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 uncertainity in the final results.
Additional polarizability terms can also be entered into the spreadsheet with the "Term=@PROP(POLAR_SUMMARY,i)" function, where 'i' can be 1,2, or 3 for 'alpha', 'beta' or 'gamma', respectively. The six unique terms in the polarizability tensor can be accessed via the "Term=@PROP(POLAR_TENSOR,i)" function. Functions should be typed into an empty column header cell in the Spartan spreadsheet. Characters to the left of the equal sign (=) will become the displayed 'label' for the new column.
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
Rather than units of:
coul*m^2/energy
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 may 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 highest occupied &
lowest unoccupied molecular orbitals. This equation is only used in the
semiempirical 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
Q-plus & Q-minus are known as the 'TLSER' parameters.
O = A/(4*pi*((3*V)/4*pi)^(2/3)) where A : Area V : Volume O : OvalityThus the He atom is 1.0 and HC24H (12 triple bonds) is ~1.7.
electronegativity | = -(HOMO + LUMO)/2 |
hardness | = -(HOMO - LUMO)/2 |
"LogP" methods can be selected with the LOGP= keyword;
LOGP=VILLAR and LOGP=GHOSE
respectively.
Spartan includes a number of ways to examine solvation.
Literature on these methods is extensive,
some important articles are:
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 forcefield 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.
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 vacuum (MMFF94).
While the energies calculated from this method are less reliable than other approaches, it may be useful to observe the effect of the water molecules (solvent) on the wavefunction of the solute. This approach generates a new wavefunction and electron density for the solute molecule. One commonly examines how atomic charges, dipoles, and graphics (such as the electrostatic potential map) change as a result of solvent.
This method is selected from the compute section of the Calculations dialogue. By default, a second "Spartan list" file is generated. This contains a sample snapshot of the water molecules. Generation of this file can be "turned off" by using the QMMM:SHOWCONFIGS=NO keyword.
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 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.
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
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 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 |
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:
|
0 |
SVDTHRESH= | .00001 | |
CHELPPOINTS= | Algorithm which places points into the shell.
| 1 |
CHELPEXTRA= | Choose more points than just nuclei. This
allows one to approximate a multipole expansion around
each nuclei.
| 0 |
Relevant references:
More information from NBO calculations can be printed with the keyword PROPPRINTLEV=2. This may be useful if problems are detected with the NBO calculation. There are known problems with Spartan's implementation of natural bond order calculations on large delocalized systems.
Full Spartan can generate a reaction path using three approaches. The simplest is via the 'energy profile' calculation, which changes specific coordinates. (See the discusion 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 signle 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 checking the IRC button when performing a transition state geometry calculation. When selected, a new file will be generated that contains the reaction path.
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.
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 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 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 375S.
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 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.
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.
It should be noted that information on each excitation can be found in the verbose output. The notation
The Transition dipole moment and oscillator strength are also printed. The oscilator strenghts 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.
1 Indicates that these should not be typed in as there is a button in the calculation dialogue for it. 2 The keyword is used by a module other than the property module, but is mentioned here for completeness. | ||
PROPPRINT=i PROPPRINTLEV=i | For 'i' greater than 1, print more information into the output file. 'i' must be 4 or less | 0 |
PRINTCOORDS | Print the cartesian coordinates of all atoms in the system. | |
ACCEPT | Accept certain error conditions and continue without a fatal error. | |
BTABLE=BAD | Print out a table on all bond distances (B), bond angles (A) and dihedral (D) angles. If only bond distances, angles or dihedrals are required, BAD can be replaced with B, A, or D respectively. | |
NEAREST=x.y | Specify the multiplication factor (applied to nearest-neighbor distances) when generating the geometric information. | 1.2 |
QSAR |
Prints various QSAR descriptors. While these values are
usually calculated, and can be found in the proparc file and
in the spreadsheet this prints them to the output file.
The list of descriptors this keyword prints is:
| |
NOQSAR | Skip the calculation of QSAR descriptors. | |
MOMENTS | Print out the moments of inertia, in both atomic units and inverse centimeters. | |
MAXVOLSIZE=i | Atomic volumes and surface areas will be calculated only for systems with fewer than 'i' atoms. | 100 |
SOLVRAD | In calculation of atomic areas and volumes, add this value to the VdW radii. | |
VPTS=i AARCS=j APTS=k | To control the internal working of the volume calculator. | |
SOLVENT=yyy1,2 | To select different solvation models. | |
TESTPROPS=1 |
Internal keyword used for debugging and QA work at
Wavefunction. This works on the 'cell' data of the spreadsheet.
