NGAUSS=6 NDFUNC=3 NFFUNC=1 NPFUNC=3
DIFFSP=.T. DIFFS=.T.
Note: there are no analytic gradients for "double hybrids".
Note: the B2PLYP family uses the conventional MP2 energy
and may be used for closed shell or spin-unrestricted open
shell cases. The wB97X-2 family uses the SCS-MP2 energy,
and thus is limited to closed shell cases at present.
meta-GGA functionals:
These are not hybridized with HF exchange, unless that is
explicitly stated below.
= VS98 Voorhis/Scuseria, 1998
= PKZB Perdew/Kurth/Zupan/Blaha, 1999
= tHCTH Boese/Handy's 2002 metaGGA akin to HCTH
= tHCTHhyb tHCTH's hybrid with 15% HF exchange
= BMK Boese/Martin's 2004 parameterization of
tHCTHhyb for kinetics
= TPSS Tao/Perdew/Staroverov/Scuseria, 2003
= TPSSh TPSS hybrid with 10% HF exchange
= TPSSm TPSS with modified parameter, 2007
= revTPSS revised TPSS, 2009
= dlDF a reparameterized M05-2X, reproducing
interaction energies which have had all
dispersion removed. This MUST be used
with a special -D correction to recover
dispersion. See 'Further References'.
= M05 Minnesota exchange-correlation, 2005
a hybrid with 28% HF exchange.
= M05-2X M05, with doubled HF exchange, to 56%
= M06 Minnesota exchange-correlation, 2006
a hybrid with 27% HF exchange.
= M06-L M06, with 0% HF exchange (L=local)
= M06-2X M06, with doubled HF exchange, to 54%
= M06-HF M06 correlation, using 100% HF exchange
= M08-HX M08 with 'high HF exchange'
= M08-SO M08 with parameters that enforce the
correct second order gradient expansion.
= M11 M11 range-separated hybrid
= M11-L M11 local (0% HF exchange) with
dual-range exchange
When the M06 family was created, Truhlar recommended M06
for the general situation, but see his "concluding remarks"
in the M06 reference about which functional is best for
what kind of test data set. The most recent M11 family is
probably a better choice, and two functionals fit all the
needs of the older M05/M06/M08 families.
An extensive bibliography for all functionals can be
found in the 'Further References' section of this manual.
Note that only a subset of these functionals can be used
for TD-DFT energy or gradients. These subsets are listed
in the $TDDFT input group.
* * * dispersion corrections * * *
Many exchange-correlation functionals fail to compute
intra- and inter-molecular dispersion interactions
accurately. Two possible correction schemes are provided
below. The first uses empirically chosen C6 and C8
coefficients, while the latter obtains these from the
molecular DFT densities. At most, only one of the LRDFLG
or DC options below may be chosen.
DC = a flag to turn on Grimme's empirical dispersion
correction, involving scaled R**(-6) terms.
N.B. This empiricism may also be added to plain
Hartree-Fock, by choosing DFTTYP=NONE with DC=.T.
Three different versions exist, see IDCVER.
(default=.FALSE., except if DFTTYP=B97-D, wB97X-D)
IDCVER = 1 means 1st 2004 implementation.
= 2 means 2nd 2006 implementation DFT-D2,
default for B97-D, wB97X-D.
= 3 means 3rd 2010 implementation DFT-D3.
Default if DC is chosen and IDCVER isn't given.
= 4 means modified 3rd implementation DFT-D3(BJ).
(-4 is used for DFT-D3(BJ) for HF-3c).
Setting IDCVER will force DC=.TRUE.
GCP = a flag for the geometric counterpoise scheme
correction in HF-3c.
SRB = a flag for short-range basis set incompleteness
(SRB) correction in HF-3c.
DCCHG = a flag to use Chai-Head-Gordon damping function
instead of Grimme's 2006 function. Pertinent only
for the DFT-D2 method. Forces DC=.TRUE.
(default=.FALSE. except for wB97X-D)
DCABC = a flag to turn on the computation of the E(3) non-
additive energy term. Pertinent only for DFT-D3,
it forces DC=.TRUE. (default=.FALSE.)
The following parameters govern Grimme's semiempirical
dispersion term. They are basis set and functional
dependent, so they exist for only a few DFTTYP. Default
values are automatically selected and printed out in the
output file for many common density functionals.
