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First-order properties

First-order properties quantify expectation values of one-electron operators in individual electronic states. For the electronic ground state, quantities such as the permanent electric dipole moment are evaluated directly from the converged Kohn–Sham density, requiring no response treatment. In contrast, expectation values for electronically excited states—most notably excited-state dipole moments—are obtained from the double residue of the quadratic response function, which provides the transition-specific way to construct expectation values in the excited-state manifold. Together, these formulations provide a consistent route to state-specific first-order properties across both ground and excited electronic states. See Norman et al. (2018) for further details.

Electric dipole moment

The electric dipole moment consists of separate nuclear and electronic contributions, arising from the distribution of nuclear charges and the electronic density, respectively. VeloxChem evaluates the total dipole moment as the sum of these two components. For charge-neutral systems, the total dipole moment is independent of the choice of gauge origin. In contrast, for ionic systems the dipole moment depends on the origin of the coordinate system. In such cases, VeloxChem reports dipole moments computed with respect to the center of nuclear charge, providing a well-defined and physically meaningful reference point.

The standard unit for electric dipole moments is Debye (D) after Peter Debye. The conversion factor between atomic units and Debye is

1  ea0=2.541746  D1 \; e a_0 = 2.541746 \; \mathrm{D}
(1)

Ground state

Python script

import veloxchem as vlx

molecule = vlx.Molecule.read_name("para-nitroaniline")
basis = vlx.MolecularBasis.read(molecule, "def2-svp")

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

prop_drv = vlx.FirstOrderPropertyDriver()

prop_drv.property = "electric dipole moment"

prop_results = prop_drv.compute(molecule, basis, scf_results)
Electric dipole moment:  8.2620 Debye
Components (a.u.):
     x        y        z
 -0.6932  -2.2896  -2.2008
Loading...

Excited state

Python script

import veloxchem as vlx

molecule = vlx.Molecule.read_name("para-nitroaniline")
basis = vlx.MolecularBasis.read(molecule, "def2-svp")

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

excmom_drv = ExcitedStateMomentDriver()

excmom_drv.state = 3

excmom_results = excmom_drv.compute(molecule, basis, scf_results)
Electric dipole moment:  13.0381 Debye
Components (a.u.):
     x        y        z
 -0.8752   4.8115   1.5481

Text file

jobs
task: response
@end

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

@response
property: transition dipole moment
initial_state: 1
final_state: 1
@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.
Properties
UV/vis absorption/emission
Properties
Polarizability