Release66:Density Functional Theory for Molecules
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Note: both TPSS and PKZB correlation require the PBE GGA CORRELATION (which is itself dependent on an LDA). The decision has been made to use these functionals with the accompanying local PW91LDA. The user does not have the ability to set the local part of these metaGGA functionals. | Note: both TPSS and PKZB correlation require the PBE GGA CORRELATION (which is itself dependent on an LDA). The decision has been made to use these functionals with the accompanying local PW91LDA. The user does not have the ability to set the local part of these metaGGA functionals. | ||
- | |||
===Range-Separated Functionals=== | ===Range-Separated Functionals=== | ||
+ | Using the Ewald decomposition | ||
+ | |||
+ | <math> \frac{1}{r_{12}} = \frac{\alpha + \beta \texttt{erf}(\mu r_{12})}{r_{12}} + | ||
+ | \frac{1 - [\alpha + \beta \texttt{erf}(\mu r_{12})]}{r_{12}}</math> | ||
+ | |||
+ | we can split the the Exchange interaction as | ||
+ | |||
+ | <math>E_{X} = E_X^{LR} + E_X^{SR} </math> | ||
+ | |||
+ | Therefore the long-range HF Exchange energy becomes | ||
+ | |||
+ | <math>E_X^{LR} = \alpha E_X^{HF} - \frac{\beta}{2} \sum_i \sum_j \int \int \phi_i(r_1)\phi_j(r_1)\frac{\texttt{erf}(\mu r_{12})}{r_{12}} \phi_i(r_2)\phi_j(r_2)</math> | ||
+ | |||
+ | cam <real cam> cam_alpha <real cam_alpha> cam_beta <cam_beta> | ||
+ | |||
+ | <tt>cam</tt> represents the attenuation parameter <math>\mu</math> , <tt>cam_alpha</tt> and <tt>cam_beta</tt> are parameters <math>\alpha</math> and <math>\beta</math> that control the amount of short-range DFT and long-range HF Exchange according to the Ewald decomposition. As <math>r_{12} \rightarrow 0 </math>, the HF exchange fraction is <math>\alpha</math>, while the DFT exchange fraction is <math>(1-\alpha)</math>. As <math>r_{12} \rightarrow \infty </math>, the HF exchange fraction approaches <math>\alpha + \beta</math> and the DFT exchange fraction approaches <math> (1- \alpha - \beta)</math>. In the HSE functional, the HF part is short-ranged and DFT is long-ranged. | ||
Range separated functionals (or long-range corrected or LC) can be specified as follows: | Range separated functionals (or long-range corrected or LC) can be specified as follows: | ||
Line 1,351: | Line 1,366: | ||
xc xwpbe 0.80 cpbe96 1.0 hfexch 1.00 | xc xwpbe 0.80 cpbe96 1.0 hfexch 1.00 | ||
cam 0.2 cam_alpha 0.20 cam_beta 0.80 | cam 0.2 cam_alpha 0.20 cam_beta 0.80 | ||
+ | |||
+ | QTP-00 | ||
+ | xc xcamb88 1.00 lyp 0.80 vwn_5 0.2 hfexch 1.00 | ||
+ | cam 0.29 cam_alpha 0.54 cam_beta 0.37 | ||
+ | |||
+ | rCAM-B3LYP | ||
+ | xc xcamb88 1.00 lyp 1.0 vwn_5 0. hfexch 1.00 becke88 nonlocal 0.13590 | ||
+ | cam 0.33 cam_alpha 0.18352 cam_beta 0.94979 | ||
HSE03 functional: | HSE03 functional: | ||
Line 1,364: | Line 1,387: | ||
cam 0.11 cam_alpha 0.0 cam_beta 1.0 | cam 0.11 cam_alpha 0.0 cam_beta 1.0 | ||
- | + | Please see the following papers (not a complete list) for further details about the theory behind these functionals and applications. | |
+ | |||
+ | #A. Savin, In Recent Advances in Density Functional Methods Part I; D.P. Chong, Ed.; World Scientific: Singapore, 1995; Vol. 129. | ||
+ | #H. Iikura, T. Tsuneda, T. Yanai, K. Hirao, J. Chem. Phys. 115, 3540 (2001) | ||
+ | #Y. Tawada, T. Tsuneda, S. Yanahisawa, T. Yanai, K. Hirao, J. Chem. Phys. 120, 8425 (2004) | ||
+ | #T. Yanai, D.P. Tew, N.C. Handy, Chem. Phys. Lett. 393, 51 (2004) | ||
+ | #M. J. G. Peach, A. J. Cohen, D. J. Tozer, Phys. Chem. Chem. Phys. 8, 4543 (2006) | ||
+ | #J.-W. Song, T. Hirosawa, T. Tsuneda, K. Hirao, J. Chem. Phys. 126, 154105 (2007) | ||
+ | #E. Livshits, R. Baer, Phys. Chem. Chem. Phys. 9, 2932 (2007) | ||
+ | #A. J. Cohen, P. Mori-Sanchez, and W. Yang, J. Chem. Phys. 126, 191109 (2007) | ||
+ | #M.A. Rohrdanz, J.M. Herbert, J. Chem. Phys. 129 034107 (2008) | ||
+ | #N. Govind, M. Valiev, L. Jensen, K. Kowalski, J. Phys. Chem. A, 113, 6041 (2009) | ||
+ | #R. Baer, E. Livshits, U. Salzner, Annu. Rev. Phys. Chem. 61, 85 (2010) | ||
+ | #J. Autschbach, M. Srebro, Acc. Chem. Res. 47, 2592 (2014) | ||
+ | #P. Verma and R. J. Bartlett, J. Chem. Phys. 140, 18A534 (2014) | ||
Example illustrating the CAM-B3LYP functional: | Example illustrating the CAM-B3LYP functional: | ||
Line 1,729: | Line 1,766: | ||
H library 6-31g* | H library 6-31g* | ||
end | end | ||
- | + | occup | |
- | # core-hole in beta | + | 6 6 # core-hole in beta |
- | + | ||
1.0 0.0 | 1.0 0.0 | ||
1.0 1.0 | 1.0 1.0 |
Latest revision as of 21:43, 10 February 2017
Density Functional Theory
The NWChem density functional theory (DFT) module uses the Gaussian basis set approach to compute closed shell and open shell densities and Kohn-Sham orbitals in the:
- local density approximation (LDA),
- non-local density approximation (NLDA),
- local spin-density approximation (LSD),
- non-local spin-density approximation (NLSD),
- non-local meta-GGA approximation (metaGGA),
- any empirical mixture of local and non-local approximations (including exact exchange), and
- asymptotically corrected exchange-correlation potentials.
The formal scaling of the DFT computation can be reduced by choosing to use auxiliary Gaussian basis sets to fit the charge density (CD) and/or fit the exchange-correlation (XC) potential.
DFT input is provided using the compound DFT directive
DFT ... END
The actual DFT calculation will be performed when the input module encounters the TASK directive.
