Properties FAQ




  • How can I calculate polarizability?

  • Spartan can calculate polarizability in 3 ways:
    1. Using the empirical formula described below. This is printed with the QSAR keyword 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 1st principle method in the full Spartan versions with the addition of the POLAR keyword. The polarizabilities are printed in the verbose output.
    3. When using semiempirical methods the polarizability can be calculated with the POLAR keyword. 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 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.




  • What are the units of polarizabilty?

  • Polarizabilty calculated in the properties module is derived from an empirical formula:
      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
    



  • 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:
    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 calcualtions). 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 varience of .404.
      The reference is:

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




  • What solvation models does Spartan provide?

  • Spartan includes a number of ways 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 calculations. The energy of solvation predicted by this model can be found in the output text. 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.

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


    2. SM50R solvation calculation
      SM50R is a solvation method derived from the semi-empirical SM54 approach described above. It is independent of the wavefunction 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 SOLVENT=SM50R keyword by using the MMFFaq forcefield described below.

    3. MMFFaq mechanics forcefield

      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).

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

      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.




  • What charge models can be accessed from Spartan?
  • We have 3 ways of decomposing the quantum mechanics wavefunction 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/wavefunction, dividing by two and placing 1/2 of the 'electron cloud' on each constituent atom. This is easy to understand (if you are doing QM) but may have convergence problems with large 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 wavefunction. These 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 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.




  • How can I control the parameters of the ESP 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 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=.

    KeywordDescriptionDefault
    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:
    1. An older, deprecated, algorithm.
    2. Don't prune points.
    3. Attempt to prune terms (vectors) which do not significantly improve the accuracy.
    0
    SVDTHRESH= .00001
    CHELPPOINTS= Algorithm which places points into the shell.
    1. Use a rectangular grid.
    2. Use a spherical grid with approximate constant density.
    3. 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.
    1. Use 1 point per nuclei.
    2. Use 7 points per nuclei.
    3. Use 10 points per non-hydrogen nuclei.
    4. Use 14 points per non-hydrogen nuclei.
    5. Use bond orientated, atom center dipoles
    6. Modified version of model 4 adding extra points on atoms with 2 bonds.
    7. same as 5, but add dipoles to hydrogens
    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:




  • What is the natural bond order?

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

    Natural Bond Order 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.




  • 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'.


  • 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.


  • What masses are used in frequency calculations?

  • The default masses are found in the "MASS.spp" parameter file. ("params.MASS" on Unix/Linux machines.) The default value is the mass of the most common isotope. This can be overriden with the AVGMASS keyword, or by changing the isotope of a specific atom in the Property dialogue..


  • How can I use the Intrinsic Reaction Coordinate (IRC) proceudre?

  • 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.




  • What does the 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 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.




  • 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.




  • 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 different molecuar orbitals.

    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.







    Keywords

    Below is a list of all keywords which the property module understands. Not all of these are actually tested and supported.
    Keywords specific to the property module

    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 less0
    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:
    • Atomic Weight
    • E-LUMO and E-HOMO
    • Electronegativity, Hardness and Est. Polariz. (AM1 only)
    • Molecular Volume, Surface Area and Ovality
    • LogP (Ghose-Crippen, Dixon, and Villar[SE only])
    • Exposed Surface Area
    • Atomic Valence
    • Q-minus and Q-plus (for any charges)
    • Free Valence
    • Total Overlap Population (ab initio only)
    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:
    • Reference_E=xxx.yy ; The energy in Kcal/mol.
    • REF_PREC_E=x.yyy ; precision (default 5.0e-8)
    • PROP_x=Equation ; Most spreadsheet equations are valid
    • REF_PROP_x=xxx.yy ; the target value
    • REF_PREC_x=x.yyy ; precision (default 1.0e-4)
    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
    Keywords related to the analysis of the electronic wavefunction
    PRINTMO1Print 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:
    1. NORMAL, the default.
    2. IONIC to see ionic contributions.
    3. 3C to examine three-center contributions.
    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
    Keywords related to frequencies and thermodynamics
    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
    Keywords related to Electrostatic Charges

    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
    Keywords related to the Intrinsic Reaction Coordinate (IRC) calculation

    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
    Keywords related to the excited state and UV/vis calculation

    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





















    Wavefunction Support
    Author: Phil Klunzinger
    Last modified: Tue Sep 5 09:23:36 PDT 2006