DFD | DAMP | DAMPDSP

[-]dfd|damp|dampdsp   0|1|2|3|4

This keyword specifies the damping function to be used for the calculation of atom-atom dispersion energies. The following damping functions are available:

Damping Functions (default choice highlighted)
Keyword value	Damping Function	Description
0		No damping
1		This damping function was introduced by Mooij et al. [1] with D1 = 7.19. Hereafter it is denoted as MDDRE function. PAMoC uses D1 = 3.54, as suggested by Wu and Yang [2].
2		This damping function was introduced by Elstner et al. [3] with D2 = 3 and hereafter it is denoted as EHFSK function.
3		Wu and Yang [2] introduced this Fermi function as a damping function, with D3 = 23. Hereafter it is referred to as WY function. Grimme [4,5] and Jurecka et al. [6] suggested variants of WY function by adding scaling factors. PAMoC implements the WY function with a lower value of the steepness parameter, D3 = 20, as suggested by Grimme [5].
4		Tang-Toennies (TT) damping function [7]. The damping parameter D0 is expressed by the sum of atomic Born-Mayer repulsion parameters Bi and Bj.

The parameter R₀ in the expression of the MDDRE, EHFSK and WY damping functions is the sum of atomic van der Waals radii. PAMoC employs the vdW radii determined by Grimme for elements H-Xe [5].

The need for a damping function arises from the fact that the dispersion energy behaves as r^-6 and becomes physically unrealistic at small distances r where it diverges.

Liu and Goddard III pointed out that the MDDRE, EHFSK and WY damping functions can be represented by a single formula with different choice of parameters [8], as shown in the following Table.

	Keyword value	a	b	m	n	Description
	1	-1	D1	3	2	MDDRE function.
	2	-1	D2	7	4	EHFSK function.
	3	exp(D3)	D3	1	-1	WY function.

The four damping functions (MDDRE, EHFSK, WY, and TT) are shown in the left figure, along with their effects on the C₆r^-6 term for the OH interaction (right figure).

It appears that the damping strength by EHFSK function is between those by funtions MDDRE and WY, with WY function being the strongest.

adp|dap|dispar  specifies which set of dispersion atomic parameters has to be used for calculation of atom-atom dispersion interaction energies.

1. "Transferable ab initio intermolecular potentials. 1. Derivation from methanol dimer and trimer calculations"
   W.T.M. Mooij, F.B. van Duijneveldt, J.G.C.M. van Duijneveldt-van de Rijdt, B.P. van Eijck
   J. Phys. Chem. A 1999, 103, 9872-9882.
2. "Empirical correction to density functional theory for van der Waals interactions"
   Q. Wu, W. Yang
   J. Chem. Phys. 2002, 116, 515-524.
3. "Hydrogen bonding and stacking interactions of nucleic acid base pairs: A density-functional-theory based treatment"
   M. Elstner, P. Hobza, T. Frauenheim, S. Suhai, E. Kaxiras
   J. Chem. Phys. 2001, 114, 5149-5155.
4. "Accurate Description of van der Waals Complexes by Density Functional Theory Including Empirical Corrections"
   S. Grimme
   J. Comput. Chem. 2004, 25, 1463-1473.
5. "Semiempirical GGA-Type Density Functional Constructed with a Long-Range Dispersion Correction"
   S. Grimme
   J. Comput. Chem. 2006, 27, 1787-1799.
6. "Density Functional Theory Augmented with an Empirical Dispersion Term. Interaction Energies and Geometries of 80 Noncovalent Complexes Compared with Ab Initio Quantum Mechanics Calculations"
   P. Jurecka, J. Cerny, P. Hobza, D. R. Salahub
   J. Comput. Chem. 2007, 28, 555-569.
7. "An improved simple model for the van der Waals potential based on universal damping functions for the dispersion coefficients."
   K. T. Tang, J. P. Toennies
   J. Chem. Phys. 1984, 80, 3726-3741.
8. "A Universal Damping Function for Empirical Dispersion Correction on Density Functional Theory"
   Yi Liu, W. A. Goddard III
   Materials Transactions 2009, 50, 1664-1670.