The following keywords are for entering non-standard
values. For DFT-D2 values, see also:
R.Peverati and K.K.Baldridge
J.Chem.Theory Comput. 4, 2030-2048 (2008).
For DFT-D3 values, and a detailed explanation of each
parameter, see:
S. Grimme, J. Antony, S. Ehrlich and H. Krieg,
J.Chem.Phys. 132, 154104/1-19(2010)
and for DFT-D3(BJ):
S. Grimme, S. Ehrlich and L. Goerigk,
J.Comput.Chem. 32, 1456-1465 (2011)
DCALP = alpha parameter in the DFT-D damping function
(same as alpha6 in Grimme's DFT-D3 notation).
Note also that alpha8 and alpha10 in DFT-D3 have
constrained values of:
alpha8 = alpha6 + 2, alpha10 = alpha8 + 2.
Default=14.0 for DFT-D3
=20.0 for DFT-D2
=23.0 for DFT-D1
=6.00 for DCCHG=.TRUE.
DCSR = sR exponential parameter to scale the van der
Waals radii (same as sR,6 in Grimme's DFT-D3
notation). Note also that sR,8 in DFT-D3 have a
fixed value of 1.0.
Optimized values are automatically selected for
some of the more common functionals, otherwise,
the default is 1.00 for DFT-D3, 1.10 for DFT-D2,
and 1.22 for DFT-D1.
DCS6 = s6 linear parameter for scaling the C6 term.
Optimized values are automatically selected for
some of the more common functionals, otherwise,
the default is 1.00.
DCS8 = s8 linear parameter for scaling the C8 term of
DFT-D3. Pertinent only for DFT-D3.
Optimized values are automatically selected for
some of the more common functionals, otherwise,
the default is 1.00.
DCA1 = a1 parameter appearing in the -D3(BJ) dispersion
model. Optimized values are automatically
selected for a set of known functionals,
otherwise the default is 0.50.
DCA2 = a2 parameter appearing in the -D3(BJ) dispersion
model. Optimized values are automatically
selected for a set of known functionals,
otherwise the default is 4.00.
The old keywords DCPAR and DCEXP were replaced by DCS6 and
DCSR in 2010. Similarly, DCOLD has morphed into IDCVER.
- - -
The Local Response Dispersion (LRD) correction includes
atomic pair-wise -C6/R**6, -C8/R**8, and -C10/R**10 terms,
whose coefficients are computed from the molecular system's
electron density and its nuclear gradient. The nuclear
gradient assumes the dispersion coefficients do not vary
with geometry, which causes only a very small error in the
gradient. Optionally, 3 and 4 center terms may be added,
at the 1/R**6 level; in this case, nuclear gradients may
not be computed at all.
Since the three numerical parameters are presently known
only for the long-range exchange corrected BOP functional,
calculations may specify simply DFTTYP=LCBOPLRD. The
"LCBOPLRD" functional will automatically select the
following:
DFTTYP=BOP LC=.TRUE. MU=0.47
LRDFLG=.TRUE. LAMBDA=0.232 KAPPA=0.600 RZERO=3.22
leaving only the choice for MLTINT up to you.
References for LRD are
T.Sato, H.Nakai J.Chem.Phys. 131, 224104/1-12(2009)
T.Sato, H.Nakai J.Chem.Phys. 133, 194101/1-9(2010)
LRDFLG = flag choosing the Local Response Dispersion (LRD)
C6, C8, and C10 corrections. Default=.FALSE.
MLTINT = flag to add the 3 and 4 center 6th order terms,
the default=.FALSE. Note that nuclear gradients
are not available if these multi-center terms
are requested.
Three numerical parameters may be input. The defaults
shown are optimized for the BOP functional with the LC
correction for long-range exchange.
LAMBDA = parameter adjusting the density gradient
correction for the atomic and atomic pair
polarizabilities. (default=0.232)
KAPPA = parameter in the damping function (default=0.600)
RZERO = parameter in the damping function (default=3.22)
It may be interesting to see a breakdown of the total
dispersion correction, using these keywords:
PRPOL = print out atomic effective polarizabilities
(default=.FALSE.)
PRCOEF = N (default N=0)
print out dispersion coefficient to N-th order.