TASK DFT
Once a user has specified a geometry and a Kohn-Sham orbital basis set the DFT module can be invoked with no input directives (defaults invoked throughout). There are sub-directives which allow for customized application; those currently provided as options for the DFT module are:
VECTORS [[input] (<string input_movecs default atomic>) || \ (project <string basisname> <string filename>)] \ [swap [alpha||beta] <integer vec1 vec2> ...] \ [output <string output_filename default input_movecs>] \ XC [[acm] [b3lyp] [beckehandh] [pbe0]\ [becke97] [becke97-1] [becke97-2] [becke97-3] [becke97-d] [becke98] \ [hcth] [hcth120] [hcth147]\ [hcth407] [becke97gga1] [hcth407p]\ [mpw91] [mpw1k] [xft97] [cft97] [ft97] [op] [bop] [pbeop]\ [xpkzb99] [cpkzb99] [xtpss03] [ctpss03] [xctpssh]\ [b1b95] [bb1k] [mpw1b95] [mpwb1k] [pw6b95] [pwb6k] [m05] [m05-2x] [vs98] \ [m06] [m06-hf] [m06-L] [m06-2x] \ [HFexch <real prefactor default 1.0>] \ [becke88 [nonlocal] <real prefactor default 1.0>] \ [xperdew91 [nonlocal] <real prefactor default 1.0>] \ [xpbe96 [nonlocal] <real prefactor default 1.0>] \ [gill96 [nonlocal] <real prefactor default 1.0>] \ [lyp <real prefactor default 1.0>] \ [perdew81 <real prefactor default 1.0>] \ [perdew86 [nonlocal] <real prefactor default 1.0>] \ [perdew91 [nonlocal] <real prefactor default 1.0>] \ [cpbe96 [nonlocal] <real prefactor default 1.0>] \ [pw91lda <real prefactor default 1.0>] \ [slater <real prefactor default 1.0>] \ [vwn_1 <real prefactor default 1.0>] \ [vwn_2 <real prefactor default 1.0>] \ [vwn_3 <real prefactor default 1.0>] \ [vwn_4 <real prefactor default 1.0>] \ [vwn_5 <real prefactor default 1.0>] \ [vwn_1_rpa <real prefactor default 1.0>] \ [xtpss03 [nonlocal] <real prefactor default 1.0>] \ [ctpss03 [nonlocal] <real prefactor default 1.0>] \ [bc95 [nonlocal] <real prefactor default 1.0>] \ [xpw6b95 [nonlocal] <real prefactor default 1.0>] \ [xpwb6k [nonlocal] <real prefactor default 1.0>] \ [xm05 [nonlocal] <real prefactor default 1.0>] \ [xm05-2x [nonlocal] <real prefactor default 1.0>] \ [cpw6b95 [nonlocal] <real prefactor default 1.0>] \ [cpwb6k [nonlocal] <real prefactor default 1.0>] \ [cm05 [nonlocal] <real prefactor default 1.0>] \ [cm05-2x [nonlocal] <real prefactor default 1.0>]] \ [xvs98 [nonlocal] <real prefactor default 1.0>]] \ [cvs98 [nonlocal] <real prefactor default 1.0>]] \ [xm06-L [nonlocal] <real prefactor default 1.0>]] \ [xm06-hf [nonlocal] <real prefactor default 1.0>]] \ [xm06 [nonlocal] <real prefactor default 1.0>]] \ [xm06-2x [nonlocal] <real prefactor default 1.0>]] \ [cm06-L [nonlocal] <real prefactor default 1.0>]] \ [cm06-hf [nonlocal] <real prefactor default 1.0>]] \ [cm06 [nonlocal] <real prefactor default 1.0>]] \ [cm06-2x [nonlocal] <real prefactor default 1.0>]] CONVERGENCE [[energy <real energy default 1e-7>] \ [density <real density default 1e-5>] \ [gradient <real gradient default 5e-4>] \ [dampon <real dampon default 0.0>] \ [dampoff <real dampoff default 0.0>] \ [diison <real diison default 0.0>] \ [diisoff <real diisoff default 0.0>] \ [levlon <real levlon default 0.0>] \ [levloff <real levloff default 0.0>] \ [ncydp <integer ncydp default 2>] \ [ncyds <integer ncyds default 30>] \ [ncysh <integer ncysh default 30>] \ [damp <integer ndamp default 0>] [nodamping] \ [diis [nfock <integer nfock default 10>]] \ [nodiis] [lshift <real lshift default 0.5>] \ [nolevelshifting] \ [hl_tol <real hl_tol default 0.1>] \ [rabuck [n_rabuck <integer n_rabuck default 25>]] GRID [(xcoarse||coarse||medium||fine||xfine) default medium] \ [(gausleg||lebedev ) default lebedev ] \ [(becke||erf1||erf2||ssf) default erf1] \ [(euler||mura||treutler) default mura] \ [rm <real rm default 2.0>] \ [nodisk] TOLERANCES [[tight] [tol_rho <real tol_rho default 1e-10>] \ [accCoul <integer accCoul default 8>] \ [radius <real radius default 25.0>]] [(LB94||CS00 <real shift default none>)] DECOMP ODFT DIRECT SEMIDIRECT [filesize <integer filesize default disksize>] [memsize <integer memsize default available>] [filename <string filename default $file_prefix.aoints$>] INCORE ITERATIONS <integer iterations default 30> MAX_OVL CGMIN RODFT MULLIKEN DISP XDM [ a1 <real a1> ] [ a2 <real a2> ] MULT <integer mult default 1> NOIO PRINT||NOPRINT
The following sections describe these keywords and optional sub-directives that can be specified for a DFT calculation in NWChem.
Specification of Basis Sets for the DFT Module
The DFT module requires at a minimum the basis set for the Kohn-Sham molecular orbitals. This basis set must be in the default basis set named "ao basis", or it must be assigned to this default name using the SET directive.
In addition to the basis set for the Kohn-Sham orbitals, the charge density fitting basis set can also be specified in the input directives for the DFT module. This basis set is used for the evaluation of the Coulomb potential in the Dunlap scheme. The charge density fitting basis set must have the name "cd basis". This can be the actual name of a basis set, or a basis set can be assigned this name using the SET directive. If this basis set is not defined by input, the O(N^{4}) exact Coulomb contribution is computed.
The user also has the option of specifying a third basis set for the evaluation of the exchange-correlation potential. This basis set must have the name "xc basis". If this basis set is not specified by input, the exchange contribution (XC) is evaluated by numerical quadrature. In most applications, this approach is efficient enough, so the "xc basis" basis set is not generally required.
For the DFT module, the input options for defining the basis sets in a given calculation can be summarized as follows;
- "ao basis" - Kohn-Sham molecular orbitals; required for all calculations
- "cd basis" - charge density fitting basis set; optional, but recommended for evaluation of the Coulomb potential
- "xc basis" - exchange-correlation (XC) fitting basis set; optional, and usually not recommended
VECTORS and MAX_OVL -- KS-MO Vectors
The VECTORS directive is the same as that in the SCF module (Section 10.5). Currently, the LOCK keyword is not supported by the DFT module, however the directive
MAX_OVL
has the same effect.
XC and DECOMP -- Exchange-Correlation Potentials
XC [[acm] [b3lyp] [beckehandh] [pbe0] [bhlyp]\ [becke97] [becke97-1] [becke97-2] [becke97-3] [becke98] [hcth] [hcth120] [hcth147] \ [hcth407] [becke97gga1] [hcth407p] \ [optx] [hcthp14] [mpw91] [mpw1k] [xft97] [cft97] [ft97] [op] [bop] [pbeop]\ [m05] [m05-2x] [m06] [m06-l] [m06-2x] [m06-hf] [m08-hx] [m08-so] [m11] [m11-l]\ [HFexch <real prefactor default 1.0>] \ [becke88 [nonlocal] <real prefactor default 1.0>] \ [xperdew91 [nonlocal] <real prefactor default 1.0>] \ [xpbe96 [nonlocal] <real prefactor default 1.0>] \ [gill96 [nonlocal] <real prefactor default 1.0>] \ [lyp <real prefactor default 1.0>] \ [perdew81 <real prefactor default 1.0>] \ [perdew86 [nonlocal] <real prefactor default 1.0>] \ [perdew91 [nonlocal] <real prefactor default 1.0>] \ [cpbe96 [nonlocal] <real prefactor default 1.0>] \ [pw91lda <real prefactor default 1.0>] \ [slater <real prefactor default 1.0>] \ [vwn_1 <real prefactor default 1.0>] \ [vwn_2 <real prefactor default 1.0>] \ [vwn_3 <real prefactor default 1.0>] \ [vwn_4 <real prefactor default 1.0>] \ [vwn_5 <real prefactor default 1.0>] \ [vwn_1_rpa <real prefactor default 1.0>]]
The user has the option of specifying the exchange-correlation treatment in the DFT Module (see table below for full list of functionals). The default exchange-correlation functional is defined as the local density approximation (LDA) for closed shell systems and its counterpart the local spin-density (LSD) approximation for open shell systems. Within this approximation the exchange functional is the Slater ρ^{1 / 3} functional (from J.C. Slater, Quantum Theory of Molecules and Solids, Vol. 4: The Self-Consistent Field for Molecules and Solids (McGraw-Hill, New York, 1974)), and the correlation functional is the Vosko-Wilk-Nusair (VWN) functional (functional V) (S.J. Vosko, L. Wilk and M. Nusair, Can. J. Phys. 58, 1200 (1980)). The parameters used in this formula are obtained by fitting to the Ceperley and Alder Quantum Monte-Carlo solution of the homogeneous electron gas.
These defaults can be invoked explicitly by specifying the following keywords within the DFT module input directive, XC slater vwn_5.
That is, this statement in the input file
dft XC slater vwn_5 end task dft
is equivalent to the simple line
task dft
The DECOMP directive causes the components of the energy corresponding to each functional to be printed, rather than just the total exchange-correlation energy which is the default. You can see an example of this directive in the sample input.
Many alternative exchange and correlation functionals are available to the user as listed in the table below. The following sections describe how to use these options.
Exchange-Correlation Functionals
There are several Exchange and Correlation functionals in addition to the default slater and vwn_5 functionals. These are either local or gradient-corrected functionals (GCA); a full list can be found in the table below.
