# Properties FAQ

• How can I calculate polarizability?

• Spartan can calculate polarizability in 4 ways:
1. Using the empirical formula described below. This available in the QSAR tab of the properties panel and is available for all quantum mechanical levels. (It can be displayed in the spreadsheet with the "Polarizability=@PROP(EST_POLARIZ)" function).
2. The polarizability can be calculated from a first principles with the addition of the POLAR keyword. For information on how to get frequency dependent polarizability see the POLAR= keyword in the keywords section of this FAQ. A summary of this calculation is printed in the output file. For more detail you can use the KEEPVERBOSE keyword
3. An external (multipole) field can be applied to any calculation and the dipole can be compared with the original value. As an example one could use EMFIELD=X~0.01 keyword with an Energy calculation then use the spreadsheet equation
=(1/2.542)*(@ref(@row-1,@prop(dipole_vec,1))-@prop(dipole_vec,1))/.01
to calculate the x component of the polarizability. (The "@row-1" assumes the molecule immediately preceding the polarized molecule has the same coordinates and method, but without the applied field.
4. When using semi-empirical methods the polarizability can be calculated with the POLAR keyword. For HF calculations this keyword also calculates the hyperpolarizability using the method described by Kurtz in H.A. Kurtz et. al., J. Comp. Chem., 11, 82, 1990. Both the polarizability and hyperpolarizability tensors are provided as well as the experimentally observed 'average polarizability' (alpha), the 'first hyperpolarizability' (beta), and the 'mean second hyperpolarizability' (gamma).

These values are printed in the output. It should be noted that in the output two different equations are used to calculate polarizabilities. (E4 is the energy equations and 'dip' is the dipole equation--from the Kurtz paper.) The main difference between these methods is sensitivity to 'round off' error. The difference can be used as an estimate of the uncertainty in the final results. Note that the details are in the verbose output, so make sure to use the KEEPVERBOSE keyword or set the "Keep Verbose" option in the "Preferences Dialog".

These values are accessible from the spreadsheet with the @PROP() possible options are
POLAR_STATIC_ALPHA POLAR_STATIC_BETA POLAR_STATIC_GAMMA POLAR_STATIC_TENSOR and POLAR2_STATIC_TENSOR (18 elements).

• What are the units of polarizability?

• Polarizability calculated in the properties module is derived from an empirical formula:
```  electronegativity:      -( E_HOMO + E_LUMO )/2
hardness         :      -( E_HOMO - E_LUMO )/2
polarizability    : 0.08 * VdW_Volume
-13.0352*hardness + 0.979920*hardness^2
+41.3791
The final units are in
10-30 m3
```
Electron Densities, Spin Densities, Dipole Moments, Charges and Electrostatic Potentials

To get the more traditional units of coul2*m/N we divide by the permittivity of free space (and 4*π) and then scale to units appropriate for the atomic scale.

To convert from "au" (as calculated by the quantum calculations) to coul2m/N (or coul2m2/J) one must multiply by

[1/bohr]3*[4*πεo] = [0.148185x10-30]*[ 111.21x10-12 ] = 16.4877x10-42
```      1 a.u. = 16.4877x10-42 coul2*m/N
1 a.u. =  0.148185 A3
1 a.u. =  0.148185 m-30
1 a.u. =  0.373803244 cm3/mol
1 a.u. = (1/2.542) D (used in the numerical calculation)

```
For example an HF/6-31+G(2df) calculation of carbon monoxide gives polarizability of "10" in the direction perpendicular to the molecular axis, which is 1.65x10-40 coul2m/N, in fair agreement with experiment (2+-0.5).

