. 2021 Dec 20;122(12):10777–10820. doi: 10.1021/acs.chemrev.1c00675

Table 2. Overview of Published Implementations of Implicit Solvation Models in Various DFT Program Packages^a.

		dielectric model (ε)
DFT package	BCs	lin model/shape s	nonloc	nonlin aniso	het noneq	salt model
Full Potential/All-Electron
Q-Chem²⁸²	F	s_{ρ_el}/s_r^147,263	×	×	√^273,274	S-MPB²⁶³
		s_{ρ_el}(275)/s_r			√^276−280	LPB
				×	(53, 278, 281)
		(ASC²⁸³)			(273, 274, 284)	(ASC²⁸⁵)
FHI-aims²⁸⁶	F	s_{ρ_el}(141,142)	×	×	×	S-MPB^132,142,144
		s_{ρ_el} (ASC¹⁴³)	×	×	×	S-MPB^132,142,144
CRYSTAL^287,288	P²⁶⁴/F	s_r	×	×	×	×
		(ASC^264,289)	×	×	×	×
Jaguar²⁹⁰	F	s_r	×	×	×	LPB
		(ASC^{145,291−294})	×	×	×	(ASC^291−293)
GAMESS²⁹⁶	F	s_{ρ_el}/s_r	×	×	√²⁹⁵	LPB
		(ASC²⁸)	×	√^262,297,298	√^299−302	(ASC³⁰³)
Gaussian³⁰⁴	P²⁶⁵/F	s_{ρ_el}/s_r	×	×	×	LPB
		(ASC²⁸)	×	√³⁰⁵	√^{277,281,306−308}	(ASC³⁰³)
Dmol³	P²⁶⁶/F	s_r	×	×	×	×
		(ASC^146,266)	×	×	×	×
TURBOMOLE³⁰⁹	F	s_{ρ_el}/s_r	×	×	×	×
		(ASC^146,310,311)	×	×	√^308,312	×
NWChem³¹³	F	ASC^146,314	×	×	×	×
			×	×	×	×
Pseudopotential
VASP³¹⁶	P	s_{ρ_el}(149,315)	×	×	×	LPB¹⁹⁰
			×	×	×	LPB¹⁹⁰
QE^317−320	P/F	s_r(139,147)	√¹³⁹	×	×	LPB, S-MPB
		s_{ρ_el}(141)	√¹³⁹	√	×	PCC^25,272
BigDFT^321−325	F/P²⁵⁹	s_r(147)	×	×	×	MPB²⁷²
		s_{ρ_el}(141)	×	×	×	MPB²⁷²
GPAW^327,328	P/F^232,326,329	s_r(326)	×	×	×	DD-S-MPB
		s_{ρ_el}(141,148)	×	×	×	LPB, PCC²³²
PWMat^330,331	P	s_{ρ_el}(141,332)	×	×	×	S-LPB^272,332
		s_{ρ_el}(141,332)	×	×	×	S-LPB^272,332
JDFTx³³⁴	P/F	s_r(147)	√	√^22,39,137		CS-MPB¹³⁷
		s_{ρ_el}(22,137,138,149)	(122, 150, 333)	(122, 150)	×	S-CS-MPB³⁹
				√³³⁵	×	LPB^137,336
CP2K³³⁸	P	s_{ρ_el}(141,148,337)	×	×	×	×
		s_{ρ_el}(141,148,337)	×	×	×	×
ONETEP³⁴¹	P/F³⁴⁰	s_r(147,271,339)	×	×	√³⁴⁰^b	S-MPB²⁷¹
		s_{ρ_el}(148,271,339,342)	×	×	×	(271, 339, 343, 344)
CASTEP³⁴⁵	F	s_{ρ_el}(148,271,339)	×	×	×	×
		s_{ρ_el}(148,271,339)	×	×	×	×

This compilation is to provide a rough picture of all the implemented features and corresponding references, with a focus on the electrostatic and ionic parts of the grand potential functional. For the shape function, if not ASC is specified, a smooth dielectric step function is used. QE = QUANTUM ESPRESSO, BC = boundary condition (referring to solvation model implementation, P = periodic, F = free), ASC = apparent surface charge, nonloc = nonlocal, nonlin = nonlinear, aniso = anisotropic (dielectric tensor), het = heterogeonous (different bulk dielectric permittivities in different regions, to model, e.g., systems at the air–water interface or liquid–liquid interfaces), noneq = nonequilibrium/frequency-dependent, PB = Poisson–Boltzmann, MPB = lattice size-modified Poisson–Boltzmann, S = Stern correction, CS = hard sphere crowding effects based on Carnahan–Starling equation of state,³⁴⁶ PCC = planar counter charge, and DD = dielectric decrement. GAMESS and Gaussian support a variety of ASC models, and the user is referred to the documentation and to Tomasi et al. for further review of the available methods.²⁸

Only supports the use of regions with vacuum permittivity, not a different permittivity.

Table 2. Overview of Published Implementations of Implicit Solvation Models in Various DFT Program Packagesa.

Table 2. Overview of Published Implementations of Implicit Solvation Models in Various DFT Program Packages^a.