The Hartree-Fock exact exchange functional, (which has O(N^{4}) computation expense), is invoked by specifying
XC HFexch
Note that the user also has the ability to include only the local or nonlocal contributions of a given functional. In addition the user can specify a multiplicative prefactor (the variable <prefactor> in the input) for the local/nonlocal component or total. An example of this might be,
XC becke88 nonlocal 0.72
The user should be aware that the Becke88 local component is simply the Slater exchange and should be input as such.
Any combination of the supported exchange functional options can be used. For example the popular Gaussian B3 exchange could be specified as:
XC slater 0.8 becke88 nonlocal 0.72 HFexch 0.2
Any combination of the supported correlation functional options can be used. For example B3LYP could be specified as:
XC vwn_1_rpa 0.19 lyp 0.81 HFexch 0.20 slater 0.80 becke88 nonlocal 0.72
and X3LYP as:
xc vwn_1_rpa 0.129 lyp 0.871 hfexch 0.218 slater 0.782 \ becke88 nonlocal 0.542 xperdew91 nonlocal 0.167
Setting up common exchange-correlation functionals
- B3LYP: xc b3lyp
- PBE0: xc pbe0
- PBE96: xc xpbe96 cpbe96
- PW91: xc xperdew91 perdew91
- BHLYP: xc bhlyp
- Becke Half and Half: xc beckehandh
- BP86: xc becke88 perdew86
- BP91: xc becke88 perdew91
- BLYP: xc becke88 lyp
Minnesota Functionals
- xc m05
- xc m05-2x
- xc m06
- xc m06-l
- xc m06-2x
- xc m06-hf
- xc m08-hx
- xc m08-so
- xc m11
- xc m11-l
Analytic second derivatives are not supported with the Minnesota functionals yet.
Combined Exchange and Correlation Functionals
In addition to the options listed above for the exchange and correlation functionals, the user has the alternative of specifying combined exchange and correlation functionals.
The available hybrid functionals (where a Hartree-Fock Exchange component is present) consist of the Becke "half and half" (see A.D. Becke, J. Chem. Phys. 98, 1372 (1992)), the adiabatic connection method (see A.D. Becke, J. Chem. Phys. 98, 5648 (1993)), B3LYP (popularized by Gaussian9X), Becke 1997 ("Becke V" paper: A.D.Becke, J. Chem. Phys., 107, 8554 (1997)).
The keyword beckehandh specifies that the exchange-correlation energy will be computed as
We know this is NOT the correct Becke prescribed implementation which requires the XC potential in the energy expression. But this is what is currently implemented as an approximation to it.
The keyword acm specifies that the exchange-correlation energy is computed as
and Δ stands for a non-local component.
The keyword b3lyp specifies that the exchange-correlation energy is computed as
Keyword | X | C | GGA | Meta | Hybr. | 2nd | Ref. |
slater | * | Y | [1] | ||||
vwn_1 | * | Y | [2] | ||||
vwn_2 | * | Y | [2] | ||||
vwn_3 | * | Y | [2] | ||||
vwn_4 | * | Y | [2] | ||||
vwn_5 | * | Y | [2] | ||||
vwn_1_rpa | * | Y | [2] | ||||
perdew81 | * | Y | [3] | ||||
pw91lda | * | Y | [4] | ||||
xbecke86b | * | * | N | [54] | |||
becke88 | * | * | Y | [5] | |||
xperdew86 | * | * | N | [53] | |||
xperdew91 | * | * | Y | [6] | |||
xpbe96 | * | * | Y | [7] | |||
gill96 | * | * | Y | [8] | |||
optx | * | * | N | [20] | |||
mpw91 | * | * | Y | [23] | |||
xft97 | * | * | N | [24] | |||
rpbe | * | * | Y | [33] | |||
revpbe | * | * | Y | [34] | |||
xpw6b95 | * | * | N | [36] | |||
xpwb6k | * | * | N | [36] | |||
perdew86 | * | * | Y | [9] | |||
lyp | * | * | Y | [10] | |||
perdew91 | * | * | Y | [6] | |||
cpbe96 | * | * | Y | [7] | |||
cft97 | * | * | N | [24] | |||
op | * | * | N | [31] | |||
hcth | * | * | * | N | [11] | ||
hcth120 | * | * | * | N | [12] | ||
hcth147 | * | * | * | N | [12] | ||
hcth407 | * | * | * | N | [19] | ||
becke97gga1 | * | * | * | N | [18] | ||
hcthp14 | * | * | * | N | [21] | ||
ft97 | * | * | * | N | [24] | ||
htch407p | * | * | * | N | [27] | ||
bop | * | * | * | N | [31] | ||
pbeop | * | * | * | N | [32] | ||
xpkzb99 | * | * | N | [26] | |||
cpkzb99 | * | * | N | [26] | |||
xtpss03 | * | * | N | [28] | |||
ctpss03 | * | * | N | [28] | |||
bc95 | * | * | N | [33] | |||
cpw6b95 | * | * | N | [36] | |||
cpwb6k | * | * | N | [36] | |||
xm05 | * | * | * | N | [37] | ||
cm05 | * | * | N | [37] | |||
m05-2x | * | * | * | * | N | [38] | |
xm05-2x | * | * | * | N | [38] | ||
cm05-2x | * | * | N | [38] | |||
xctpssh | * | * | N | [29] | |||
bb1k | * | * | N | [34] | |||
mpw1b95 | * | * | N | [35] | |||
mpwb1k | * | * | N | [35] | |||
pw6b95 | * | * | N | [36] | |||
pwb6k | * | * | N | [36] | |||
m05 | * | * | N | [37] | |||
vs98 | * | * | N | [41] | |||
xvs98 | * | * | N | [41] | |||
cvs98 | * | * | N | [41] | |||
m06-L | * | * | * | N | [40] | ||
xm06-L | * | * | N | [40] | |||
cm06-L | * | * | N | [40] | |||
m06-hf | * | * | N | [41] | |||
xm06-hf | * | * | * | N | [41] | ||
cm06-hf | * | * | N | [41] | |||
m06 | * | * | N | [42] | |||
xm06 | * | * | * | N | [42] | ||
cm06 | * | * | N | [42] | |||
m06-2x | * | * | N | [42] | |||
xm06-2x | * | * | * | N | [42] | ||
cm06-2x | * | * | N | [42] | |||
cm08-hx | * | * | N | [46] | |||
xm08-hx | * | * | N | [46] | |||
m08-hx | * | * | * | * | N | [46] | |
cm08-so | * | * | N | [46] | |||
xm08-so | * | * | N | [46] | |||
m08-so | * | * | * | * | N | [46] | |
cm11 | * | * | N | [47] | |||
xm11 | * | * | N | [47] | |||
m11 | * | * | * | * | N | [47] | |
cm11-l | * | * | N | [48] | |||
xm11-l | * | * | N | [48] | |||
m11-l | * | * | * | N | [48] | ||
csogga | * | * | N | [49] | |||
xsogga | * | * | N | [49] | |||
sogga | * | * | * | N | [49] | ||
csogga11 | * | * | N | [50] | |||
xsogga11 | * | * | N | [50] | |||
sogga11 | * | * | * | N | [50] | ||
csogga11-x | * | N | [51] | ||||
xsogga11-x | * | * | N | [51] | |||
sogga11-x | * | * | * | * | N | [51] | |
dldf | * | * | * | * | N | [52] | |
beckehandh | * | * | * | Y | [13] | ||
b3lyp | * | * | * | * | Y | [14] | |
acm | * | * | * | * | Y | [14] | |
becke97 | * | * | * | * | N | [15] | |
becke97-1 | * | * | * | * | N | [11] | |
becke97-2 | * | * | * | * | N | [22] | |
becke97-3 | * | * | * | * | N | [30] | |
becke97-d | * | * | * | * | N | [45] | |
becke98 | * | * | * | * | N | [16] | |
pbe0 | * | * | * | * | Y | [17] | |
mpw1k | * | * | * | * | Y | [25] | |
xmvs15 | * | * | N | [55] |
- J.C. Slater and K. H. Johnson, Phys. Rev. B 5, 844 (1972)
- S.J. Vosko, L. Wilk and M. Nusair, Can. J. Phys. 58, 1200 (1980)
- J. P. Perdew and A. Zunger, Phys. Rev. B 23, 5048 (1981).
- J.P. Perdew and Y. Wang, Phys. Rev. B 45, 13244 (1992)
- A.D. Becke, Phys. Rev. A 88, 3098 (1988)
- J.P. Perdew, J.A. Chevary, S.H. Vosko, K.A. Jackson, M.R. Pederson, D.J. Singh and C. Fiolhais, Phys. Rev. B 46, 6671 (1992)
- J.P. Perdew, K. Burke and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996); 78 , 1396 (1997)
- P.W.Gill , Mol. Phys. 89, 433 (1996)
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Meta-GGA Functionals
One way to calculate meta-GGA energies is to use orbitals and densities from fully self-consistent GGA or LDA calculations and run them in one iteration in the meta-GGA functional. It is expected that meta-GGA energies obtained this way will be close to fully self consistent meta-GGA calculations.