Cells with the following names are analyzed:
| |
PARCFORMAT=i |
[for internal to wavefunction use] If i=1 write both formats of frequency information. If i=2 write only new format of frequency information. | i=1 |
| ||
PRINTMO1 | Print the Molecular orbitals. | |
ORBE | Print molecular orbital energies | |
POSTHF | Use the post hartree-fock wavefunction if available. On by default for MP2 type calculations. | |
NOPOSTHF | Do not use the post HF calculations. For MP2 this means, to use the HF wavefunction instead of the corrected MP2 wavefunction, | |
IGNOREWVFN | Skip all wavefunction dependent properties. | |
NBO NBO=yy |
Do the natural bond order hybridization analysis. See the
above discussion. Possible values
for yy are:
| |
MULPOP1 | Print the Mulliken charges. | |
NOMULCHARGE NOMULPOP | Skip the mulliken charge calculation | |
POP1 | Print the natural atomic charges | |
NONATCHARGE NOPOP | Skip the natural atomiccharge calculation | |
DEORTHOG | Deorthogonalize semiempirical MOs before calculating properties. | |
DIPOLE | Print out the Cartesian components of the dipole moment | |
NODIPOLE | Skip the calculation of the dipole moment. | |
BONDORDER | Print out Mulliken and Lowdin bond order matrices, plus atomic and free valencies for open-shell wavefunctions. | |
PRINTNBO | Print the AO to NBO transformation | |
PRINTS | Print the atomic orbital overlap matrix (S). See the discussion of atomic orbitals for more information. | |
LOGP= | See the discussion on the LogP calculation | |
ELP | Specify that the elpot+polpot grid will be used to generate atomic charges. This is valid for closed-shell HF-only molecules. | |
USEQCPOT | ||
| ||
NOFREQ | Do not do any frequency or thermodynamic calculation even if there is a good Hessian. (By default, if a high quality Hessian is available frequencies will be calculated. | |
FREQSCALE=x FSCALE=x | Scale all the frequencies by a factor 'x'. | |
DROPVIBS=x | When calculating thermodynamics values, ignore all modes with frequencies below 'x'. | |
PRINTMODE | Print thermodynamic information for each mode | |
TEMPERATURE= | Change the default termerature used in the thermodynamic calculation. | 298.15 K |
PRESSURE= | Change the default pressure used in the thermodynamic calculation. | 1.0 atm |
PRINTFREQ1 | Print the Cartesian values of the normal mode vibrations. This is what the 'Print Virbrational Mode' button in the calculation dialogue panel controlls. | |
THERMO1 | Print standard thermodynamic data. This is the 'Print Thermodynamics' button in the calculation dialogue. | |
PRINTIR | Print Infrared and thermodynamic information for each normal mode vibration. | |
AVGMASS | Use the terrestrial average mass of atoms when doing thermodynamics calculations. The default is to use the most common isotope. (Changing the isotope of a specific atom overrides the mass for only that atom.) | |
APPROXFREQ | Calculate frequency and thermodynamic information on the intermediate low quality Hessian. (Not recommended.) | |
GXTHERMO | Calculate G3 type results. (Internal keyword, should not be used unless you know what you are doing.) | |
FREQ1,2 FREQ=CD2 FREQ=FD2 |
Calculate frequencies by numerical differentiaion, using central differences (CD) or forward differences (FD) as opposed to analytically. Analytical methods are usually much faster and more accurate than numerical methods as numerical methods requires 6 single point calculations for each atom in the molecule. Forward difference is usually %50 faster than central differences, but is significantly less accurate and is not recommended. The default is to use analytical frequencies if available. | |
FD=xx.yy2 | Step size for for numerical differentiation. | 0.005 bohr |
See How can I control the parameters of the ESP model? for more details and some more keywords | ||
ELCHARGE1 | Print information about the electrostatic charges. | |
NOELCHARGE | Skip the electrostatic charge calculation. | |
CHELPPRINT=i | Print more information about the ESP charge calculation. Integers greater than 1 cause successivly more printing. Also available are TERSE | 1 |
See How can I use the Intrinisic Reaction Coordinate procedure? for more details | ||
IrcSteps=2 | Specifies the maximum number of points to find on the reaction path. | 20 |
IrcStepSize=2 | Specifies the maximum step size to be taken. This is in thousandths of a Bohr. The default of 150 means 0.15 Bohr. | 150 |
RPATH_TOL_DISPLACEMENT=2 | Specifies the convergence threshold for the step. If the atoms are moving less than this value, configuration is assumed to be at a minima and the algorithm will stop. The units are in millionths of a Bohr. The default value of 5000 corresponds to 0.005 Bohr. | 5000 |
see Controlling an excited state calculation | ||
ESTATE=n1,2 | Choose the excited state to calcualte the gradient for. Usualy this is not entered as a keyword, but is selected by choosing 'First Excited State' in the calculation dialogue. | 1 |
CIS_N_ROOTS=2 | To examine more orbitals in the excitation. For systems where there are many delocalized atoms you may want to increase this number from the default. Despite the "CIS" in this keywords spelling, it is also appropriate for TDDFT calculations. | >=5 |
UVSTATES=2 | To examine more orbitals in the UV/Vis calculations. For systems where there are many delocalized atoms you may want to increase this number from the default. Only valid when the "UV/Vis" button is selected. | >=5 |
CIS_TRIPLETS2 | To examine triplet excitations as well as singlet excitations. | |
CORE=FROZEN2 | By neglecting core electrons the calculation can be speeded up. | |
N_FROZEN_VIRTUAL=n2 | Reduces the number of virtual molecular orbitals used in the calculation. Changing this number from the default, may speed up the calculation, but may also cause inaccuracies in the calculation. | |
MAX_CIS_CYCLES=n2 | To change the number of SCF cycles to try before 'giving up' on the CIS calculation. Increase if you are having convergence problems, but waiting longer might work. | 10 |
CIS_CONVERGENCE=x2 | Decrease this number if you want quicker convergence at the cost of precision. (Reducing to a number below 5 can give unphysical results.) | 6 |