MP2D — dispersion correction for MP2

The MP2D method is a version of MP2 with a dispersion correction that replaces the "bad" (uncoupled Hartree-Fock) dispersion present in MP2 with a "good" (coupled Kohn-Sham) one. The concept is similar to the MP2C method where these terms are explicitly calculated, but it is formulated as an empirical correction using precalculated atomic C₆ coefficients so its computational cost is negligible. More details can be found in the recently published paper.[Řezáč, Chandler and Beran, JCTC 2018]

While MP2C is applicable only to intermolecular interaction energies, MP2D can be applied also to intramolecular cases. It has been shown to improve not only properties directly related to non-covalent interactions such as conformerenergies, but also thermochemistry. The availability of analytical gradients make it useful also for geometry optimizations.

Implementation in Cuby

Cuby was used as a platform for the reference implementation of MP2D. The correction can be added to any MP2 calculation performed in a software interfaced by Cuby. The current implementation is not completely straightforward to use, but we provide working examples below.

The UCHF C6 coefficients are distributed as a part of Cuby. They are available for the following elements: H, B, C, N, O, F, Ne, P, S, Cl, Ar, Br.

Examples

The following input file calculates MP2D/CBS interaction energy in ethene dimer (geometry from the A24 data set).

Energy calculation

job: interaction
geometry: A24:14

# MP2/CBS calculation
interface: extrapolate_cbs
extrapolate_cbs_correction: no
calculation_common:
  interface: psi4
  method: mp2
  charge: 0
calculation_mp2_small:
  basisset: aug-cc-pVTZ
  basisset_zeta: 3
calculation_mp2_large:
  basisset: aug-cc-pVQZ
  basisset_zeta: 4

# The MP2D correction:
# The mixer interface is used to remove the UCHF and add the CKS dispersion
modifiers: mixer
modifier_mixer:
  mixer_weight_a: 1.0
  mixer_weight_b: -1.0
  
  calculation_common:
    interface: dispersion3
    d3_s6: 1.0
    d3_damping: tt
    d3_hybridization: grimme_mod
    d3_3body: false
    development:
      d3_double_damping4: yes
      d3_double_damping_r: 0.72
      d3_double_damping_w: 0.20
    d3_s8: 1.187
  calculation_a: # CKS
    d3_a1: 0.944
    d3_a2: 0.480
  calculation_b: # UCHF
    d3_data_patch: mp2d_uchf_c6.yaml
    d3_a1: 0.944
    d3_a2: 0.480

Geometry optimization

job: optimize
geometry: A24:14

interface: psi4
method: mp2
# Rather small basis is used to make the example run faster, for high-quality
# results, it is recommended to use larger basis.
basisset: cc-pVTZ

# The MP2D correction
modifiers: mixer
modifier_mixer:
  mixer_weight_a: 1.0
  mixer_weight_b: -1.0
  
  calculation_common:
    interface: dispersion3
    d3_s6: 1.0
    d3_damping: tt
    # Analytical gradient of the continuous valence is not implemented,
    # using fixed integer valence introduces no appreciable error:
    d3_hybridization: fixed
    d3_3body: false
    development:
      d3_double_damping4: yes
      d3_double_damping_r: 0.72
      d3_double_damping_w: 0.20
    d3_s8: 1.187
  calculation_a: # CKS
    d3_a1: 0.944
    d3_a2: 0.480
  calculation_b: # UCHF
    d3_data_patch: mp2d_uchf_c6.yaml
    d3_a1: 0.944
    d3_a2: 0.480