Properties FAQ

  electronegativity:      -( E_HOMO + E_LUMO )/2
  hardness         :      -( E_HOMO - E_LUMO )/2

  polarizabilty    : 0.08 * VdW_Volume
                     -13.0352*hardness + 0.979920*hardness^2
                     +41.3791
  The final units are in
      10^-30 m^3

Weird units you say? The real units should be:

coul*m^2/energy

but we divide by the permittivity of free space (and 4*pi) and then scale to units appropriate to the atomic scale.

Where do those terms come from?
Though these coefficients appear arbitrary, the first term is derived from an estimation that assumes all atoms have the polorizability of hydrogen, with a correction applied from the energy gap of the humo & lumo. This equation is only used in the semiempirical methods- it turns out this is a fairly good first guess. From a freshman physics textbook, the answer should be (for atomic groups):

     H    0.66
     He   0.21
     Li  12
     Be   9.3
     C    1.5
     Ne   0.4
     Na  27
     Ar   1.6
     K   34

The polarizability can be calculated from a 1st principle method in the advanced product whenever frequencies are calculated (for QM methods). The polarizabilities are printed in the verbose output.

When using semiempirical with the POLAR keyword,the information can be found in the output file.

In Semiempirical we calculate the polarizabilities and hyperpolarizabilities using the Kurtz method: (H.A. Kurtz et. al., J. Comp. Chem., 11, 82, 1990) This can be accessed with the POLAR keyword.

The polarizibility can also be calculated from the empirical formula listed above.

Q-minus & Q-plus are known as the 'TLSER' parameters.

    O = A/(4*pi*((3*V)/4*pi)^(2/3))
      where
        A : Area
        V : Volume
        O : Ovality

1. Villar is a model which only works on semi-empirical wavefunctions with no d-orbitals. The Villar method examines the overlap matrix, searching for the type and number of lone pairs as well as the surface area of each atom. It is parameterized for H,C,N,O,F,S,CL.
   The reference is:
   • Ibon Alkorta, Hugo O. Villar, Int. J. Quant. Chem. Vol. 44, 203-218 (1992)
     
   • Angelina Kantola, Hugo O. Villar, Gilda H. Loew, J. Comp. Chem. vol. 12, No. 6, 681-689 (1991)
   
   
2. Ghose-Crippen is our default method of calculating LOGp. This method depends only on the connectivity of the molecule, and is independent of the wavefunction. (i.e. one will get the same results for semi-empirical, HF, and DFT methods but is dependent on how the molecule is drawn/connected.) The Ghose-Crippen model is parameterized for 110 atom types, including common bondings of H,C,N,O, S and the Halogens. For a test suite of 494, it gives a standard deviation of .347 and correlated coefficient of .962. In a test suite of 69 compounds beyond the original test suite it predicts a varience of .404.
   The reference is:
   
   • Ghose, Pritchett and Crippen J. Comput. Chem., 9, 80 (1988)
   
   

"LogP" methods can be selected with the LOGP= keyword;
LOGP=VILLAR and LOGP=GHOSE respectively.

Spartan 04 has a number of tools to examine solvation.

1. Cramer-Truhlar solvation
   We currently implement the Cramer-Truhlar SM54 solvation methods for water. This calculation is done, by default, for all quantum mechanics jobs. The energy of solvation predicted by this model can be found in the output window. The "solvated energy" (calculated by adding the electronic energy and the solvation energy) is labeled as "Energy(Aq)" in the spreadsheet window and in the property dialogue.

   The literature on these methods are extensive, but some of the important articles are:
   

   • Chistopher J. Cramer, Donald G. Truhlar J. Comp. Chem, Vol. 13, no. 9, 1089-1097 (1992) "PM3-SM3: A General Parameterization for Including aqueous Solvation Effects in the PM3 Molecular Orbital Model"
   • Candee C. Chambers, Gregory D. Hawkins, Christopher J. Cramer Donald G. Truhlar J. Phys. Chem. Vol 100, 16385-16398 (1996) "Model for Aqueous Solvation Based on Class IV Atomic Charges and First Solvation Shell Effects"
   
   
2. SM50R solvation calculation
   The SM50R is a solvation method derived from the semi-empirical SM54 method described above but is independent of the wavefunction and depends only on the geometry of the molecule. As such it is very fast and applicable to large systems and molecular mechanics jobs. This can be accessed by using the SOLVENT=SM50R keyword or the MMFFaq forcefield described below.
   
   
3. MMFFaq mechanics forcefield

   The MMFFaq is an extension to the MMFF94 forcefield, in which the SM50R energy term is added onto the molecular mechanics energy. We define the MMFFaq forcefield such that the solvation energy is only added on after the geometry has been optimized. (This is because analytical gradients are not pratical for the SM50R methodolgy.) Thus the coordinates and geometry of MMFF94 and MMFFaq are the same, even if the energy is different.

   This method is most useful in the context of conformational searching as the energy ordering of any conformers will likely be different in water (MMFFaq) than in vacume (MMFF94).

4. QmMm solvation calculation (windows only)
   For Hartree-Fock (HF) jobs we have implemented a QM/MM mixed procedure. In this approach the solute is modeled with standard Hartree-Fock methods. The solute is surrounded with an ensemble of molecular mechanics water molecules in a periodic box. The water molecules are sampled using a standard molecular dynamics method.

   While the energy calculated from this method is not reliable, it is interesting to observe the effect of the water molecules on the wavefunction of the solute. Thus we use this method to generate a new wavefunction and electron density. One commonly examines how the atomic charges and dipoles change as well as observing graphics such as the electrostatic potential on the density surface.