It is possible to calculate metaGGA energies both ways in NWChem, that is, self-consistently or with GGA/LDA orbitals and densities. However, since second derivatives are not available for metaGGAs, in order to calculate frequencies, one must use task dft freq numerical. A sample file with this is shown below, in Sample input file. In this instance, the energy is calculated self-consistently and geometry is optimized using the analytical gradients.
(For more information on metaGGAs, see S. Kurth, J. Perdew, P. Blaha, Int. J. Quant. Chem 75, 889 (1999) for a brief description of meta-GGAs, and citations 14-27 therein for thorough background )
Note: both TPSS and PKZB correlation require the PBE GGA CORRELATION (which is itself dependent on an LDA). The decision has been made to use these functionals with the accompanying local PW91LDA. The user does not have the ability to set the local part of these metaGGA functionals.
Range-Separated Functionals
Using the Ewald decomposition
we can split the the Exchange interaction as
Therefore the long-range HF Exchange energy becomes
cam <real cam> cam_alpha <real cam_alpha> cam_beta <cam_beta>
cam represents the attenuation parameter μ , cam_alpha and cam_beta are parameters α and β that control the amount of short-range DFT and long-range HF Exchange according to the Ewald decomposition. As , the HF exchange fraction is α, while the DFT exchange fraction is (1 − α). As , the HF exchange fraction approaches α + β and the DFT exchange fraction approaches (1 − α − β). In the HSE functional, the HF part is short-ranged and DFT is long-ranged.
Range separated functionals (or long-range corrected or LC) can be specified as follows:
CAM-B3LYP:
xc xcamb88 1.00 lyp 0.81 vwn_5 0.19 hfexch 1.00 cam 0.33 cam_alpha 0.19 cam_beta 0.46
LC-BLYP:
xc xcamb88 1.00 lyp 1.0 hfexch 1.00 cam 0.33 cam_alpha 0.0 cam_beta 1.0
LC-PBE:
xc xcampbe96 1.0 cpbe96 1.0 HFexch 1.0 cam 0.30 cam_alpha 0.0 cam_beta 1.0
LC-PBE0 or CAM-PBE0:
xc xcampbe96 1.0 cpbe96 1.0 HFexch 1.0 cam 0.30 cam_alpha 0.25 cam_beta 0.75
BNL (Baer, Neuhauser, Lifshifts):
xc xbnl07 0.90 lyp 1.00 hfexch 1.00 cam 0.33 cam_alpha 0.0 cam_beta 1.0
LC-wPBE:
xc xwpbe 1.00 cpbe96 1.0 hfexch 1.00 cam 0.3 cam_alpha 0.00 cam_beta 1.00
LC-wPBEh:
xc xwpbe 0.80 cpbe96 1.0 hfexch 1.00 cam 0.2 cam_alpha 0.20 cam_beta 0.80
QTP-00
xc xcamb88 1.00 lyp 0.80 vwn_5 0.2 hfexch 1.00 cam 0.29 cam_alpha 0.54 cam_beta 0.37
rCAM-B3LYP
xc xcamb88 1.00 lyp 1.0 vwn_5 0. hfexch 1.00 becke88 nonlocal 0.13590 cam 0.33 cam_alpha 0.18352 cam_beta 0.94979
HSE03 functional: 0.25*Ex(HF-SR) - 0.25*Ex(PBE-SR) + Ex(PBE) + Ec(PBE), where gamma(HF-SR) = gamma(PBE-SR)
xc hse03
or it can be explicitly set as
xc xpbe96 1.0 xcampbe96 -0.25 cpbe96 1.0 srhfexch 0.25 cam 0.33 cam_alpha 0.0 cam_beta 1.0
HSE06 functional:
xc xpbe96 1.0 xcampbe96 -0.25 cpbe96 1.0 srhfexch 0.25 cam 0.11 cam_alpha 0.0 cam_beta 1.0
Please see the following papers (not a complete list) for further details about the theory behind these functionals and applications.
- A. Savin, In Recent Advances in Density Functional Methods Part I; D.P. Chong, Ed.; World Scientific: Singapore, 1995; Vol. 129.
- H. Iikura, T. Tsuneda, T. Yanai, K. Hirao, J. Chem. Phys. 115, 3540 (2001)
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- T. Yanai, D.P. Tew, N.C. Handy, Chem. Phys. Lett. 393, 51 (2004)
- M. J. G. Peach, A. J. Cohen, D. J. Tozer, Phys. Chem. Chem. Phys. 8, 4543 (2006)
- J.-W. Song, T. Hirosawa, T. Tsuneda, K. Hirao, J. Chem. Phys. 126, 154105 (2007)
- E. Livshits, R. Baer, Phys. Chem. Chem. Phys. 9, 2932 (2007)
- A. J. Cohen, P. Mori-Sanchez, and W. Yang, J. Chem. Phys. 126, 191109 (2007)
- M.A. Rohrdanz, J.M. Herbert, J. Chem. Phys. 129 034107 (2008)
- N. Govind, M. Valiev, L. Jensen, K. Kowalski, J. Phys. Chem. A, 113, 6041 (2009)
- R. Baer, E. Livshits, U. Salzner, Annu. Rev. Phys. Chem. 61, 85 (2010)
- J. Autschbach, M. Srebro, Acc. Chem. Res. 47, 2592 (2014)
- P. Verma and R. J. Bartlett, J. Chem. Phys. 140, 18A534 (2014)
Example illustrating the CAM-B3LYP functional:
start h2o-camb3lyp geometry units angstrom O 0.00000000 0.00000000 0.11726921 H 0.75698224 0.00000000 -0.46907685 H -0.75698224 0.00000000 -0.46907685 end basis spherical * library aug-cc-pvdz end dft xc xcamb88 1.00 lyp 0.81 vwn_5 0.19 hfexch 1.00 cam 0.33 cam_alpha 0.19 cam_beta 0.46 direct iterations 100 end task dft energy
Example illustrating the HSE03 functional:
echo start h2o-hse geometry units angstrom O 0.00000000 0.00000000 0.11726921 H 0.75698224 0.00000000 -0.46907685 H -0.75698224 0.00000000 -0.46907685 end basis spherical * library aug-cc-pvdz end dft xc hse03 iterations 100 direct end task dft energy #or alternatively dft xc xpbe96 1.0 xcampbe96 -0.25 cpbe96 1.0 srhfexch 0.25 cam 0.33 cam_alpha 0.0 cam_beta 1.0 iterations 100 direct end task dft energy
SSB-D functional
The recently developed SSB-D is a small correction to the non-empirical PBE functional and includes a portion of Grimme's dispersion correction (s6=0.847455). It is designed to reproduce the good results of OPBE for spin-state splittings and reaction barriers, and the good results of PBE for weak interactions. The SSB-D functional works excellent for these systems, including for difficult systems for DFT (dimerization of anthracene, branching of octane, water-hexamer isomers, C12H12 isomers, stacked adenine dimers), and for NMR chemical shieldings.
- M. Swart, M. Solà, F.M. Bickelhaupt, J. Chem. Phys. 131, 094103 (2009)
- M. Swart, M. Solà, F.M. Bickelhaupt, J. Comp. Meth. Sci. Engin. 9, 69 (2009)
It can be specified as
xc ssb-d
Semi-empirical hybrid DFT combined with perturbative MP2
This theory combines hybrid density functional theory with MP2 semi-empirically. The B2PLYP functional, which is an example of this approximation, can be specified as:
dft xc HFexch 0.53 becke88 0.47 lyp 0.73 mp2 0.27 dftmp2 direct direct convergence energy 1e-8 iterations 100 end
This can also be performed in semidirect mode as
dft xc HFexch 0.53 becke88 0.47 lyp 0.73 mp2 0.27 dftmp2 semidirect direct convergence energy 1e-8 iterations 100 end
For details of the theory, please see the following reference:
- S. Grimme, "Semiempirical hybrid density functional with perturbative second-order correlation" Journal of Chemical Physics 124, 034108 (2006)
LB94 and CS00 -- Asymptotic correction
The keyword LB94 will correct the asymptotic region of the XC definition of exchange-correlation potential by the van-Leeuwen-Baerends exchange-correlation potential that has the correct − 1 / r asymptotic behavior. The total energy will be computed by the XC definition of exchange-correlation functional. This scheme is known to tend to overcorrect the deficiency of most uncorrected exchange-correlation potentials.