PRPAIR = print out atomic pair dispersion energies
(default=.FALSE.)
* * * range separation * * *
LC = flag to turn on the long range correction (LC),
which smoothly replaces the DFT exchange by the
HF exchange at long inter-electron distances.
(default=.FALSE.)
This option can be used only with the Becke
exchange functional (Becke) and a few correlation
functionals: DFTTYP=BVWN, BOP, BLYP, BPBE only.
For example, B3LYP has a fixed admixture of HF
exchange, so it cannot work with the LC option.
See H.Iikura, T.Tsuneda, T.Yanai, and K.Hirao,
J.Chem.Phys. 115, 3540 (2001).
MU = A parameter for the long range correction scheme.
Increasing MU increases the HF exchange used,
very small MU produces the DFT limit.
(default=0.33)
Other range-separated options exist, invoked by naming the
functional, such as DFTTYP=CAMB3LYP (see the DFTTYP keyword
for a full list).
* * * B2x-PLYP double hybrid functionals * * *
B2xPLYP Double Hybrid functionals have the general formula:
Exc = (1-cHF) * ExGGA + cHF * ExHF
+ (1-cMP2) * EcGGA + cMP2 * E(2)
The next keywords allow the choice of cHF and cMP2. Both
values must be between 0 and 1 (0-100%).
CHF = amount of HF exchange. (default=0.53)
CMP2 = amount of MP2. (default=0.27)
Some other common double hybrid functionals are available
simply by choosing DFTTYP=B2PLYP, and changing the CHF and
CMP2 parameters. Popular parametrizations are:
CHF CMP2
------------------------------------------
B2-PLYP (default) | 0.53 | 0.27 |
------------------------------------------
B2K-PLYP | 0.72 | 0.42 |
------------------------------------------
B2T-PLYP | 0.60 | 0.31 |
------------------------------------------
B2GP-PLYP | 0.65 | 0.36 |
------------------------------------------
* * * Grid Input * * *
Only one of the three grid types may be chosen for the run.
The default (if no selection is made) is the Lebedev grid.
In order to duplicate results obtained prior to April 2008,
select the polar coordinate grid NRAD=96 NTHE=12 NPHI=24.
Energies can be compared if and only if the identical grid
type and density is used, analogous to needing to compare
with the identical basis set expansions. See REFS.DOC for
more information on grids. See similar inputs in $TDDFT.
Lebedev grid:
NRAD = number of radial points in the Euler-MacLaurin
quadrature. (default=96)
NLEB = number of angular points in the Lebedev grids.
(default=302). Possible values are 86, 110, 146,
170, 194, 302, 350, 434, 590, 770, 974, 1202,
1454, 1730, 2030...
Meta-GGA functionals require a tighter grid to achieve the
same accuracy. For this reason a tighter default grid of
NRAD=99 and NLEB=590 is chosen by default with all meta-GGA
functionals.
The default for NLEB means that nuclear gradients will be
accurate to about the default OPTTOL=0.00010 (see $STATPT),
590 approaches OPTTOL=0.00001, and 1202 is "army grade".
The next two specify radial/angular in a single keyword:
SG1 = a flag to select the "standard grid 1", which has
24 radial points, and various pruned Lebedev
grids, from 194 down to 6. (default=.FALSE.
This grid is very fast, but produces gradients
whose accuracy reaches only OPTTOL=0.00050.
This grid should be VERY USEFUL for the early
steps of a geometry optimization.
JANS = two unpublished grids due to Curtis Janssen,
implemented here differently than in MPQC:
= 1 uses 95 radial points for all atoms, and prunes
from a Lebedev grid whose largest size is 434,
thus using about 15,000 grid points/atom.
= 2 uses 155 radial points for all atoms, and prunes
from a Lebedev grid whose largest size is 974,
thus using about 71,000 grid points/atom.
This is a very accurate grid, e.g. "army grade".
The information for pruning exists only for H-Ar,
so heavier elements will use the large radial/
Lebedev grid without any pruning.
polar coordinate grid:
NRAD = number of radial points in the Euler-MacLaurin
quadrature. (96 is reasonable)
NTHE = number of angle theta grids in Gauss-Legendre
quadrature (polar coordinates). (12 is reasonable)
NPHI = number of angle phi grids in Gauss-Legendre
quadrature. NPHI should be double NTHE so points
are spherically distributed. (24 is reasonable)
The number of angular points will be NTHE*NPHI. The values
shown give a gradient accuracy near the default OPTTOL of
0.00010, while NTHE=24 NPHI=48 approaches OPTTOL=0.00001,
and "army grade" is NTHE=36 NPHI=72.
