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Weak interactions

C6 dispersion coefficients

The C6C_6 dispersion coefficient relates to the electric-dipole polarizability according to

C6=3ℏπ∫0∞αˉA(iω)αˉB(iω)dωC_6 = \frac{3\hbar}{\pi} \int^{\infty}_0 \bar{\alpha}_A(i\omega) \bar{\alpha}_B(i\omega) d\omega
(1)

where αˉA(iω)\bar{\alpha}_A(i\omega) is the isotropic average of the polarizability tensor for molecular system AA.

The integral over the positive imaginary frequency axis is performed in VeloxChem using a Gauss–Legendre quadrature after substituting the integration variables according to

iωI=iω01−t1+t,dωI=−2ω0dt(1+t)2,i\omega^I = i\omega_0 \frac{1-t}{1+t},\quad d\omega^I = \frac{-2\omega_0 dt}{(1+t)^2},
(2)

where a transformation factor of ω0=0.3\omega_0 = 0.3 a.u. is used.

The polarizabilities are calculated from the complex polarization propagator (CPP), or complex linear response function Norman et al. (2018). The user may specify the number of frequency points used in the quadrature, or otherwise a default value is adopted. For more detail on this approach, see Norman et al. (2003).

Python script

import veloxchem as vlx

molecule = vlx.Molecule.read_name("methane")
basis = vlx.MolecularBasis.read(molecule, "def2-svpd")

scf_drv = vlx.ScfRestrictedDriver()
scf_drv.xcfun = "b3lyp"
scf_results = scf_drv.compute(molecule, basis)

c6_drv = vlx.C6Driver()

c6_results = c6_drv.compute(molecule, basis, scf_results)
C6 coefficient: 127.7308 (a.u.)

Text file

@jobs
task: response
@end

@method settings
xcfun: b3lyp
basis: def2-svpd
@end

@response
property: C6
@end

@molecule
charge: 0
multiplicity: 1
xyz:
...
@end
References
  1. Norman, P., Ruud, K., & Saue, T. (2018). Principles and practices of molecular properties. John Wiley & Sons, Ltd.
  2. Norman, P., Jiemchooroj, A., & Sernelius, B. E. (2003). Polarization propagator calculations of the polarizability tensor at imaginary frequencies and long-range interactions for the noble gases and n -alkanes. J. Chem. Phys., 118(20), 9167–9174. 10.1063/1.1568082
Properties
Magnetic resonances
Properties
Multi-photon interactions