The keyword CS00, when supplied with a real value of shift (in atomic units), will perform Casida-Salahub '00 asymptotic correction. This is primarily intended for use in conjunction with TDDFT. The shift is normally positive (which means that the original uncorrected exchange-correlation potential must be shifted down).
When the keyword CS00 is specified without the value of shift, the program will automatically supply it according to the semi-empirical formula of Zhan, Nichols, and Dixon (again, see TDDFT for more details and references). As the Zhan's formula is calibrated against B3LYP results, it is most meaningful to use this in conjunction with the B3LYP functional, although the program does not prohibit (or even warn) the use of any other functional.
Sample input files of asymptotically corrected TDDFT calculations can be found in the corresponding section.
NWXC -- higher order derivatives for density functionals
Whereas first order derivatives of density functionals are sufficient to calculate the Kohn-Sham energy and perform geometry optimizations, higher order derivatives are required for many properties. These properties include commonly used vibrational frequencies and excitation energies as well as others. To address the need for these derivatives a new library of density functionals was added that generates derivatives using either automatic differentiation or symbolic algebra approaches.
To request a functional from this library add the NEW keyword to the XC line. By default this will use the automatic differentiation based implementation. However, the automatic differentiation based implementation can also be requested explicitly by adding the AUTODIFF keyword. The alternative symbolic algebra implementation can be requested by adding the MAXIMA keyword.
Examples:
xc new b3lyp
xc new autodiff b3lyp
xc new maxima b3lyp
All three these examples request the B3LYP functional. The first two examples are equivalent in that they both use the automatic differentiation approach. The third example uses the symbolic algebra generated code.
The library in question is also available in the NWPW module providing the same set of functionals to the plane wave capabilities as are available in the local basis set DFT capabilities.
Sample input file
A simple example calculates the geometry of water, using the metaGGA functionals xtpss03 and ctpss03. This also highlights some of the print features in the DFT module. Note that you must use the line task dft freq numerical because analytic hessians are not available for the metaGGAs:
title "WATER 6-311G* meta-GGA XC geometry" echo geometry units angstroms O 0.0 0.0 0.0 H 0.0 0.0 1.0 H 0.0 1.0 0.0 end basis H library 6-311G* O library 6-311G* end dft iterations 50 print kinetic_energy xc xtpss03 ctpss03 decomp end task dft optimize task dft freq numerical
ITERATIONS or MAXITER -- Number of SCF iterations
ITERATIONS or MAXITER <integer iterations default 30>
The default optimization in the DFT module is to iterate on the Kohn-Sham (SCF) equations for a specified number of iterations (default 30). The keyword that controls this optimization is ITERATIONS, and has the following general form,
iterations <integer iterations default 30>
or
maxiter <integer iterations default 30>
The optimization procedure will stop when the specified number of iterations is reached or convergence is met. See an example that uses this directive in Sample input file.
CONVERGENCE -- SCF Convergence Control
CONVERGENCE [energy <real energy default 1e-6>] \ [density <real density default 1e-5>] \ [gradient <real gradient default 5e-4>] \ [hl_tol <real hl_tol default 0.1>] [dampon <real dampon default 0.0>] \ [dampoff <real dampoff default 0.0>] \ [ncydp <integer ncydp default 2>] \ [ncyds <integer ncyds default 30>] \ [ncysh <integer ncysh default 30>] \ [damp <integer ndamp default 0>] [nodamping] \ [diison <real diison default 0.0>] \ [diisoff <real diisoff default 0.0>] \ [(diis [nfock <integer nfock default 10>]) || nodiis] \ [levlon <real levlon default 0.0>] \ [levloff <real levloff default 0.0>] \ [(lshift <real lshift default 0.5>) || nolevelshifting] \ [rabuck [n_rabuck <integer n_rabuck default 25>]]
Convergence is satisfied by meeting any or all of three criteria;
- convergence of the total energy; this is defined to be when the total DFT energy at iteration N and at iteration N-1 differ by a value less than some value (the default is 1e-6). This value can be modified using the key word,
CONVERGENCE energy <real energy default 1e-6>
- convergence of the total density; this is defined to be when the total DFT density matrix at iteration N and at iteration N-1 have a RMS difference less than some value (the default is 1e-5). This value can be modified using the key word,
CONVERGENCE density <real density default 1e-5>
- convergence of the orbital gradient; this is defined to be when the DIIS error vector becomes less than some value (the default is 5e-4). This value can be modified using the key word,
CONVERGENCE gradient <real gradient default 5e-4>
The default optimization strategy is to immediately begin direct inversion of the iterative subspace. Damping is also initiated (using 70% of the previous density) for the first 2 iteration. In addition, if the HOMO - LUMO gap is small and the Fock matrix somewhat diagonally dominant, then level-shifting is automatically initiated. There are a variety of ways to customize this procedure to whatever is desired.
An alternative optimization strategy is to specify, by using the change in total energy (from iterations when N and N-1), when to turn damping, level-shifting, and/or DIIS on/off. Start and stop keywords for each of these is available as,
CONVERGENCE [dampon <real dampon default 0.0>] \ [dampoff <real dampoff default 0.0>] \ [diison <real diison default 0.0>] \ [diisoff <real diisoff default 0.0>] \ [levlon <real levlon default 0.0>] \ [levloff <real levloff default 0.0>]
So, for example, damping, DIIS, and/or level-shifting can be turned on/off as desired.
Another strategy can be to simply specify how many iterations (cycles) you wish each type of procedure to be used. The necessary keywords to control the number of damping cycles (ncydp), the number of DIIS cycles (ncyds), and the number of level-shifting cycles (ncysh) are input as,
CONVERGENCE [ncydp <integer ncydp default 2>] \ [ncyds <integer ncyds default 30>] \ [ncysh <integer ncysh default 0>]
The amount of damping, level-shifting, time at which level-shifting is automatically imposed, and Fock matrices used in the DIIS extrapolation can be modified by the following keywords
CONVERGENCE [damp <integer ndamp default 0>] \ [diis [nfock <integer nfock default 10>]] \ [lshift <real lshift default 0.5>] \ [hl_tol <real hl_tol default 0.1>]]
Damping is defined to be the percentage of the previous iterations density mixed with the current iterations density. So, for example
CONVERGENCE damp 70
would mix 30% of the current iteration density with 70% of the previous iteration density.
Level-Shifting is defined as the amount of shift applied to the diagonal elements of the unoccupied block of the Fock matrix. The shift is specified by the keyword lshift. For example the directive,
CONVERGENCE lshift 0.5
causes the diagonal elements of the Fock matrix corresponding to the virtual orbitals to be shifted by 0.5 a.u. By default, this level-shifting procedure is switched on whenever the HOMO-LUMO gap is small. Small is defined by default to be 0.05 au but can be modified by the directive hl_tol. An example of changing the HOMO-LUMO gap tolerance to 0.01 would be,
CONVERGENCE hl_tol 0.01
Direct inversion of the iterative subspace with extrapolation of up to 10 Fock matrices is a default optimization procedure. For large molecular systems the amount of available memory may preclude the ability to store this number of N^{2} arrays in global memory. The user may then specify the number of Fock matrices to be used in the extrapolation (must be greater than three (3) to be effective). To set the number of Fock matrices stored and used in the extrapolation procedure to 3 would take the form,
CONVERGENCE diis 3
The user has the ability to simply turn off any optimization procedures deemed undesirable with the obvious keywords,
CONVERGENCE [nodamping] [nodiis] [nolevelshifting]
For systems where the initial guess is very poor, the user can try using fractional occupation of the orbital levels during the initial cycles of the SCF convergence (A. D. Rabuck and G. E. Scuseria, J. Chem. Phys 110,695 (1999)). The input has the following form
CONVERGENCE rabuck [n_rabuck <integer n_rabuck default 25>]]
where the optional value n_rabuck determines the number of SCF cycles during which the method will be active. For example, to set equal to 30 the number of cycles where the Rabuck method is active, you need to use the following line
CONVERGENCE rabuck 30
CDFT -- Constrained DFT
This option enables the constrained DFT formalism by Wu and Van Voorhis described in the paper: Q. Wu, T. Van Voorhis, Phys. Rev. A 72, 024502 (2005).
CDFT <integer fatom1 latom1> [<integer fatom2 latom2>] (charge||spin <real constaint_value>) \ [pop (becke||mulliken||lowdin) default lowdin]
Variables fatom1 and latom1 define the first and last atom of the group of atoms to which the constraint will be applied. Therefore the atoms in the same group should be placed continuously in the geometry input. If fatom2 and latom2 are specified, the difference between group 1 and 2 (i.e. 1-2) is constrained.