Where do the terms of the empirical polarizability formula come from?
Though these coefficients may appear arbitrary, the first term is derived from an estimation that assumes all atoms have the polarizability of hydrogen, with a correction applied from the energy gap of the highest occupied & lowest unoccupied molecular orbitals. This equation is only used in the semi-empirical methods--and it turns out that 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
```

• What are Q-plus and Q-minus?

• Q-plus is the largest positive charge on hydrogens.
Q-minus is the largest negative charge.

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

• What is ovality and how is it calculated?

• Ovality is a measure of how the shape of the molecule approaches a sphere or cigar. Ovality is described by the ratio of volume and area:
```    O = A/(4*pi*((3*V)/4*pi)^(2/3))
where
A : Area
V : Volume
O : Ovality
```
Thus the He atom is 1.0 and HC24H (12 triple bonds) is ~1.7.

• What are electronegativity and hardness?

• The molecular electronegativity and hardness are generalizations of the same concept at the atomic level:

 electronegativity = -(HOMO + LUMO)/2 hardness = -(HOMO - LUMO)/2

• What "logP" models does Spartan provide?

1. The Villar method is available from semi-empirical calculations (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 Spartan's default method for calculating logP. This method is independent of the energy/wavefunction. (i.e. one will get the same results from mechanics, semi-empirical, HF, DFT, and MP2 calculations). However, the Ghose-Crippen method is dependent on how the molecule is drawn/connected. The Ghose-Crippen method is parameterized for 110 atom/bonding types, including common bondings of H,C,N,O,S and the Halogens. For a test suite of 494 compounds, it provides 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 variance of .404.
The reference is:
• Ghose, Pritchett and Crippen J. Comput. Chem., 9, 80 (1988)

3. LogP can also be calculated directly from solvation energy. For example one can run a calculation with the POSTSOLVENT=SM12:1OCTANOL and then POSTSOLVENT=SM12:WATER keywords and use those energies in the equation
LogP = [ SolvEwater - SolvE1-octanol ] / 5.707
(all energies in kJ/mol; the 5.707 is log(10)*RT )
The solvation energy is printed in the output, or can be put into the spreadsheet by putting the following equation into a column header:
SolvE = @energySolv*@hart2kj

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

An example Spartan file shows some of these logP examples on a broad range of simple molecules. While one can argue over which of these calculations is most precise or efficient, the noise in all these methods is typically better than the uncertainity in using LogP to predict common properties like blood/brain barriers.

• What solvation models does Spartan provide?

• Spartan includes a number of ways to examine solvation.

1. C-PCM

The default solvation model which we advise for geometry and frequency calculations is the C-PCM model (Conductor like Polarizable continuum model). This depends on the shape and charge distribution of the molecule (solute) and the dielectric of the solvent.

Continuum models such as C-PCM do not account for explicit solvent-solute interactions such as hydrogen bonding or 'explicit hydrophobic'. For this reason we do not report an "energy of solvation".

Spartan gives easy access to three different dielectrics: "NonPolar" (7.43 same as THF), "Polar" (37.22, same as dimethylformamide), and "Water" (78.3). From the pull-down menu in the Calculations dialogue. You can add another solvent by appending a dielectric constant or a solvent name, i.e.:

SOLVENT=CPCM:1BROMOPENTANE or
SOLVENT=CPCM:DIELECTRIC~10.3
(You can type the SOLVENT keyword in the option line, but when you hit return it will move to the pull-down menu.)

Some references for C-PCM models are:

• X. Zhang and J. M. Herbert, J. Phys. Chem. B 118, 7806 (2014) "Excited-State Deactivation Pathways in Uracil versus Hydrated Uracil: Solvatochromatic Shift in the 1* State is the Key"
• A. W. Lange, J. M. Herbert, Chem. Phys. Lett. 509 77-87 (2011) "Symmetric versus asymmetric discretization of the integral equations in polarizable continuum solvation models"
• T. N. Truong and E. V. Stefanovich, Chem. Phys. Lett. 240, 253 (1995)
• V. Barone and M. Cossi, J. Phys. Chem. A 102, 1995 (1998)

2. C-PCM variations.

There is a large and diverse literature on C-PCM methods. Spartan's defaults should probably be used as these have been tested and are reasonable for organic systems. However for those familiar with the C-PCM literature we allow some access to the variations. There are 3 main "methods" to treat the polarizable continuum. One can replace the CPCM in the SOLVENT= keyword above with

1. CPCM which uses a dielectric screening factor of fe=(ε-1)/ε.
2. SSVPE which is a symmetrized version of an integral equation formalism (IEF-PCM) model with a screening factor of fe=(ε-1)/(ε+1/2).
3. SMD is a Cramer-Trular SMx method which uses the CPCM formulation for the polarization term.
By appending
SOLVENT=SSVPE:DIELECTRIC~10.3

SSVPE has been argued to be the best method for solvated excited states. an example of using SSVPE that might be appropriate for excited states is

(The ADDSOLVENT= is a pseudonym for SOLVENT= but this keyword stays in the Options line as opposed to popping over to the pull-down menu. This has the advantage of being able to more easily edit the line if needed.)

There are a number of other parameters which can be changed in C-PCM models which can be added as comma separated options appended to the keyword after the dielectric. These are:

• DIELECTRIC (If using a solvent name this is not required)
• OPTICALDIELECTRIC While formally required for excited state calculations we use an appropriate value if using a solvent name)
• TEMPERATURE
• PRESSURE
• SOLVENTRHO
• STATESPECIFIC
• CHARGESEPARATION
For a full list and more in depth discussion we follow the notation and keywords found in the Q-Chem 4.0 Manual.

3. Cramer-Truhlar SM5.4 solvation

We currently implement the Cramer-Truhlar SM5.4P and SM5.4A solvation methods for water, and is available to any molecule SM5 parameterized atoms.

This is a very fast method and is appropriate to get quick "energy of solvation" energies at a given geometry. To use this model, for "solvation energy" calculations use the SM54 keyword in the option line.

The energy of solvation predicted by this model can be found in the output text. You can print this in the spreadsheet with the equation

Solve.E.=@prop(SOLV_CORRECTION)*@hart2kj,

In Spartan "10 and Spartan "14 this calculation was done by default for all HF and DFT jobs.

Literature on these methods is extensive, some important articles are:

• Christopher J. Cramer, Donald G. Truhlar J. Comp. Chem. 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. 100, 16385-16398 (1996) "Model for Aqueous Solvation Based on Class IV Atomic Charges and First Solvation Shell Effects"

4. MMFFaq mechanics force field (SM5.0R)

SM5.0R is a solvation method derived from the semi-empirical SM54 approach described above. It is independent of the wave function and depends only on the geometry of the molecule. As such, it is very fast and is applicable to large systems and molecular mechanics calculations. This method can be accessed by using the POSTSOLVENT=SM50R keyword.