* * * Grid Switching * * *
At the first geometry of the run, pure HF iterations will
be performed, since convergence of DFT is greatly improved
by starting with the HF density matrix. After DFT engages,
most runs (at all geometries, except for PCM or numerical
Hessians) will use a coarser grid during the early DFT
iterations, before reaching some initial convergence.
After that, the full grid will be used. Together, these
switchings can save considerable CPU time.
SWOFF = turn off DFT, to perform pure SCF iterations,
until the density matrix convergence falls below
this threshold. This option is independent of
SWITCH and can be used with or without it. It is
reasonable to pick SWOFF > SWITCH > CONV in $SCF.
SWOFF pertains only to the first geometry that the
run computes, and is automatically disabled if you
choose GUESS=MOREAD to provide initial orbitals.
The default is 5.0E-3.
SWITCH = when the change in the density matrix between
iterations falls below this threshhold, switch
to the desired full grid (default=3.0E-4)
This keyword is ignored if the SG1 grid is used.
NRAD0 = same as NRAD, but defines initial coarse grid.
default = smaller of 24 and NRAD/4
NLEB0 = same as NLEB, but defines initial coarse grid.
default = 110
NTHE0 = same as NTHE, but defines initial coarse grid.
default = smaller of 8, NTHE/3
NPHI0 = same as NPHI, but defines initial coarse grid.
default = smaller of 16, NPHI/3
technical parameters:
THRESH = threshold for ignoring small contributions to the
Fock matrix. The default is designed to produce
no significant energy loss, even when the grid is
as good as "army grade". If for some reason you
want to turn all threshhold tests off, of course
requiring more CPU, enter 1.0e-15.
default: 1.0e-4/Natoms/NRAD/NTHE/NPHI
GTHRE = threshold applied to gradients, similar to THRESH.
< 1 assign this value to all thresholds
= 1 use the default thresholds (default).
> 1 divide default thresholds by this value.
If you wish to increase accuracy, set GTHRE=10.
The default introduces an error of roughly 1e-7
(a.u./bohr) in the gradient.
The keyword $DFTTYP is given in $CONTRL, and may have these
values if the grid-free program is chosen:
----- options for METHOD=GRIDFREE -----
DFTTYP = NONE means ab initio computation (default)
exchange functionals:
= XALPHA X-Alpha exchange (alpha=0.7)
= SLATER Slater exchange (alpha=2/3)
= BECKE Becke's 1988 exchange
= DEPRISTO Depristo/Kress exchange
= CAMA Handy et al's mods to Becke exchange
= HALF 50-50 mix of Becke and HF exchange
correlation functionals:
= VWN Vosko/Wilke/Nusair correlation, formula 5
= PWLOC Perdew/Wang local correlation
= LYP Lee/Yang/Parr correlation
exchange/correlation functionals:
= BVWN Becke exchange + VWN5 correlation
= BLYP Becke exchange + LYP correlation
= BPWLOC Becke exchange + Perdew/Wang correlation
= B3LYP hybrid HF/Becke/LYP using VWN formula 5
= CAMB CAMA exchange + Cambridge correlation
= XVWN Xalpha exchange + VWN5 correlation
= XPWLOC Xalpha exchange + Perdew/Wang correlation
= SVWN Slater exchange + VWN5 correlation
= SPWLOC Slater exchange + PWLOC correlation
= WIGNER Wigner exchange + correlation
= WS Wigner scaled exchange + correlation
= WIGEXP Wigner exponential exchange + correlation
AUXFUN = AUX0 uses no auxiliary basis set for resolution
of the identity, limiting accuracy.
= AUX3 uses the 3rd generation of RI basis sets,
These are available for the elements H to
Ar, but have been carefully considered for
H-Ne only. (DEFAULT)
THREE = a flag to use a resolution of the identity to
turn four center overlap integrals into three
center integrals. This can be used only if
no auxiliary basis is employed. (default=.FALSE.)
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