The constraint can be either on the charge or the spin density (# of alpha - beta electrons) with a user specified constraint_value. Note: No gradients have been implemented for the spin constraints case. Geometry optimizations can only be performed using the charge constraint.
To calculate the charge or spin density, the Becke, Mulliken, and Lowdin population schemes can be used. The Lowdin scheme is default while the Mulliken scheme is not recommended. If basis sets with many diffuse functions are used, the Becke population scheme is recommended.
Multiple constraints can be defined simultaniously by defining multiple cdft lines in the input. The same population scheme will be used for all constraints and only needs to be specified once. If multiple population options are defined, the last one will be used. When there are convergence problems with multiple constraints, the user is advised to do one constraint first and to use the resulting orbitals for the next step of the constrained calculations.
It is best to put "convergence nolevelshifting" in the dft directive to avoid issues with gradient calculations and convergence in CDFT. Use orbital swap to get a broken-symmetry solution.
An input example is given below.
geometry symmetry C 0.0 0.0 0.0 O 1.2 0.0 0.0 C 0.0 0.0 2.0 O 1.2 0.0 2.0 end basis * library 6-31G* end dft xc b3lyp convergence nolevelshifting odft mult 1 vectors swap beta 14 15 cdft 1 2 charge 1.0 end task dft
SMEAR -- Fractional Occupation of the Molecular Orbitals
The SMEAR keyword is useful in cases with many degenerate states near the HOMO (eg metallic clusters)
SMEAR <real smear default 0.001>
This option allows fractional occupation of the molecular orbitals. A Gaussian broadening function of exponent smear is used as described in the paper: R.W. Warren and B.I. Dunlap, Chem. Phys. Letters 262, 384 (1996). The user must be aware that an additional energy term is added to the total energy in order to have energies and gradients consistent.
FON -- Calculations with fractional numbers of electrons
- Restricted
fon partial 3 electrons 1.8 filled 2
Here 1.8 electrons will be equally divided over 3 valence orbitals and 2 orbitals are fully filled. The total number of electrons here is 5.8
Example input:
echo title "carbon atom" start carbon_fon geometry units angstrom nocenter symmetry c1 C 0.0 0.0 0.0 end basis * library 6-31G end dft direct grid xfine convergence energy 1d-8 xc pbe0 fon partial 3 electrons 1.8 filled 2 end task dft energy
- Unrestricted
fon alpha partial 3 electrons 0.9 filled 2 fon beta partial 3 electrons 0.9 filled 2
Here 0.9 electrons will be equally divided over 3 alpha valence orbitals and 2 alpha orbitals are fully filled. Similarly for beta. The total number of electrons here is 5.8
Example input:
echo title "carbon atom" start carbon_fon geometry units angstrom nocenter symmetry c1 C 0.0 0.0 0.0 end basis * library 6-31G end dft odft fon alpha partial 3 electrons 0.9 filled 2 fon beta partial 3 electrons 0.9 filled 2 end task dft energy
To set fractional numbers in the core orbitals, add the following directive in the input file:
- set dft:core_fon .true.
Example input:
dft print "final vectors analysis" odft direct fon alpha partial 2 electrons 1.0 filled 2 fon beta partial 2 electrons 1.0 filled 2 xc pbe0 convergence energy 1d-8 end task dft
OCCUP -- Controlling the occupations of molecular orbitals
Example:
echo start h2o_core_hole memory 1000 mb geometry units au O 0 0 0 H 0 1.430 -1.107 H 0 -1.430 -1.107 end basis O library 6-31g* H library 6-31g* end occup 6 6 # core-hole in beta 1.0 0.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.0 0.0 end dft odft mult 1 xc beckehandh end task dft
GRID -- Numerical Integration of the XC Potential
GRID [(xcoarse||coarse||medium||fine||xfine) default medium] \ [(gausleg||lebedev ) default lebedev ] \ [(becke||erf1||erf2||ssf) default erf1] \ [(euler||mura||treutler) default mura] \ [rm <real rm default 2.0>] \ [nodisk]
A numerical integration is necessary for the evaluation of the exchange-correlation contribution to the density functional. The default quadrature used for the numerical integration is an Euler-MacLaurin scheme for the radial components (with a modified Mura-Knowles transformation) and a Lebedev scheme for the angular components. Within this numerical integration procedure various levels of accuracy have been defined and are available to the user. The user can specify the level of accuracy with the keywords; xcoarse, coarse, medium, fine, and xfine. The default is medium.
GRID [xcoarse||coarse||medium||fine||xfine]
Our intent is to have a numerical integration scheme which would give us approximately the accuracy defined below regardless of molecular composition.
Keyword | Total Energy Target Accuracy |
xcoarse | 1x10^{ − 4} |
coarse | 1x10^{ − 5} |
medium | 1x10^{ − 6} |
fine | 1x10^{ − 7} |
xfine | 1x10^{ − 8} |
In order to determine the level of radial and angular quadrature needed to give us the target accuracy we computed total DFT energies at the LDA level of theory for many homonuclear atomic, diatomic and triatomic systems in rows 1-4 of the periodic table. In each case all bond lengths were set to twice the Bragg-Slater radius. The total DFT energy of the system was computed using the converged SCF density with atoms having radial shells ranging from 35-235 (at fixed 48/96 angular quadratures) and angular quadratures of 12/24-48/96 (at fixed 235 radial shells). The error of the numerical integration was determined by comparison to a "best" or most accurate calculation in which a grid of 235 radial points 48 theta and 96 phi angular points on each atom was used. This corresponds to approximately 1 million points per atom. The following tables were empirically determined to give the desired target accuracy for DFT total energies. These tables below show the number of radial and angular shells which the DFT module will use for for a given atom depending on the row it is in (in the periodic table) and the desired accuracy. Note, differing atom types in a given molecular system will most likely have differing associated numerical grids. The intent is to generate the desired energy accuracy (with utter disregard for speed).
Keyword | Radial | Angular |
xcoarse | 21 | 194 |
coarse | 35 | 302 |
medium | 49 | 434 |
fine | 70 | 590 |
xfine | 100 | 1202 |
Radial | Angular | |
xcoarse | 42 | 194 |
coarse | 70 | 302 |
medium | 88 | 434 |
fine | 123 | 770 |
xfine | 125 | 1454 |
Radial | Angular | |
xcoarse | 75 | 194 |
coarse | 95 | 302 |
medium | 112 | 590 |
fine | 130 | 974 |
xfine | 160 | 1454 |
Radial | Angular | |
xcoarse | 84 | 194 |
coarse | 104 | 302 |
medium | 123 | 590 |
fine | 141 | 974 |
xfine | 205 | 1454 |
Angular grids
In addition to the simple keyword specifying the desired accuracy as described above, the user has the option of specifying a custom quadrature of this type in which ALL atoms have the same grid specification. This is accomplished by using the gausleg keyword.
Gauss-Legendre angular grid
GRID gausleg <integer nradpts default 50> <integer nagrid default 10>
In this type of grid, the number of phi points is twice the number of theta points. So, for example, a specification of,
GRID gausleg 80 20
would be interpreted as 80 radial points, 20 theta points, and 40 phi points per center (or 64000 points per center before pruning).
Lebedev angular grid
A second quadrature is the Lebedev scheme for the angular components11.6. Within this numerical integration procedure various levels of accuracy have also been defined and are available to the user. The input for this type of grid takes the form,
GRID lebedev <integer radpts > <integer iangquad >
In this context the variable iangquad specifies a certain number of angular points as indicated by the table below:
IANGQUAD | N_{angular} | l |
1 | 38 | 9 |
2 | 50 | 11 |
3 | 74 | 13 |
4 | 86 | 15 |
5 | 110 | 17 |
6 | 146 | 19 |
7 | 170 | 21 |
8 | 194 | 23 |
9 | 230 | 25 |
10 | 266 | 27 |
11 | 302 | 29 |
12 | 350 | 31 |
13 | 434 | 35 |
14 | 590 | 41 |
15 | 770 | 47 |
16 | 974 | 53 |
17 | 1202 | 59 |
18 | 1454 | 65 |
19 | 1730 | 71 |
20 | 2030 | 77 |
21 | 2354 | 83 |
22 | 2702 | 89 |
23 | 3074 | 95 |
24 | 3470 | 101 |
25 | 3890 | 107 |
26 | 4334 | 113 |
27 | 4802 | 119 |
28 | 5294 | 125 |
29 | 5810 | 131 |
Therefore the user can specify any number of radial points along with the level of angular quadrature (1-29).