MMFFaq is an extension to the MMFF94 forcefield, in which the SM50R energy term is added to the molecular mechanics energy. In Spartan, the MMFFaq force field is implemented such that the solvation energy is only added AFTER the geometry has been optimized. Thus the structures of molecules from MMFF94 and MMFFaq calculations will be the same, but their energies will be different. The MMFFaq method is most useful in the context of conformational searching or in an energy profile as the energy ordering of any conformers will likely be different in water (MMFFaq) than in vacuum (MMFF94).

The reference for SM5.0R is

• G.D. Hawkins, C.J. Cramer, D.G. Truhlar J. Phys. Chem. B 101, 7147-7157 (1997) "Parameterized Model for Aqueous Free Energies of Solvation using Geometry-dependent Atomic Surface Tensions with Implicit Electrostatics"

5. SM8, SM12 and SMD solvation calculation

The SM8 and SM12 model allow both water and a number of organic solvents and treats both neutral and charged solutes. This method is notable for the large suite of experimental data used to parameterize the model and uses the HF or DFT wave functions. To run SM8 as a property calculation (to calculate the energy of solvation) use the keyword POSTSOLVENT=SM8:WATER (and POSTSOLVENT=SM12 where water can be replaced with many different organic solvents. This method is dependent on the basis set, and is parameterized for the 6-31G* sets. (While the method will function for other variants in the 6-31G series, experience has shown that using larger basis sets worsens the results.

Technically, it is possible to do geometry optimizations with these models, but because of the discontinuous nature of the derivatives (due to the SCF like nature of solvated charge calculation) optimizations and frequency are problematic except for the simplest of molecules. Use the SOLVENT=SM12:WATER keyword for optimizations. (When you type in this keyword and hit 'enter'; the keyword will replace the "in Gas" pull-down menu in the upper right of the Calculations dialogue.)

For SM8, SM12 and SMD you can use a number of different solvents in place of water. The list of supported solvents follows:
WATER, 111TRICHLOROETHANE, 112TRICHLOROETHANE, 11DICHLOROETHANE, 124TRIMETHYLBENZENE, 14DIOXANE, 1BROMO2METHYLPROPANE, 1BROMOPENTANE, 1BROMOPROPANE, 1BUTANOL, 1CHLOROPENTANE, 1CHLOROPROPANE, 1DECANOL, 1FLUOROOCTANE, 1HEPTANOL, 1HEXANOL, 1HEXENE, 1HEXYNE, 1IODOBUTANE, 1IODOPENTENE, 1IODOPROPANE, 1NITROPROPANE, 1NONANOL, 1OCTANOL, 1PENTANOL, 1PENTENE, 1PENTYNE, 1PROPANOL, 222TRIFLUOROETHANOL, 224TRIMETHYLPENTANE, 24DIMETHYLPENTANE, 24DIMETHYLPYRIDINE, 26DIMETHYLPYRIDINE, 2BROMOPROPANE, 2CHLOROBUTANE, 2HEPTANONE, 2HEXANONE, 2METHYLPENTANE, 2METHYLPYRIDINE, 2NITROPROPANE, 2OCTANONE, 2PENTANONE, 2PROPANOL, 2PROPEN1OL, 3METHYLPYRIDINE, 3PENTANONE, 4HEPTANONE, 4METHYL2PENTANONE, 4METHYLPYRIDINE, 5NONANONE, ACETICACID, ACETONE, ACETONITRILE, ANILINE, ANISOLE, BENZALDEHYDE, BENZENE, BENZONITRILE, BENZYLALCOHOL, BROMOBENZENE, BROMOETHANE, BROMOOCTANE, BUTANAL, BUTANOICACID, BUTANONE, BUTANONITRILE, BUTYLETHANOATE, BUTYLAMINE, BUTYLBENZENE, CARBONDISULFIDE, CARBONTET, CARBONTETRACHLORIDE, CCL4, CHLOROBENZENE, CHLOROTOLUENE, CIS12DIMETHYLCYCLOHEXANE, DECALIN CYCLOHEXANE, CYCLOHEXANONE, CYCLOPENTANE, CYCLOPENTANOL, CYCLOPENTANONE, DECANE, DIBROMOMETHANE, DIBUTYLETHER, DICHLOROMETHANE, DIETHYLETHER, DIETHYLSULFIDE, DIETHYLAMINE, DIIODOMETHANE, DIMETHYLDISULFIDE, DIMETHYLACETAMIDE, DIMETHYLFORMAMIDE, DMF, DIMETHYLPYRIDINE, DMSO, DIMETHYLSULFOXIDE, DIPROPYLAMINE, DODECANE, E12DICHLOROETHENE, TRANS12DICHLOROETHENE, E2PENTENE, ETHANETHIOL, ETHANOL ETHYLETHANOATE, ETHYLMETHANOATE, ETHYLPHENYLETHER, ETHYLBENZENE, ETHYLENEGLYCOL, FLUOROBENZENE, FORMAMIDE, FORMICACID, HEXADECYLIODIDE, HEXANOIC, IODOBENZENE, IODOETHANE, IODOMETHANE, ISOBUTANOL, ISOPROPYLETHER, ISOPROPYLBENZENE, ISOPROPYLTOLUENE, MCRESOL, MESITYLENE, METHANOL, METHYLBENZOATE, METHYLETHANOATE, METHYLMETHANOATE, METHYLPHENYLKETONE, METHYLPROPANOATE, METHYLBUTANOATE, METHYLCYCLOHEXANE, METHYLFORMAMIDE, MXYLENE, HEPTANE, HEXADECANE, HEXANE, NITROBENZENE, NITROETHANE, NITROMETHANE, METHYLANILINE, NONANE, OCTANE, PENTANE, OCHLOROTOLUENE, OCRESOL, ODICHLOROBENZENE, ONITROTOLUENE, OXYLENE, PENTADECANE, PENTANAL, PENTANOICACID, PENTYLETHANOATE, PENTYLAMINE, PERFLUOROBENZENE, PHENYLETHER, PROPANAL, PROPANOICACID, PROPANONITRILE, PROPYLETHANOATE, PROPYLAMINE, PXYLENE, PYRIDINE, PYRROLIDINE, SECBUTANOL, TBUTANOL, TBUTYLBENZENE, TETRACHLOROETHENE, THF, TETRAHYDROFURAN, TETRAHYROTHIOPHENEDIOXIDE, TETRALIN, THIOPHENE, THIOPHENOL, TOLUENE TRANSDECALIN, TRIBROMOMETHANE, TRIBUTYLPHOSPHATE, TRICHLOROETHENE, TRICHLOROMETHANE, TRIETHYLAMINE, UNDECANE, Z12DICHLOROETHENE

It is important to notice that no spaces are allowed in the name, thus "acetic acid" is spelled "ACETICACID".

SM12 has been defined for multiple charge models. The default uses Charge Model 5 (CM5) but Merz-Singh-Kollman (MK) and ChElpG (CHELPG) charges are also available. You can access these by adding to the end of the POSTSOLVENT= keyword. For example:

POSTSOLVENT=SM12:1OCTANOL,CHARGES:chelpg

Some useful reference are

• A.V. Marenich, R.M. Olson, C.P. Kelly, C.J. Cramer, D.G. Truhlar, "Self-Consistent Reaction Field Model for Aqueous and Nonaqueous Solutions Based on Accurate Polarized Partial Charges," J. Chem. Theory Comput. 3, 2011-2033 (2007)
• A.V. Marenich, C.J. Cramer, D.G. Truhlar, "Generalized Born Solvation Model SM12" J. Chem. Theory Comput. 9, 609-620 (2013)

6. (iso)SS(V)PE solvation calculation

(In Spartan'14 this was called SS(V)PE but has been renamed to distinguish it from the SS(V)PE variants of C-PCM model

The Surface and Simulations of Volume Polarization for Electrostatics (SS(V)PE) method treats the solvent as a continuum dielectric, solving Poisson's equation on the boundary. A dielectric constant is needed for the calculation. For example, POSTSOLVENT=ISOSVP,78.39 would be use for water. References for this method can be found in

• D. M. Chipman, J. Chem. Phys. 112, 5558, (2000)
• D. M. Chipman, Theor. Chem. Acc. 107, 80, (2002)
• D. M. Chipman, Theor. Chem. Acc. 107, 90, (2002)

It should be noted that analytical gradients are not available, so transition state searches with this solvent model should only be applied to small molecules. Another important constraint of our implementation is that only molecules with 'star-like' volumes are allowed. Any ray emanating out from the center can only pass through the surface once.

Our implementation has been designed for small molecules. So for larger molecules one may have to modify internal parameters to get good results. Specifically NPTLEB=, which controls the number of Lebedev points set to 1202. This has been shown to be precise enough for .1 kcal/mol on solutes the size of monosubstituted benzenes. Other possible values are (974,1202,1454,1730,2030,2354,2702,3074,3470,3890,4334,4801,5294).

7. SM3 solvation method

For legacy purposes Spartan also implements the Cramer-Truhlar SM3 method. The SM54P and SM8 method are much improved over SM3 and should not be used in the future, but can be accessed with the POSTSOLVENT=SM3 keyword.

• What is the distinction between the "POSTSOLVENT", "ADDSOLVENT" and "SOLVENT" keywords?
• We use the POSTSOLVENT keyword to do an energy of solvation calculation. This calculation is useful to determine the energy differences among different conformers of the same molecule as the bond lengths and angles do not change significantly when solvent is added.

If one wants to see the effect of solvation on the geometry, (for example for a transition state structure) the ADDSOLVENT= or SOLVENT= should be used. SOLVENT= is a synonym for ADDSOLVENT=. When typed in, it will be erased (following pressing of the Enter/Return key) from the Options line and the "in-solvent" pull down menu will be updated to reflect the specified solvent.

A longer discussion of how the solvation energy is calculated can be found under solvation methods in the "Quantum Mechanical Energy FAQs".

