Damping Functions for Atom-Atom Dispersion Energy

Synopsis

[-](DampDisp | dfde | damp)   0|1|2|3|4

Description

This keyword specifies the function which has to be used to dampen atom-atom dispersion energies. Available functions are reported in the following table:

Damping Functions (the default choice is highlighted)
Damping Function, f6(r) Keyword value Description
1    ∀ r 0 No damping
{1 − exp[−D1 (r R0 )3
 ]}  2
  		1 This damping function was introduced by Mooij et al. [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.] with D1 = 7.19. Hereafter it is denoted as MDDRE function. PAMoC uses D1 = 3.54, as suggested by Wu and Yang [2"Empirical correction to density functional theory for van der Waals interactions"
Q. Wu, W. Yang   J. Chem. Phys. 2002, 116, 515-524.].
{1 − exp[−D2 (r R0 )7
 ]}  4
  		2 This damping function was introduced by Elstner et al. [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.] with D2 = 3 and hereafter it is denoted as EHFSK function.
1 1 + exp[ −D3 ( r R0 − 1) ] 3 Wu and Yang [2"Empirical correction to density functional theory for van der Waals interactions"
Q. Wu, W. Yang   J. Chem. Phys. 2002, 116, 515-524.] introduced this Fermi function as a damping function, with D3 = 23. Hereafter it is referred to as WY function. Grimme [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.] and Jurecka et al. [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.] 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"Semiempirical GGA-Type Density Functional Constructed with a Long-Range Dispersion Correction"
S. Grimme   J. Comput. Chem. 2006, 27, 1787-1799.].
1 − e−D0 r 6 ∑k=0 (D0 r)k k! 4 Tang-Toennies (TT) damping function [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.]. The damping parameter D0 is expressed by the sum of atomic Born-Mayer repulsion parameters Bi and Bj.

Remarks

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.

The parameter R0 in the expression of 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"Semiempirical GGA-Type Density Functional Constructed with a Long-Range Dispersion Correction"
S. Grimme   J. Comput. Chem. 2006, 27, 1787-1799.].

Liu and Goddard III pointed out that MDDRE, EHFSK and WY damping functions can be represented by a single formula

f6(r) = {1 + a exp[−b (r R0 )m
 ]}  n
  		 

with different choices of the parameters a, b, m, and n [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.], as shown in the following Table.

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

The trend of the four damping functions (MDDRE, EHFSK, WY, and TT) along the distance r is shown in the left figure below, whereas their effects on the C6 r-6 term for the OH interaction potential is shown in the right figure.

dampdisp

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

Related Keywords

Related Topics

References

  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.