   This method may be selected in the compute section of the calculations dialogue. By default, a second "Spartan list" is generated, which contains a sample snapshot of the water molecules. The creation of this file can be turned off by using the QMMM:SHOWCONFIGS=NO keyword

1. Mulliken uses the standard mulliken analysis which simply takes each two-center term of the density/wavefunction, divides by two and places 1/2 of the 'electron cloud' on each constituent atom. This is easy to understand (if you are doing QM) but has some convergence problems with large basis sets.


2. Natural charges are similar in spirit to the Mulliken charges but with some more advanced mathematics such that the results behave better for large basis sets. Natural and mulliken charges are best used for determining chemical reactivities as a function of charge per atom. (See the discussion on natural bond order for references.)


3. Electrostatic charge (ESP) is a numerical method whose purpose is to generate charges which reproduce the electrostatic field from the entire wavefunction. These charges are more appropriate if the property one is concerned with depends on the mid to far electrostatic potential of the molecule/atom. This produces charges which are suitable for mechanics calculations, but can produce meaningless results for atoms which have little exposed surface area.
   

   In more recent versions of Spartan, you may notice that in the output we produce two sets of electrostatic charges. The traditional method calculates a charge for each atom. The newer method places a charge, a dipole, a quadrapole and an octopole on each heavy atom. (We are using these later values in internal projects.) The use of atomic dipoles does a better job of modeling the electrostatic potential.

   If the printing of charges is turned on 'Q0' represents the atomic charge; 'Qx', 'Qy' and 'Qz' represent the atomic dipole; 'Qxx', 'Qxy', etc. are the components of the traceless qudrapole.

Our ESP charge calculation is based on the 'CHELP' algorithm. In this algorithm the charges at the atom-centers are chosen to best describe the external field surrounding the molecule. Ideally this area should be everything outside of the Van der Waal radii. Of course this would be time consuming and may work too hard to get very exact long-range dipole terms at the cost of inaccuracies in the field near the atom. As a compromise, a shell surrounding the atoms is used. The thickness of this shell is 5.5 au. This default value can be modified using the SHELL= keyword in the option line. You may also change the inner value of this shell from the VDW to (VDW + WITHIN) with the keyword WITHIN=.

Keyword	Description	Default
SHELL=	The farthest extent of the shell of points to used to fit the electrostatic potential.	5.5
WITHIN=	A buffer between the standard VdW radii and the nearest points in the shell of external points.	0.0 bohrs
ELCHARGE=	An integer number representing the number of points per cubic Bohr.	1
SVD=	Use the CHELP-SVD (Single value decomposition) algorithm to calculate the charges. Setting to 0 turns off. There are a number of variants to this algorithm: An older, deprecated, algorithm. Don't prune points. Attempt to prune terms (vectors) which do not significantly improve the accuracy.	0
SVDTHRESH=		.00001
CHELPPOINTS=	Algorithm which places points into the shell. Use a rectangular grid. Use a spherical grid with approximate constant density. Use a spherical grid with density decreasing ~1/R.	1
CHELPEXTRA=	Choose more points than just nuclei. This allows one to approximate a multipole expansion around each nuclei. Use 1 point per nuclei. Use 12 points per non-hydrogen nuclei. Use 16 points per non-hydrogen nuclei.	0

Some relevant references:

• Chirlian and Francl (J. Comp. Chem. 8 (1987) 894)
• Besler, Merz, Kollman (J. Comp. Chem. 11 (1991) 431)

• A. Reed, R. Weinstock and F. Weinhold, "Natural Population Analysis", J. Chem. Phys. 83, 735 (1985)
• J.P. Foster and F. Weinhold, "Natural Hybrid Orbitals", JACS 102, 7211 (1980)

Spartan can generate a reaction path using two methods. The simplest is via the 'energy profile' calculation, which changes specific coordinates. (See the discusion of energy profile.) This works well for simple systems where the reaction coordinate can be simply represented as internal coordinates (such as bond stretch).

Spartan has also implemented a reaction coordinate algorithm to generate a reaction path given a transition state using the algorithm by Schmidt. (M.W. Schmidt, M.S. Gordon, M. Dupuis, J. Am. Chem. Soc. (1985), 107, 2585) This can be accessed by selecting the IRC button which is enabled for transition state searches. When selected, a new file will be generated which contains the reaction path.

This calculation is rather time consuming, and it is often difficult to use. We suggest that one ensures that a 'good transition state' has been found before resubmitting the job with IRC by checking ensuring the gradient is small and there is only 1 negative eigenvalue.

There are some keywords related specifically to IRC calculation and they can be found in the keyword section.

The UV/Vis spectra is calculated by running a single point CIS calculation (or TD-DFT calculation for DFT methods) after the main wavefunction has been calculated. In CIS theory, the absorption energies are the difference between the HF ground state energy and CIS excited state energies.

For DFT calculations, excited states are obtained using time dependent DFT calculations. [E. Runge, U. Gross, Phys. Rev. Lett. (1984) 961533] A CIS-like Tamm-Dancoff approximation [S. Hirata, M. HeadGordon, Chem. Phys. Lett. (1999) 302 375] [S. Hirata, M. HeadGordon, Chem. Phys. Lett. (1999) 314 291] This calculation is similar to the CIS calculation, and most keywords controlling the excited state CIS calculation are used in the TDDFT calculation.

A UV/Vis calculation is done by default whenever a single-point excited state calculation is done. If one needs to modify the UV/Vis calculation, (other than with the UVSTATES keyword) one must do a single point excited state calculation using the keywords described below.

See the keyword section on CIS/TDDFT for some relevant keywords. If you want a geometry optimization for something other than the first excited state, use the ESTATE=n keyword to choose a different excited state.

It should be noted that information on each excitation can be found in the verbose output. The notation