• What atoms are parameterized for Spartan's solvation methods?
• The Cramer-Truhlar methods (SM8, SM54, SM50R, SM3) work only with common organic atoms: H, C, N, O, F, S, Cl, Br, and I. (SM8 adds Si and P if bonded to oxygen.) SM12 covers the entire periodic table. The calculation may proceed with other elements, but important terms of the approximation will be set to zero. If the atoms "aren't very important" relative solvation energies of conformers might be useful, but absolute values will be poor.

In principle the C-PCM and SS(V)PE methods are not parameterized and are available for any atom of the underlying basis-set, however they do require atomic radii to generate the cavity. By default we use the "Bondi Radii" increased by 20% to construct the cavity in the PCM solvation calculation. These are vdW radii originally proposed by Bondi, verified by Rowland and Taylor and extended by Cramer and Truhlar.

• Bondi, J. Phys. Chem. 68, 441 (1964)
• Rowland Taylor, J. Phys. Chem. 100, 7384 (1996)
• Mantina et al, J.Phys.Chem. 100, 7384 (2009)
This covers the standard main group atoms:

H-Ca, Ga-Kr, Rb,Sr, In-Xe, Cs,Ba, Tl-Rn, Fr,Ra
and a few metals: Ti, Ni, Zn, Ag, Cd, Pt, Au

If alternate atoms are required you may use the PCMRAD= keyword. For example to use a Radii for Iron of 2.2 angstroms one would use PCMRAD=FE~2.2 Note that this is the presumed vdW radii, before being multiplied by the default 1.2 (20%). If there are multiple atoms you can comma separate them. i.e.: PCMRAD=FE~2.2,NI~2.2

• What charge models can be accessed from Spartan?
• We have 3 ways of decomposing the quantum mechanics wave function into a set of nuclear charges. These are Mulliken charges, natural charges and electrostatic (ESP) charges.

1. Mulliken uses a standard Mulliken analysis, taking each two-center term of the density/wave-function, dividing by two and placing 1/2 of the 'electron cloud' on each constituent atom. This approximation is a fair approximation for small, well-balanced basis sets but becomes increasingly poor for larger basis sets.

2. Natural charges are similar to Mulliken charges, but include 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 that generates charges that reproduce the electrostatic field from the entire wave function. This method is appropriate when the property one is concerned with depends on the mid-to-far electrostatic potential of the molecule/atom. Electrostatic charges may produce poor results for atoms that have little exposed surface area.

In more recent versions of Spartan, the output includes 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 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 ("Charges & Bond Orders" is checked in the Calculations dialogue) 'Q0' represents the atomic charge; 'Qx', 'Qy' and 'Qz' represent the atomic dipole; 'Qxx', 'Qxy', etc. are the components of the traceless quadrapole.

• How can I control the parameters of the ESP charge model?
• Spartan's 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 include everything outside of the van der Waals 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 Options field of the Calculations dialogue. 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 bohrs 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 CHELPDENSITY= 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/radius. 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 7 points per nuclei. Use 10 points per non-hydrogen nuclei. Use 14 points per non-hydrogen nuclei. Use bond orientated, atom centered dipoles Modified version of model 4 adding extra points on atoms with 2 bonds. same as 5, but add dipoles to hydrogens Dipoles on all terminal atoms A flag to cycle through all models By default electrostatic charges are reported using method '0'. However, points using method '2' are also calculated and available to be used. 0

Relevant references:

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

• What is natural bond order?

• Natural bond order uses similar mathematics to natural charges but is used to analyze the charge density between atoms, not centered on each atom. See the NBO keyword

Natural Bond Order references:
• 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)

More information from NBO calculations can be printed with the keyword PROPPRINTLEV=2. This keyword may be useful if you are interested in atomic hybridization of each atom or problems are detected with the NBO calculation.

Spartan's version of natural bond order attempts to find the "natural" Kekule bonding of each molecule. As such it has issues with delocalized systems. When strong delocalization is detected the calculation will not complete, but one can force the calculation to complete by adding the PROP:IGNORE_WARN keyword (and the PROPRERUN keyword to force the properties module to rerun). In this case the atomic polarization will likely be useful, but the total natural bond order is not to be trusted.

• The sum of the square of the coefficients of my MO is not 1. Shouldn't it be normalized?

The MO (molecular orbital) is normalized, and the AO (atomic orbitals) are normalized. But the AOs are not orthogonal. This is why the simple algebraic norm of the coefficients is not 1.0. In order to do any quantitative work with the coefficients of the MO you will need to know the values the AO overlap integral. This is usually referred to as the overlap matrix and is represented as 'S' in the literature.

• How can I print the overlap matrix?
• The overlap matrix is the overlap of different atomic orbitals. It can be printed with the PRINTOVERLAP keyword. The ordering of the coefficients is the same as that displayed for the molecular orbitals when the "Orbitals & Energies" check box is selected in the Calculations dialogue.

• What is the spin operator <S2> and what does it say about the wave function?

• <S2> is the spin operator, and it is relevant in UHF calculations. While UHF (or ROHF) is required for open shell systems and to get certain bond separation energies correctly, it suffers from the disadvantage that its wave functions are not (exact) eigen-functions of the total spin operator. This is because the UHF ground state can be contaminated with functions corresponding to states of higher spin multiplicity.

<S2> is a measure of spin contamination and is often used as a test of how good the UHF wave function is. Singlet states should have a value of 0.0, doublets 0.75, and triplets 2.0. If <S2> is within +- .02 of these values the wave function is usually considered acceptable.

M = 1(singlet), 2(doublet), 3(triplet), ...
s = (M-1)/2
<S2> = s*(s+1)
<S2> = 0, 3/4, 2, ...

The <S2> is printed out when the PROPPRINTLEV=1 keyword is used, and is represented in the output file as <S**2>

• What masses are used in frequency calculations?
• The default masses are found in the "MASS.spp" parameter file. ("params.MASS" on Linux machines.) The default value is the mass of the most common isotope. This can be overridden with the AVGMASS keyword, or by changing the isotope of a specific atom in the Atom Properties dialogue.

• How is the Raman spectra calculated?
• The strength of RAMAN frequencies are calculated from the change in polarization of the molecule with respect the vibrational mode. As such, this can be much slower than just calculating standard IR intensities (dependent on the change in the dipole). It should be noted that the Intensities shown in the "Output Summary" and plotted in the RAMAN graphs are scaled by the laser frequency [vo] (which can be changed in the Options menu -> Preferences -> Settings dialogue), plotted logarithmically and broadened with a Lorentzian.

