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VEM (Vertical Excitation or Emission) Model


The VEM is a model for calculating the vertical excitation (absorption) or vertical emission (fluorescence) energy in solution according to a two-time-scale model of solvent polarization. The model is described in reference1.

The current implementation is based on the VEM(d,RD) algorithm as described in the above paper. The method is available only at the TDDFT level of theory, including both full-linear response TDDFT (sometimes called LR-TDDFT or regular TDDFT) and the Tamm–Dancoff approximation, TDDFT-TDA (sometimes just called TDA). The configuration interaction singles (CIS) wave function method can also be used along with VEM by considering CIS to be a special case of TDDFT-TDA.

The abbreviation VEM originally referred to the vertical excitation model of reference2, but the current implementation of VEM extends to both excitation and emission calculations in solution, and the E in VEM now stands for excitation/emission. Furthermore, the current version of VEM (based on the Marenich et al. paper1) does not reduce to the original VEM of Li et al., but is improved as described in reference1.

The VEM model is based on a nonequilibrium dielectric-continuum approach in terms of two-time-scale solvent response. The solvent’s bulk-electrostatic polarization is described by using the reaction field partitioned into slow and fast components, and only the fast component is self-consistently (iteratively) equilibrated with the charge density of the solute molecule in its final state. During the VEM calculation, the slow component is kept in equilibrium with the initial state’s solute charge density but not with the final state’s one. In the case of vertical absorption the initial state is the ground electronic state of the solute molecule in solution and the final state is an excited electronic state in solution (and vice versa in the case of an emission spectrum). Both the ground- and excited-state calculations involve an integration of the nonhomogeneous-dielectric Poisson equation for bulk electrostatics in terms of the COSMO model as implemented in NWChem with the modified COSMO scaling factor (iscren 0) and by using the SMD intrinsic atomic Coulomb radii (by default; see the section of the manual describing SMD). The excited-state electron density is calculated using the Z-Vector “relaxed density” approach.

The VEM excitation or emission energy includes only a bulk-electrostatic contribution without any cavity–dispersion–solvent-structure (CDS) contributions (such contributions are used in SMD ground-state calculations as described in the SMD section of this manual, but are not used in VEM calculations). When one considers solvatochromic shifts, the main contributions beyond bulk electrostatics are solute–solvent dispersion interactions, hydrogen bonding (the latter is most important in protic solvents), and perhaps charge transfer between the solute and the solvent. To explicitly account for solute–solvent charge transfer and hydrogen bonding, the user can run a VEM calculation on a supersolute that involves a solute–solvent molecular cluster with one or a few solvent molecules added explicitly to a bare solute. The solute–solvent dispersion contribution to the solvatochromic shift, if desired, can be estimated by the solvation model with state-specific polarizability (SMSSP) described in reference3.

In this case, the user needs to provide values of ground- and excited-state spherically averaged molecular polarizabilities of the solvent.


The VEM-specific input options are as follows:


 do_cosmo_vem <integer do_cosmo_vem default 0>

The do_cosmo_vem can be set to the following values:
- 0 (do not do any VEM calculation even if the task tddft gradient line is present; default).
- 1 (do a nonequilibrium VEM excitation energy calculation;
in this case the task tddft gradient line should be present, too)
- 2 (do an equilibrium VEM excitation energy calculation followed by
a nonequilibrium emission energy calculation;
task tddft gradient line should be present)

VEM Solvent

The VEM solvent (which is water by default) can be specified by using the solvent keyword described in the SMD section of this manual or by specifying the VEM solvent descriptors such as

dielec (real input)
static dielectric constant

dielecinf (real input)
optical dielectric constant which is set (by default) to the squared value of the solvent’s index of refraction
(see the keyword soln, but note that if the solvent is specified with the solvent keyword,
the refractive index is set by the program without needing the user to supply it.)

Solvent descriptors set by the program are based on the Minnesota Solvent Descriptor Database4:

If the option do_cosmo_vem 1 or do_cosmo_vem 2 is specified the program will run VEM ground- and excited-state bulk-electrostatic calculations using the COSMO algorithm with the SMD Coulomb radii by default. If the user wants to use the default COSMO radii in such calculations (this is not recommended) the option do_cosmo_smd .false. should be specified.

SMSSP estimate of the solute–solvent dispersion contribution

If the SMSSP estimate of a solute–solvent dispersion contribution to the solvatochromic shift is desired, the following options should be used:

polgs_cosmo_vem (real input)
user-provided value of the spherically-averaged molecular polarizability of the solute in the ground state (in Å3)

poles_cosmo_vem (real input)
user-provided value of the spherically-averaged molecular polarizability of the solute in an exited state of interest (in Å3)


An example of the VEM input file is provided below.

title  'VEM/TDDFT-B3LYP/6-311+G(d) vertical excitation energy + SMSSP for formaldehyde in methanol'  
geometry nocenter  
 O    0.0000000000    0.0000000000    0.6743110000  
 C    0.0000000000    0.0000000000   -0.5278530000  
 H    0.0000000000    0.9370330000   -1.1136860000  
 H    0.0000000000   -0.9370330000   -1.1136860000  
symmetry c1  
* library 6-311+G*  
 XC b3lyp  
 do_cosmo_smd true  
 do_cosmo_vem 1  
 solvent methanol  
 polgs_cosmo_vem 2.429  
 poles_cosmo_vem 3.208  
 nroots 10  
 target 1  
 algorithm 1  
  root 1  
  solve_thresh 1d-05  
task tddft gradient


  1. Marenich, A. V.; Cramer, C. J.; Truhlar, D. G.; Guido, C. A.; Mennucci, B.; Scalmani, G.; Frisch, M. J. Practical Computation of Electronic Excitation in Solution: Vertical Excitation Model. Chemical Science 2011, 2 (11), 2143.

  2. Li, J.; Cramer, C. J.; Truhlar, D. G. Two-Response-Time Model Based on CM2/INDO/S2 Electrostatic Potentials for the Dielectric Polarization Component of Solvatochromic Shifts on Vertical Excitation Energies. International Journal of Quantum Chemistry 2000, 77 (1), 264–280.<264::aid-qua24>;2-j

  3. Marenich, A. V.; Cramer, C. J.; Truhlar, D. G. Uniform Treatment of Solute-Solvent Dispersion in the Ground and Excited Electronic States of the Solute Based on a Solvation Model with State-Specific Polarizability. Journal of Chemical Theory and Computation 2013, 9 (8), 3649–3659.

  4. Winget, P.; Dolney, D. M.; Giesen, D. J.; Cramer, C. J.; Truhlar, D. G. Minnesota Solvent Descriptor Database. Minneapolis, MN: Department of Chemistry and Supercomputer Institute 1999