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Properties FAQ

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  • How can I calculate polarizability?

  • Spartan can calculate polarizability in 3 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 1st principle method in the full Spartan versions 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 data you can use the KEEPVERBOSE keyword

    3. When using semiempirical 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 put in the verbose output, so make sure to use the KEEPVERBOSE keyword or set the "Keep Verbose" option in the "Preferences Panel".

      These values are accessible from the spreadsheet with the @PROP() possible options are

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  • 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
        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 to 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
    For example a 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 those terms 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 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): Electron Densities, Spin Densities, Dipole Moments, Charges and Electrostatic Potentials

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

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  • 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.

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  • 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))
            A : Area
            V : Volume
            O : Ovality
    Thus the He atom is 1.0 and HC24H (12 triple bonds) is ~1.7.

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  • 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

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  • 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)

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

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  • What solvation models does Spartan provide?

  • Spartan includes a number of ways to examine solvation.

    1. Cramer-Truhlar SM5.4 solvation

      We currently implement the Cramer-Truhlar SM5.4P and SM5.4A solvation methods for water. If no other solvation method is chosen, this solvation calculation is done, by default, for all quantum mechanics calculations which have SM5 parameterized atoms. 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 molecule properties dialogue.

      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"

    2. MMFFaq mechanics forcefield (SM5.0R)

      SM5.0R 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 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 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. Thus, the MMFFaq method is most useful in the context of conformational searching or 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"

    3. SM8 solvation calculation

      The SM8 model allows both water and 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 wavefunctions. To run SM8 as a property calculation (to calculate the energy of solvation) use the keyword POSTSOLVENT=WATER 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 SM8 results. The list of supported solvents is as follows:


      The solvents in bold are available from the pull-down 'in-solvent' menu. It is important to notice that no spaces are allowed in the name, thus "acetic acid" is spelled "ACETICACID".

      The reference for SM8 is

      • 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)

    4. SS(V)PE solvation calculation

      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=SVP,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).

    5. 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.

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  • What is the distinction between the "POSTSOLVENT", "ADDSOLVENT" and "SOLVENT" keywords?
  • We use the POSTSOLVENT keyword to do a energy of solvation calculation. By default Spartan 14 has an implied POSTSOLVENT=SM54 to calculate the energy of solvation for any molecule which has atoms parameterized for SM54. This does a quick semi-empirical calculation (or SM50R for molecular mechanics jobs) at the end of the main calculation step. The resulting free energy of solvation is displayed in the output and the combined energy is available in the molecule properties panel with the "Energy(aq)" label. This calculation is also useful to determine the energy differences among different conformers of the same molecule as the bond lengths and angles do not change significantly solvent is added.

    If one wants to see the affect of solvation on the geometry, (for example for a transition state structure) the ADDSOLVENT= should be used. This is what the "in-solvent" pull down menu in the calculation panel does (for HF and DFT calculations). SOLVENT= is a synonym for ADDSOLVENT=, but if typed in will be erased from the option line and the "in-solvent" pull down menu will be modified to match what was typed in.

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

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  • 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.) 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.

    The SS(V)PE method is not parameterized and is available for any atom of the underlying basis-set.

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  • 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 quadrapole.

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  • 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 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=.

    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.
    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.
    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
    8. Dipoles on all terminal atoms
    9. 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.

    Relevant references:

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

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  • What is the natural bond order?

  • The 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 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.

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  • 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'.

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  • 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 "Print: Orbitals & Energies" check box is selected.

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

  • <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 wavefunctions are not (exact) eigenfunctions 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 wavefunction 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 wavefunction 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>

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  • 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 overridden with the AVGMASS keyword, or by changing the isotope of a specific atom in the Property dialogue..

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  • 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 show in the "Output Summary" and plotted in the RAMAN graphs are scaled by the laser frequency [vo] (which can be changed in the "Options" panel), plotted logarithmically and broadend with a Lorenztian.

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


    However, what is measured is the integrated absorption A

    A = int{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.

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

  • Full 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 'Frequency' 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.

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  • 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 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 the Tamm-Dancoff approximation (TDA) of time dependent density functional theory (TD-DFT):

    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.

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  • 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 setup panel.

    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.

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  • 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 look 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.

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  • 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

    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.