I(vi) = S(vi) * [ (vo-vi)4 ] / [ vi*(1-exp(vi*C2)/T) ]
Where C2 is the "Second radiation Constant"; 1.438777 cm-K.

• What is the absorbance unit?

• The units of absorbance is kilometers per mol, km/mol. The justification for this unit can be surprising, so we derive this unit here. The molar absorption coefficient e

e(v) = [1/Cd]log[Io(v)/I(v)] == A(v)/Cd

where C is the concentration, (mol/L), d is the path length (cm), Io/I is the intensity ratio (unitless, incident over transmitted) and 'v' is the wavenumber (1/cm). Thus the unit is

[L/(mol*cm)]

However, what is measured is the integrated absorption A

A = ∫A(v)dv ; over the band in question
Thus A is in units of
[L/(mol*cm)]*[1/cm] == [1000cm3/mol*cm2] = 10m/mol.
Multiplying by a hundred gives the units most often used in experiment and in Spartan:
1000m/mol = km/mol.

• How can I use the intrinsic reaction coordinate (IRC) procedure?

• Spartan can generate a reaction path using three approaches. The simplest is via the 'energy profile' calculation, which changes specific coordinates. (See the discussion of energy profile.) This works well for simple systems when the reaction coordinate can be well represented as internal coordinates (such as bond distance).

A reaction path can also be generated by the calculation of the Transition State Geometry along with a frequency calculation. A list file can be generated for the single imaginary frequency corresponding to the reaction coordinate.

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 specified by selecting the IRC checkbox when performing a transition state geometry calculation. When selected, a new file will be generated that contains the reaction path. The IR check box should also be selected. If you know you have a good transition point and a good Hessian the IRC can be run as a single point "Energy" calculation with the BE:IRC keyword.

The IRC calculations are time consuming. It is suggested that users confirm that a 'good transition state' has been found before resubmitting the with the IRC algorithm enabled. Confirm both, that the gradient is small and that there is only 1 negative eigenvalue.

Keywords related specifically to IRC calculation can be found in the keyword section.

• What is the best way to work with an excited state?

• Spartan offers a number of ways to work with excited states, of varying complexity and cost. However, since nearly all ground states are singlets, and the first excited state is almost always the lowest triplet the easiest thing to do is look at the "Ground State" with two unpaired electrons. This is almost always "accurate enough" and much faster than any of the more advanced methods.

As an example I'll look at benzene. I first optimized structure for benzene in its ground state. (The HOMO-LUMO gap of 6.6 ev for this singlet would be a first approximation of the excited state energy.) I next Copy+Pasted that in the spreadsheet and redid the calculation as a triplet. I did this twice; once with a triplet optimization, and once at the same Singlet Geometry. The energy gain from going from singlet to triplet is shown in the "Rel. E (eV)" column (Notice equation highlighted) The Single point energy would be the appropriate number for fluorescence (vertical excitation) , and the triplet optimization would be for phosphorescence. Notice that for the triplet opt, I turned off symmetry with the IGNORESYMMETRY keyword and checked the IR checkbox (which becomes the FREQ keyword) to ensure that I've found the real triplet minimum. (Any negative frequencies would indicate that symmetry was not broken enough.)

As an example of a different approach/theory notice that I checked UV/Vis check-box on the ground-state singlet. (The UVVIS keyword.) [I added KEEPVERBOSE, INCLUDETRIPLETS as mentioned in our help. I also added UVSTATES=4 because benzene is a difficult case==bad convergence] If you examine the verbose output for this you will see that using full TDDFT theory, the excited state energy (vertical excitation) is 3.88 ev. (The TDA approximation gives 4.24 ev.)

...TDDFT is probably better ..... needed for other excited states or singlet->singlet transitions.

We can do optimizations at the TDDFT level, as is shown in the final row. This can be very slow, (prohibitively slow for DFT functionals where we do not have analytical gradients such as EDF2).

• What does the UV/Vis calculation do?

• The UV/Vis spectra is calculated by running a single point CIS calculation (or TD-DFT calculation for DFT methods) after the main wave function has been calculated. In CIS theory, the absorption energies are the difference between the HF ground state and CIS excited state energies. A reference for Spartan's CIS implementation:

J.B. Foresman, M. Head-Gordon, J.A. Pople, M.J. Frisch, J. Phys. Chem. (1992), 96, 135.

For DFT calculations, excited states are obtained using the time-dependent density functional theory (TD-DFT) approach to generate excited states from excitations of the ground state molecular orbitals. The Tamm-Dancoff approximation (TDA) is also available to speed up the calculations:

E. Runge, U. Gross, Phys. Rev. Lett. (1984) 961533] A CIS-like Tamm-Dancoff approximation [S. Hirata, M. Head-Gordon, Chem. Phys. Lett. (1999) 302 375S.

Hirata, M. Head-Gordon, 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 specified. If one needs to modify the UV/Vis calculation, (other than with the UVSTATES keyword) a single point excited state calculation must be performed, using the keywords described below.

• How can I control an excited state calculation?

• See the keyword section on CIS/TDDFT for 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. (Note that when you hit the "Enter" key the ESTATE keyword disappears and the n appears where the "First Excited" in the first line of the calculations dialogue.

Often you may want the first excited singlet state, which may or may not be the actual first excited state. To limit the search of possible excited states to singlets you can type in the keyword CIS_TRIPLETS=FALSE.

• What is the difference between the "first excited state" and "ground state doublet"?

• Assuming that the real ground state is a singlet, and the first excited state is not a triplet, these both refer to the same electronic state. A difference exists in how Spartan calculates these; excited state calculations use either CIS or TDFT methods while ground state calculations use HF or DFT methods. The later may not be as accurate, but are much faster, especially in the context of geometry optimizations.

It is also possible that the first excited state is another singlet, and not a triplet. If in doubt you can do an energy calculations with the "UV/Vis Spectrum" and the INCLUDETRIPLETS keyword to examine all the excited states. Note that the description of singlet/triplet is found in the verbose output so you will need to add the KEEPVBOSE keyword. Graphically, the intensity of the singlet to triplet will be very small.

• How can I read the verbose output of excited state calculations?

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

D(10)->V(2)
refers to the excitation of an electron from the 10-th doubly occupied MO to the 2nd virtual MO. Often, an excitation will take contributions from multiple molecular orbitals.

The Transition dipole moment and oscillator strength are also printed. The oscillator strengths are used by Spartan to graphically display the UV/Vis spectrum. To convert the oscillator strength to absorbance, we divide by 4.319x10-7. Usually the log (base 10) of the absorbance is used to display the spectrum.