The user can also specify grid parameters specific for a given atom type: parameters that must be supplied are: atom tag and number of radial points. As an example, here is a grid input line for the water molecule
grid lebedev 80 11 H 70 8 O 90 11
Partitioning functions
GRID [(becke||erf1||erf2||ssf) default erf1]
- becke : A. D. Becke, J. Chem. Phys. 88, 1053 (1988).
- ssf : R.E.Stratmann, G.Scuseria and M.J.Frisch, Chem. Phys. Lett. 257, 213 (1996).
- erf1 : modified ssf
- erf2 : modified ssf
Erfn partioning functions
Radial grids
GRID [[euler||mura||treutler] default mura]
- euler : Euler-McLaurin quadrature wih the transformation devised by C.W. Murray, N.C. Handy, and G.L. Laming, Mol. Phys.78, 997 (1993).
- mura : Modification of the Murray-Handy-Laming scheme by M.E.Mura and P.J.Knowles, J Chem Phys 104, 9848 (1996) (we are not using the scaling factors proposed in this paper).
- treutler : Gauss-Chebyshev using the transformation suggested by O.Treutler and R.Alrhichs, J.Chem.Phys 102, 346 (1995).
Disk usage for Grid
NODISK
This keyword turns off storage of grid points and weights on disk.
TOLERANCES -- Screening tolerances
TOLERANCES [[tight] [tol_rho <real tol_rho default 1e-10>] \ [accCoul <integer accCoul default 8>] \ [radius <real radius default 25.0>]]
The user has the option of controlling screening for the tolerances in the integral evaluations for the DFT module. In most applications, the default values will be adequate for the calculation, but different values can be specified in the input for the DFT module using the keywords described below.
The input parameter accCoul is used to define the tolerance in Schwarz screening for the Coulomb integrals. Only integrals with estimated values greater than 10^{( − accCoul)} are evaluated.
TOLERANCES accCoul <integer accCoul default 8>
Screening away needless computation of the XC functional (on the grid) due to negligible density is also possible with the use of,
TOLERANCES tol_rho <real tol_rho default 1e-10>
XC functional computation is bypassed if the corresponding density elements are less than tol_rho.
A screening parameter, radius, used in the screening of the Becke or Delley spatial weights is also available as,
TOLERANCES radius <real radius default 25.0>
where radius is the cutoff value in bohr.
The tolerances as discussed previously are insured at convergence. More sleazy tolerances are invoked early in the iterative process which can speed things up a bit. This can also be problematic at times because it introduces a discontinuity in the convergence process. To avoid use of initial sleazy tolerances the user can invoke the tight option:
TOLERANCES tight
This option sets all tolerances to their default/user specified values at the very first iteration.
DIRECT, SEMIDIRECT and NOIO -- Hardware Resource Control
DIRECT||INCORE SEMIDIRECT [filesize <integer filesize default disksize>] [memsize <integer memsize default available>] [filename <string filename default $file_prefix.aoints$>] NOIO
The inverted charge-density and exchange-correlation matrices for a DFT calculation are normally written to disk storage. The user can prevent this by specifying the keyword noio within the input for the DFT directive. The input to exercise this option is as follows,
noio
If this keyword is encountered, then the two matrices (inverted charge-density and exchange-correlation) are computed ``on-the-fly whenever needed.
The INCORE option is always assumed to be true but can be overridden with the option DIRECT in which case all integrals are computed ``on-the-fly.
The SEMIDIRECT option controls caching of integrals. A full description of this option is described in User Manual 10.8. Some functionality which is only compatible with the DIRECT option will not, at present, work when using SEMIDIRECT.
ODFT and MULT -- Open shell systems
ODFT MULT <integer mult default 1>
Both closed-shell and open-shell systems can be studied using the DFT module. Specifying the keyword MULT within the DFT directive allows the user to define the spin multiplicity of the system. The form of the input line is as follows;
MULT <integer mult default 1>
When the keyword MULT is specified, the user can define the integer variable mult, where mult is equal to the number of alpha electrons minus beta electrons, plus 1.
When MULT is set to a negative number. For example, if MULT = -3, a triplet calculation will be performed with the beta electrons preferentially occupied. For MULT = 3, the alpha electrons will be preferentially occupied.
The keyword ODFT is unnecessary except in the context of forcing a singlet system to be computed as an open shell system (i.e., using a spin-unrestricted wavefunction).
CGMIN -- Quadratic convergence algorithm
The cgmin keyword will use the quadratic convergence algorithm. It is possible to turn the use of the quadratic convergence algorithm off with the nocgmin keyword.
RODFT -- Restricted open-shell DFT
The rodft keyword will perform restricted open-shell calculations. This keyword can only be used with the CGMIN keyword.
SIC -- Self-Interaction Correction
sic [perturbative || oep || oep-loc <default perturbative>]
The Perdew and Zunger (see J. P. Perdew and A. Zunger, Phys. Rev. B 23, 5048 (1981)) method to remove the self-interaction contained in many exchange-correlation functionals has been implemented with the Optimized Effective Potential method (see R. T. Sharp and G. K. Horton, Phys. Rev. 90, 317 (1953), J. D. Talman and W. F. Shadwick, Phys. Rev. A 14, 36 (1976)) within the Krieger-Li-Iafrate approximation (J. B. Krieger, Y. Li, and G. J. Iafrate, Phys. Rev. A 45, 101 (1992); 46, 5453 (1992); 47, 165 (1993)) Three variants of these methods are included in NWChem:
- sic perturbative This is the default option for the sic directive. After a self-consistent calculation, the Kohn-Sham orbitals are localized with the Foster-Boys algorithm (see section 10.15) and the self-interaction energy is added to the total energy. All exchange-correlation functionals implemented in the NWChem can be used with this option.
- sic oep With this option the optimized effective potential is built in each step of the self-consistent process. Because the electrostatic potential generated for each orbital involves a numerical integration, this method can be expensive.
- sic oep-loc This option is similar to the oep option with the addition of localization of the Kohn-Sham orbitals in each step of the self-consistent process.
With oep and oep-loc options a xfine grid (see section 11.10) must be used in order to avoid numerical noise, furthermore the hybrid functionals can not be used with these options. More details of the implementation of this method can be found in J. Garza, J. A. Nichols and D. A. Dixon, J. Chem. Phys. 112, 7880 (2000). The components of the sic energy can be printed out using:
print "SIC information"
MULLIKEN -- Mulliken analysis
Mulliken analysis of the charge distribution is invoked by the keyword:
MULLIKEN
When this keyword is encountered, Mulliken analysis of both the input density as well as the output density will occur. For example, to perform a mulliken analysis and print the explicit population analysis of the basis functions, use the following
dft mulliken print "mulliken ao" end task dft
FUKUI -- Fukui Indices
Fukui inidces analysis is invked by the keyword:
FUKUI
When this keyword is encounters, the condensed Fukui indices will be calculated and printed in the output. Detailed information about the analysis can be obtained using the following
dft fukui print "Fukui information" end task dft
BSSE -- Basis Set Superposition Error
Particular care is required to compute BSSE by the counter-poise method for the DFT module. In order to include terms deriving from the numerical grid used in the XC integration, the user must label the ghost atoms not just bq, but bq followed by the given atomic symbol. For example, the first component needed to compute the BSSE for the water dimer, should be written as follows
geometry h2o autosym units au O 0.00000000 0.00000000 0.22143139 H 1.43042868 0.00000000 -0.88572555 H -1.43042868 0.00000000 -0.88572555 bqH 0.71521434 0.00000000 -0.33214708 bqH -0.71521434 0.00000000 -0.33214708 bqO 0.00000000 0.00000000 -0.88572555 end basis H library aug-cc-pvdz O library aug-cc-pvdz bqH library H aug-cc-pvdz bqO library O aug-cc-pvdz end
Please note that the ``ghost oxygen atom has been labeled bqO, and not just bq.
DISP -- Empirical Long-range Contribution (vdW)
DISP [ vdw <real vdw integer default 2]] [[s6 <real s6 default depends on XC functional>] \ [ alpha <real s6 default 20.0d0] \ [ off ] \
When systems with high dependence on van der Waals interactions are computed, the dispersion term may be added empirically through long-range contribution DFT-D, i.e. E_{DFT − D} = E_{DFT − KS} + E_{disp}, where:
In this equation, the s_{6} term depends in the functional and basis set used, is the dispersion coefficient between pairs of atoms. R_{vdw} and R_{ij} are related with van der Waals atom radii and the nucleus distance respectively. The α value contributes to control the corrections at intermediate distances.