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  • 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 an 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 part-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 HF, BP, BLYP, B3LYP, EDF1 and EDF2 models with the common 6-31 and 6-311G basis sets.

    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.

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  • 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.

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

  • The NMR calculation has it 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 clicking the converge checkbox in the setup panel.

    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 about "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.

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  • 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 'ro,/sub>' is 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 angstorm. 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.

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  • What is the score used to rank molecules in the similarity module
  • The score used in alignment is used in the 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 "Conformer Libraries". This score can be displayed in the resulting spreadsheet by typing

    into a column header of the spreadsheet.

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  • 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 kcal/mol, but are also available in au, kJ/mol and eV.

      Strain energies from molecular mechanics calculations are typically given in kcal/mol, but are also available in au, kJ/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 - 1.084x10-2
      1 eV 3.675x10-2 2.306x101 9.224x101 -

    • 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).

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  • What are the conversion factors used in Spartan?

  • Below are some commonly used conversion factors:
       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              *
       4.184 J       =       1                     Calorie (a constant)
       1 kT (T=300K) ~       2.495                 kJ
       1 e.u.        =       4.184                 J/mol*K
                     =       1                     cal/mol*K
       1 kbar        =       10^8                  Pa
                     =    986.923267               atm
       1 atm         =    101.325                  k Pa (exact)   *
       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)
       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
       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)
       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
       1 au          =       14.83e-30        m^3
                     =       14.83            A^3
       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).

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  • 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).

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  • 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 20 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.

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

    KEEPVERBOSE By default the verbose output file is deleted/pruned. (For many jobs this can dramatically decrease the size of .spartan files.) Instead of using this keywords, one can set the "Keep Verbose" check box in the "Preferences Panel".
    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.
    To control the internal working of the volume calculator.
    To select different solvation models. See the discussion on solvent methods and the SOLVENT= keyword.
    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.

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    Keywords related to the analysis of the electronic wavefunction
    PRINTMO1Print the Molecular orbitals.
    Print molecular orbital energies
    Delete unoccupied molecular orbitals 'x' above the LUMO. This is useful in decreasing the size of the molecular data stored on the disk and in making the output of PRINTORBE and PRINTMO more reasonable. 10
    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.
    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.
    Print the Mulliken charges. With a value of 3, the full matrix is printed,1
    Skip the Mulliken charge calculation
    POP1 Print the natural atomic charges
    NONATCHARGE Skip the natural atomic charge calculation
    Print a summary of charges and bond order. A (much) shortened version of what is printed with the MULPOP, POP, BONDORDER and NBO keywords. If x=1 only atomic charges are printed. If x=2 Mulliken bond orders are shown. If x=2 natural bond orders are shown.
    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 valences for open-shell wavefunctions.
    PRINTNBO Print the AO to NBO transformation
    NOPOP Skip the natural bond order (NBO), and natural charge calculation.
    DOEPN Print out the "Electronic Potential at Nuclei" for Oxygen and Nitrogen. DOEPN=SKIP to skip calculation. (By default the calculation is stored in archive but not printed. Enter DOEPN=ALL to print all atoms.
    PRINTS Print the atomic orbital overlap matrix (S).
    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.
    Print the overlap matrix as a lower triangle. Use in conjunction with the "Print: Orbitals & Energies" check box if you want to do your own 'home-brew' quantum mechanics calculation. See the discussion of atomic orbitals for more information. (The PRINTS is spelling is deprecated.)
    POLAR Calculate the static polarizability of the molecule. For Hartree-Fock and semi-empirical methods this will also calculate the static hyperpolarizability. See our discussion above for more details on how to calculate polarizability for more details.
    HYPERPOLAR Calculate the static polarizability and hyperpolarizability of the molecule. Not available for DFT methods using pure basis sets (i.e. 6-311G etc.).
    Calculate the polarizability at different frequencies. There can be multiple frequencies, here represented by 'a','b', and 'c', but could be more (or fewer) comma separated values. UNIT should be replaced with au, nm, ev, hz or cmInv. For example:
    Note that an energy of 'zero' (0.0) is a way of specifing the static (infinite wavelength) case.
    POLAR=WALK,start,end,step,UNIT This format of the POLAR keyword allows one to specify a range of frequencies/energies. This WALK format is also available for the HYPERPOLAR keyword. As an example:

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    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.
    Scale all the frequencies by a factor 'x'.
    DROPVIBS=x When calculating thermodynamics values, ignore all modes with frequencies below 'x'.
    When calculating thermodynamics values, clamp enthalpy terms at 'x'RT. (If no 'x' given 1/2 is used.) Entropy and the heat capacity will be clamped at 'x'R. For 'x'=1/2 these limits imply a break in the enthalpy, entropy and heat capacity at ~260 cm-1, ~116 cm-1 and ~2 cm-1 respectively. To turn "clamping" off use CLAMPTHERMO=NO 0.5
    PRINTMODE Print thermodynamic information for each mode
    TEMPERATURE= Change the default temperature used in the thermodynamic calculation. 298.15 K
    TEMPRANGE=start,end,step Print thermodynamic properties for a range of temperatures.
    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 Vibrational Mode' button in the calculation dialogue panel controls.
    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.
    PRINVIBCOORDS Print the coordinates of each vibrational mode.
    By default Spartan '14 uses the terrestrial average mass of atoms when doing thermodynamics calculations. (Changing the isotope of a specific atom in the property panel overrides the mass for only that atom.)
    1. DEFAULT: the default use average mass.
    2. COMMON: use the most common isotope as the default atomic mass. (This was the default in previous versions of Spartan.)
    3. STANDARD: use the average mass, and ignore any specific atomic mass settings set in the atom property panel.
    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.)
    Calculate frequencies by numerical differentiation, 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.
    NUMERICALFREQ Calculate frequencies by numerical differentiation, using central differences. 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.
    FD=xx.yy2 Step size for numerical differentiation. 0.005 bohr
    DORAMAN2 Calculate the Raman intensities along with the standard IR intensities.

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    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 successively more printing. Also available are TERSE 1

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    Keywords related to the Intrinsic Reaction Coordinate (IRC) calculation

    See How can I use the Intrinsic Reaction Coordinate procedure? for more details
    IrcSteps=2 Specifies the maximum number of points to find on the reaction path. (Should be odd. The default value of 41 yields 20 steps forward and 20 backwards.) 41
    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

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    Keywords related to the excited state and UV/vis calculation

    see Controlling an excited state calculation
    ESTATE=n1,2 Choose the excited state to calculate the gradient for. Usually this is not entered as a keyword, but is selected by choosing 'First Excited State' in the calculation dialogue. 1
    TDA Use the Tamm-Dancoff approximation (TDA) to then standard Time Dependent DFT (TDDFT) algorithm. (The TDA was the default method for DFT calculations prior to Spartan'14v117.) This can be up to twice as fast as the default "Full TDDFT" and produces similar, but not as precise.
    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
    CIS_TRIPLETS=FALSE2 To limit the search of excited states to only singlets. Use this keyword only for excited state calculations. If this is used when doing an UV/Vis spectrum calculations this keyword will interfere with the INCLUDESINGLETS and INCLUDETRIPLETS keywords. =TRUE
    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
    INCLUDETRIPLETS2 To include triplets in the UV/Vis calculation of singlet wavefunctions. The intensity of the excitation will be small (zero) but can be useful if interested in all lower energy excited states.
    INCLUDESINGLETS2 To include singlet excitations in the UV/Vis calculation of triplet wavefunctions. The intensity of the excitation will be small (zero) but can be useful if interested in all lower energy excited states.
    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
    CIS_AMPL_PRINT=x To print filled/unfilled molecular orbital pairs which have coefficients larger than x. This value is in hundredths so the default value of 15 implies an amplitude of 0.15. (This will go in the verbose output file, so make sure to use the KEEPVERBOSE keyword.) 15

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    Keywords related to the NMR calculations

    see Difficulty with NMR calculation
    D_SCF_MAX_2=n The maximum number of SCF-NMR steps to try before giving up. Typically, increasing this will allow difficult systems to converge. 75
    D_SCF_CONV_2=n The tolerance/precision used in the inner (2nd) part of the convergence algorithm. "n" is the decimal so the default of 2 implies 10-2=0.01 2
    D_SCF_MAX_1=n Maximum number of tries in the inner NMR convergence step. 40
    D_SCF_CONV_1=n The tolerance of the inner NMR convergence step. 0
    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.

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    Last modified: Thu Jun 20 10:47:57 PDT 2013