By default only pairs of filled/unfilled orbitals which have amplitudes larger than 0.15. To see more components you can use the CIS_AMPL_PRINT=1 keyword to see (nearly) all of the components. The sum of the square of all components will add to 1.0.

• How is the NMR spectrum calculated

Spartan's NMR package is based on the Kussman Ochsenfeld linear scaling algorithm using "gauge-including" atomic orbitals:

• C. Ochsenfeld, J. Kussmann, F. Koziol, Angew. Chem., 116, 4585, (2004).
• F. London, J. Phys. Radium, 8, 397, (1937)
• K. Wolinski, J. F. Hinton, P. Pulay, J. Am. Chem. Soc., 112, 8251, (1990).
This scheme has been proven to be reliable and accurate for many applications, see
• T. Helgaker, M. Jaszunski and K. Ruud, Chem. Rev., 99, 293, (1990).
• C. Ochsenfeld and M. Head{Gordon, Chem. Phys. Lett., 270, 399, (1997).
• S. P. Brown, T. Schaller, U. P. Seelbach, F. Koziol, C. Ochsenfeld, F.-G. Klarner, H. W. Spiess, Angew. Chem. Int. Ed., 40, 717, (2001).
• C. Ochsenfeld, F. Koziol, S. P. Brown, T. Schaller, U. P. Seelbach, F.-G. Klarner, Solid StateNucl. Magn. Reson., 22, 128, (2002).
• C. Ochsenfeld, J. Kussmann, F. Koziol, Angew. Chem., 116, 4585, (2004).

Chemical shifts are given in parts-per-million (ppm) relative to the appropriate standard (nitromethane for nitrogen, fluorotrichloromethane for fluorine, and TMS for hydrogen, carbon and silicon). These relative shifts are available for most common DFT functionals and basis sets. One can edit the "NMR_References.spp" file found in the Spartan shipping directory to add new standards.

Spartan can also apply systematic corrections to the Carbon NMR depending on the nearby chemical environment. These are referred to as "corrected shifts" in Spartan.

• How is the H-H coupling spectrum calculated?

We use modified Karplus equations to predict hydrogen coupling constants.

• "Vuister and Bax", 1993a and "Wang and Bax 1996" for amide bonds.
• "Haasnoot, de Leeuw and Altona (1980)" for sp3-sp3 3JHH linkages
• When 2JHH couplings are calculated, we have a few empirical values from table 4.6 (pg. 151) "Organic Structure Analysis 2nd ed." P.Crews, J.Rodriguez, M.Jaspers.

• NMR calculations are having difficulty converging. What can I do?

• The NMR calculation has its own set of SCF convergence issues. Usually the default parameters are good enough to get reasonable answers, but at times you may need to change these to get difficult systems to converge. The first thing to do is to make sure the integrals are more accurate than usual by typing the CONVERGE keyword in the Options line of the Calculations dialogue.

If you continue to have difficulty you will have to adjust some of the internal parameters to the multi-step SCF logic. The most common problem is errors with "level-2" iterations. By default this fails after 75 steps. This can be increased with the D_SCF_MAX_2= keyword. A list of other NMR related keywords can be found in the keyword table below.

• What is the score used to rank alignments?

• The score used for alignment is designed to be 1 for a perfect fit and 0 for a terrible fit. For a system with N centers:

score = 1 - U/N
U = sum[i=1,N; Gi(ri-roi)]

'ri' is the i'th center of the trial molecule, and 'roi' is the corresponding center of the template molecule. G is a function which behaves like the usual Hookean spring for small values. (~(ri-roi)2) but approaches 1 as the difference in distances (ri-roi) goes to infinity

G = (1/3)*[ (ri-roi)/Ri]2
G = (1/3)*{3 - 3[(ri-roi)/Ri]-2 + [(ri-roi)/Ri]-4 }

The second equation is used when (ri-roi)/Ri is greater than 1.0. The normalizing Ri is (3/5) of the van-der-Wall radii for atoms, and for CFD's is the radii given in the property panel when a CFD is selected.

The distinguishing feature of this function when compared to a simple RMSD type function ((ri-roi)2 is that in the case where most of the centers will line up exactly, but only 1 is nowhere near matching, the latter center will adversely affect the alignment of the former centers. As an example, let's try to map the H2 molecule onto a template of the Br2 molecule with RCl set anomalously small, say 1/10 of an angstrom. The 'best' (and only) minima found by the RMSD function is the H2 molecule centered symmetrically at the center of the Br2 molecule. The score we use would find an off-center minima with one hydrogen directly on one Bromine, and the other Hydrogen near the center of the Br2 molecule.

When aligning two separate sets of centers, a number of alignments are examined. It should be noted that the 6-dimensional translation/rotation space of the above function can have many local minima, or alignments. These are minimized and examined, and the best one is returned. Also, a second score is used internally: 'the number of 'matched centers'. This score closely matches the reported score, but any alignment in which some center-pairings do not line up with Ri are rejected, prior to comparing actual score values.

• What is the score used to rank molecules in the similarity module
• The score used in alignment is used in the similarity task. The similarity task is more time consuming than alignment in that similarity will look at multiple ways of matching two molecules using different atom mappings and/or pharmacophores, and can look at multiple conformations stored in "Similarity Libraries". This score can be displayed in the resulting spreadsheet by typing

SimilarityScore=@SCORE()

• What are the units used in Spartan?
• Geometries

Cartesian coordinates are typically given in Ångstroms (Å), but are also available in nanometers (nm) and atomic units (au).

Bond distances are typically given in Å, but are also available in nm and au. Bond angles and dihedral angles are given in degrees (°).

Surface areas are typically given in Å 2 and volumes inÅ3, but are also available in nm2 (nm3) and au2 (au3).

1 Å = 0.1 nm = 1.889762 au

• Energies, Heats of Formation and Strain Energies

Total energies from Hartree-Fock, density functional and MP2 calculations are typically given in au, but are also available in kcal/mol, kJ/mol and electron volts (eV).

Heats of formation from semi-empirical calculations are typically given in kJ/mol, but are also available in au, kcal/mol and eV.

Strain energies from molecular mechanics calculations are typically given in kJ/mol, but are also available in au, kcal/mol and eV.

• Orbital Energies

Orbital energies from Hartree-Fock, density functional and MP2 calculations are typically given in au, but are also available in kcal/mol, kJ/mol and eV.

Orbital energies from semi-empirical calculations are typically given in eV, but are also available in kcal/mol, kJ/mol and au.

• Energy Conversions

Energy Conversionsa
 au kcal/mol kJ/mol eV 1 au - 6.275x102 2.625x103 2.721x101 1 kcal/mol 1.593x10-3 - 4.184 4.337x10-2 1 kJ/mol 3.809x10-4 2.390x10-1 - 1.036x10-2 1 eV 3.675x10-2 2.306x101 96.485 -

• Graphical Properties

Electron densities and spin densities are given in electrons/au3.

Dipole moments are given in debyes.

Electrostatic potentials are given in kcal/mol.

• Other Properties

Atomic charges are given in electrons.

Vibrational frequencies are given in wavenumbers (cm-1).

• What are the conversion factors used in Spartan?

• Below are some commonly used conversion factors:
``` Energy:
1 au (Hartree)=       me*e^4/h-bar^2
=       4.3597482(26) 10^-18  J              *
=       4.35974381(34)10^-18  J      (1998 CODATA)
=     627.510                 kcal/mol
627.5095602             kcal/mol       *
627.50947093            kcal/mol (1998 CODATA [new Na])
1 ev          =       1.60217733(49) 10^-19 J              *
1 ev          =     96.485                  kJ/mol
4.184 J       =       1                     Calorie (a constant)
1 kT (T=300K) ~       2.495                 kJ