There are available three ways to compute :
- where N_{eff} and C_{6} are obtained from Q. Wu and W. Yang, J. Chem. Phys. 116 515 (2002) and U. Zimmerli, M Parrinello and P. Koumoutsakos J. Chem. Phys. 120 2693 (2004). (Use vdw 0)
- . See details in S. Grimme J. Comp. Chem. 25 1463 (2004). (Use vdw 1)
- See details in S. Grimme J. Comp. Chem. 271787 (2006). (Use vdw 2)
Note that in each option there is a certain set of C_{6} and R_{vdw}. ALso note that Grimme only defined parameters for elements up to Z=54 for the dispersion correction above. C_{6} values for elements above Z=54 have been set to zero.
For options vdw 1 and vdw 2 , there are s_{6} values by default for some functionals and triple-zeta plus double polarization basis set (TZV2P):
- vdw 1. BLYP 1.40, PBE 0.70 and BP86 1.30.
- vdw 2. BLYP 1.20, PBE 0.75, BP86 1.05, B3LYP 1.05, Becke97-D 1.25 and TPSS 1.00.
Grimme's DFT-D3 is also available. Here the dispersion term has the following form:
This new dispersion correction covers elements through Z=94. are coordination and geometry dependent. Details about the functional form can be found in S. Grimme, J. Antony, S. Ehrlich, H. Krieg, J. Chem. Phys. 132, 154104 (2010).
To use the Grimme DFT-D3 dispersion correction, use the option
- vdw 3 (s6 and alpha cannot be set manually). Functionals for which DFT-D3 is available in NWChem are BLYP, B3LYP, BP86, Becke97-D, PBE96, TPSS, PBE0, B2PLYP, BHLYP, TPSSH, PWB6K, B1B95, SSB-D, MPW1B95, MPWB1K, M05, M05-2X, M06L, M06, M06-2X, and M06HF
- vdw 4 triggers the DFT-D3BJ dispersion model. Currently only BLYP, B3LYP, BHLYP, TPSS, and TPSSh are supported.
This capability is also supported for energy gradients and Hessian. Is possible to be deactivated with OFF.
NOSCF --Non Self-Consistent Calculations
The noscf keyword allows one to calculate the non self-consistent energy for a set of input vectors. For example, the following input shows how a non self-consistent B3LYP energy can be calculated using a self-consistent set of vectors calculated at the Hartree-Fock level.
start h2o-noscf
geometry units angstrom O 0.00000000 0.00000000 0.11726921 H 0.75698224 0.00000000 -0.46907685 H -0.75698224 0.00000000 -0.46907685 end
basis spherical * library aug-cc-pvdz end dft xc hfexch vectors output hf.movecs end task dft energy dft xc b3lyp vectors input hf.movecs noscf end task dft energy
XDM -- Exchange-hole dipole moment dispersion model
XDM [ a1 <real a1> ] [ a2 <real a2> ]
See details (including list of a1 and a2 parameters) in A. Otero-de-la-Roza and E. R. Johnson, J. Chem. Phys. 138, 204109 (2013) and the website http://gatsby.ucmerced.edu/wiki/XDM
geometry O -0.190010095135 -1.168397415155 0.925531922479 H -0.124425719598 -0.832776238160 1.818190662986 H -0.063897685990 -0.392575837594 0.364048725248 O 0.174717244879 1.084630474836 -0.860510672419 H -0.566281023931 1.301941006866 -1.427261487135 H 0.935093179777 1.047335209207 -1.441842151158 end basis spherical * library aug-cc-pvdz end dft direct xc b3lyp xdm a1 0.6224 a2 1.7068 end task dft optimize
Print Control
PRINT||NOPRINT
The PRINT||NOPRINT options control the level of output in the DFT. Please see some examples using this directive in Sample input file. Known controllable print options are:
Name | Print Level | Description |
"all vector symmetries" | high | symmetries of all molecular orbitals |
"alpha partner info" | high | unpaired alpha orbital analysis |
"common" | debug | dump of common blocks |
"convergence" | default | convergence of SCF procedure |
"coulomb fit" | high | fitting electronic charge density |
"dft timings" | high | |
"final vectors" | high | |
"final vectors analysis" | high | print all orbital energies and orbitals |
"final vector symmetries" | default | symmetries of final molecular orbitals |
"information" | low | general information |
"initial vectors" | high | |
"intermediate energy info" | high | |
"intermediate evals" | high | intermediate orbital energies |
"intermediate fock matrix" | high | |
"intermediate overlap" | high | overlaps between the alpha and beta sets |
"intermediate S2" | high | values of S2 |
"intermediate vectors" | high | intermediate molecular orbitals |
"interm vector symm" | high | symmetries of intermediate orbitals |
"io info" | debug | reading from and writing to disk |
"kinetic_energy" | high | kinetic energy |
"mulliken ao" | high | mulliken atomic orbital population |
"multipole" | default | moments of alpha, beta, and nuclear charge densities |
"parameters" | default | input parameters |
"quadrature" | high | numerical quadrature |
"schwarz" | high | integral screening info & stats at completion |
"screening parameters" | high | integral accuracies |
"semi-direct info" | default | semi direct algorithm |
Spin-Orbit Density Functional Theory (SODFT)
The spin-orbit DFT module (SODFT) in the NWChem code allows for the variational treatment of the one-electron spin-orbit operator within the DFT framework. The implementation requires the definition of an effective core potential (ECP) and a matching spin-orbit potential (SO). The current implementation does NOT use symmetry.
The actual SODFT calculation will be performed when the input module encounters the TASK directive (TASK).
TASK SODFT
Input parameters are the same as for the DFT. Some of the DFT options are not available in the SODFT. These are max_ovl and sic.
Besides using the standard ECP and basis sets, see Effective Core Potentials for details, one also has to specify a spin-orbit (SO) potential. The input specification for the SO potential can be found in Effective Core Potentials. At this time we have not included any spin-orbit potentials in the basis set library.
Note: One should use a combination of ECP and SO potentials that were designed for the same size core, i.e. don't use a small core ECP potential with a large core SO potential (it will produce erroneous results).
Also, note that charge fitting basis sets will not work with spin-orbit calculations.
The following is an example of a calculation of UO_{2}:
start uo2_sodft echo Memory 32 mw charge 2 geometry noautoz noautosym units angstrom U 0.00000 0.00000 0.00000 O 0.00000 0.00000 1.68000 O 0.00000 0.00000 -1.68000 end basis "ao basis" cartesian print U S 12.12525300 0.02192100 7.16154500 -0.22516000 4.77483600 0.56029900 2.01169300 -1.07120900 U S 0.58685200 1.00000000 U S 0.27911500 1.00000000 U S 0.06337200 1.00000000 U S 0.02561100 1.00000000 U P 17.25477000 0.00139800 7.73535600 -0.03334600 5.15587800 0.11057800 2.24167000 -0.31726800 U P 0.58185800 1.00000000 U P 0.26790800 1.00000000 U P 0.08344200 1.00000000 U P 0.03213000 1.00000000 U D 4.84107000 0.00573100 2.16016200 -0.05723600 0.57563000 0.23882800 U D 0.27813600 1.00000000 U D 0.12487900 1.00000000 U D 0.05154800 1.00000000 U F 2.43644100 0.35501100 1.14468200 0.40084600 0.52969300 0.30467900 U F 0.24059600 1.00000000 U F 0.10186700 1.00000000 O S 47.10551800 -0.01440800 5.91134600 0.12956800 0.97648300 -0.56311800 O S 0.29607000 1.00000000 O P 16.69221900 0.04485600 3.90070200 0.22261300 1.07825300 0.50018800 O P 0.28418900 1.00000000 O P 0.07020000 1.00000000 END ECP U nelec 78 U s 2 4.06365300 112.92010300 2 1.88399500 15.64750000 2 0.88656700 -3.68997100 U p 2 3.98618100 118.75801600 2 2.00016000 15.07722800 2 0.96084100 0.55672000 U d 2 4.14797200 60.85589200 2 2.23456300 29.28004700 2 0.91369500 4.99802900 U f 2 3.99893800 49.92403500 2 1.99884000 -24.67404200 2 0.99564100 1.38948000 U g 2 3.81742200 -36.04097700 2 0.26250100 -0.09051100 O nelec 2 O s 2 10.44567000 50.77106900 O p 2 18.04517400 -4.90355100 O d 2 8.16479800 -3.31212400 END SO U p 2 3.986181 1.816350 2 2.000160 11.543940 2 0.960841 0.794644 U d 2 4.147972 0.353683 2 2.234563 3.499282 2 0.913695 0.514635 U f 2 3.998938 4.744214 2 1.998840 -5.211731 2 0.995641 1.867860 END dft mult 1 xc hfexch odft grid fine convergence energy 1.000000E-06 convergence density 1.000000E-05 convergence gradient 1E-05 iterations 100 mulliken end task sodft