Entropy:
1 e.u.        =       4.184                 J/mol*K
=       1                     cal/mol*K

Pressure:
1 kbar        =       10^8                  Pa
=    986.923267               atm
1 atm         =    101.325                  k Pa (exact)   *

Length:
1 A           =       10^-10                m
=       1.8897269             au   (old value)
=       1.889725988579        au
1 au (Bohr)   =       h-bar^2/(me*e^2)
=       0.529177249(24)       A              *
=       0.5291772083(19)      A (new CODATA 1998)

Mass:
1 AMU         =       1.6605402(10)  10^-27 Kg (Atomic Mass Unit)
=       1.66053873(13) 10^-27 Kg (new CODATA 1998)
Mass C12      =      12.0                   AMU
=      12.0                   g/mol/Na
1 mn          =       1.67492716(13) 10^-27 Kg (Mass of neutron)
1 mp          =       1.67262158(13) 10^-27 Kg (Mass of proton)
1.007276470(12)       AMU
1 me          =       9.1034897(54) 10^-31 Kg (Mass of electron)
9.10938188(72)10^-31 Kg
0.5109906(15)         Mev
Wavenumber:
1 cm^-1       =       2.9979 10^-10 s^-1
=       0.29979 THz
2.19474.7 cm-1=       1 Hartree^-1/2 Bohr^-1 AMU^-1/2

Wavelength:             (for light = 1/Wavenumber)
=       h*c/Energy      (for light)
1 nm          =       1239.837/ev     (ie. homo-lumo gap)
=       1.9166 10^-4/kJ (Na in energy)

Charge:
1 au          =       1                e
=       1.602 10^-19     C
=       2.452 10^-18     esu*cm

Dipole moment:
1 debye(D)    =       3.336e-30        C*m
=       0.20824          e*A
1 au          =       8.479e-30        C*m
=       2.542e-18        esu*cm
=       2.542            D

Polarizability:
1 au          =       14.83e-30        m^3
=       14.83            A^3

Moment-of-Inertia:
I  cm^-1      =       60.1997601/I[ AMU*bhors^2 ]
I  cm^-1      =       16.8576522/I[ AMU*A^2     ]
```
*In places where multiple values are listed for a given conversion, the first is the approximation used in Spartan, the second is the 'exact' value (as of 1973, 1986 or 1998).

• What are the fundamental constants used in Spartan?

• Below are some important constants used in quantum chemistry:
```Speed of Light   :    c :  2.99792458    10^10   cm/s      * (exact)
Avogadro's Num.  :   Na :  6.0221367(36) 10^23             *
Na :  6.02214199(47)10^23             (1998 CODATA)
Gas Constant     :    R :  8.314510(70)          J/K/mol   *
R :  8.314472(15)          J/K/mol   (1998 CODATA)
Boltzmann const. :    k :  1.380658(12)  10^-23  J/K       *
1.3806503(24) 10^-23  J/K       (1998 CODATA)
Planck's const.  :    h :  6.626075(40)  10^-34  J s       *
6.62606876(52)10^-34  J s       (1998 CODATA)
fine-structure   : alpha:  1/137.0359895(61)
7.297352533(27) 10^-3           (1998 CODATA)
```
*In places where multiple values are listed for a given conversion the first is the approximation used in Spartan, the second is the 'exact' value (as of 1973, 1986 or 1998).

• New research has resulted in the measurement of a more accurate value for an important constant. Will Spartan reflect this change?
• No. Data sets using the older constants have been generated for more than 25 years. To make sure newer versions maintain backward compatibility we continue to use the older values for these fundamental constants and conversion factors. Even though each new digit is an important scientific achievement, the increased precision is well beneath the noise present in the chemical measurements Spartan deals with.

## Keywords

Below is a list of all keywords which the property module understands.

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