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Quantum Mechanics Energy FAQ

  • How do I calculate the heat of reaction?

    Quantum chemical methods can be used to calculate heats of reactions. The Heat of formation (HOF) is a special type of reaction.

    For example, to calculate the bond separation energy of

    CH3CH2NH2 + CH4 -> CH3CH3 + CH3NH2

    one would perform 4 energy calculations (one for each molecule) and subtract the energies.
    E-reaction = E[CH3CH3] + E[Ch3NH2] - (E[CH3CH2NH2] + E[CH4])

    (The Spartan "Reaction Calculator" is a great tool for easily calculating this type of equation, see the User Guide for more information).

    Experience has shown us that the quality of the calculated heats of reaction depends on both the method used to calculate the energy (E[..]) and the type of reaction.

    Our guide book explains that the "best" type of reaction is an "isodesmic" reaction. (An Isodesmic reaction is one in which the number and type of bonds remain the same during the reaction. For an example see the discussion on basicities.) The book also lists other types of reactions and gives quantitative examples of the accuracy one can expect for different theories and basis sets.

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  • How do I calculate the heat of formation?

    In principle the heat of formation (HOF) is calculated like any other reaction, see the discussion above. Sadly, the experimental HOF consists of some of the most difficult reactions to calculate: breaking all bonds and creating atomically pure compounds such as H2 for hydrogen and graphite for carbon.

    2(CH3CH2NH2) -> 7(H2) + N2 + 4(C-graphite)

    Thus, good HOF calculations usually require methods better than MP6 with very large basis sets. These can be extremely time-consuming, even for molecules of only a few heavy atoms! The G3 method is a good place to start if you are interested in accurate Heats of Formation.

    Chances are that if you think you want the HOF formation, you may only need to compare the relative differences in energy of certain reactions, and can use a less time-consuming approach than the methods required for Heat of formation calculations. The guide book includes many examples of HF/6-31G* without vibrational corrections performing well (against experiment). The discussion on finding the *best* energy also covers this and other common theory levels.

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  • What is the G3 method?

  • The G3 method (the most used of the Gx series) is a time consuming recipe for calculating accurate "Heats of Formation" (HOF) from first principles. G3 consists of 10 calculations:

    1. HF/6-31G* optimization
    2. HF/6-31G* frequency and vibrational free energy
    3. MP2(full)/6-31G* geometry calculation
    4. MP2 and MP4 6-31G* single points
    5. MP2 and MP4 6-31+G(d) single points
    6. MP2 and MP4 6-31G(2df,p) single points
    7. QCISD(T) 6-31G(d) single points
    8. MP2(full)/6-311+(2df almost) single point (the G3large basis set)
    9. A spin-orbit correction term.
    10. An empirical "higher level correction" for valence electrons

    All these energies are combined, along with similar calculations done for each atomic species. The result is then subtracted by experimental energies of the "standard state atomically pure" systems to arrive at a good approximation for the actual HOF. A quick overview of how these steps are used can be found in our discussion of calculating the exact energy.

    Note that each of these steps is relatively time consuming and practical only for very small systems. The G3(MP2) method is often more than twice as fast, but still prohibitively time consuming for all but small molecules.

    The reference to the G3 papers can be found at the end of this FAQ.

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  • What is the T1 method?

  • The T1 method is a simpler recipe to calculate the absolute heat of formation. It is similar in concept to the G3 method but replaces the post MP2 calculations with empirical relations based on Mulliken bond order and implements a faster MP2 approximation. Thus it is much faster than G3 or G3(MP2) and can be applied to much larger molecules. The steps of the calculation are:

    1. HF/6-31G* optimization
    2. RI-MP2/6-311+G(2d,p)[6-311G*] single point energy. This is a dual basis set approximation to the MP2 energy
    3. A empirical correction using the HF/6-31G* Mulliken bond orders to capture the majority of post MP2 energy, and bond vibrational energy.
    This is discussed in full in the defining paper.

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  • What is the "Enthalpy of Vibration"?
  • The quantum mechanical calculations in Spartan assume that molecules are isolated, with a temperature of zero Kelvin, and with stationary nuclei. Real experiments are carried out with vibrating molecules at finite temperature (often 298.15 K). In order to correct for these differences Spartan can use calculated frequency data to determine a set of normal-mode vibrational frequencies (vi). (These are the same data used to generate IR spectra.)

    Using this approximation, energy corrections are fairly straightforward. Splitting the Enthalpy correction into four (4) parts to include the 'Zero point energy' (Zp), the temperature correction (Hv), enthalpy due to translation (Ht) , and enthalpy due to rotation (Hr).

    Zp = (1/2)*sum[ vi ]
    Hv = N*h*sum[ vi / ( eh*vi/kT - 1 ) ]
    Ht = (3/2)RT
    Hr = (3/2)RT (or RT for linear molecules)

    Note that for small molecules this is a very good approximation. However as molecules get larger the 'normal-mode' approximation becomes less valid. For example:

    • floppy side groups, (such as methyl rotors) behave like a 3 well system, not the single well assumed in the normal-mode approximation,
    • anharmonic effects become more important,
    • large scale flexing motion, which is difficult to accurately calculate, begins to dominate the energy correction.
    • conformational flexibility becomes an issue which (energetically) may be more important than the vibrational temperature correction (Hv).

    These problems are magnified if one is examining the entropy or free energies of larger molecules. For these reasons low frequency vibrations are often systematically ignored.

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  • How is the entropy calculated in Spartan?
  • The entropy in Spartan is calculated from the same data as vibrational enthalpy (Hv). The equation for entropy (S) can be written as follows:

    S = Str + Srot + Svib + Sel

    Str = nR{(3/2) + ln[ (pi*MkT)3/2*(nRT/P) ] - ln(nNo) + 1}
    Srot = nR{(3/2) + ln[ (pi*vA*vB*vC)1/2/s ]
    Svib = nR*sum[ (ui*eui-1) -1 - ln(1-eui)]
    Sel = nR*ln[ "electronic ground state degeneracy" ]

    The constants ui are proportional to the vibrational frequencies and vA are inversely proportional to the moment of inertia of the rigid body. It is important to note that these equations ignore any entropy due to conformational flexibility, which may dominate for larger molecules. Also note that low frequency vibrations will dominate the calculation of entropy. It is these modes which break the normal mode assumption, thus making entropy calculations of larger molecules suspect.

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  • How can I calculate basicity?
  • You can use the isodesmic proton transfer reaction relative to a standard to calculate the relative basicities. For example if we choose the ammonia molecule as a standard we would write:

    BH+ + NH3 -> B + NH4+

    where B is the compound of interest. Then the relative proton affinity is:

    E[BH+] + E[NH3] - E[B] - E[NH4+]

    Relative proton affinity is a measure of the basicity which can easily be converted to pH. In our methods book (table 6-17) we show the accuracy of this calculation for a number of methods and basis sets for series of Nitrogen Bases. A regression analysis shows that even simple HF/6-31G* methods provide results with an accuracy of less than 4 kcal/mol on a system covering 125 kcal/mol range.

    There is also an interesting example of predicting pKa's from the graphical map of the electrostatic potential. This can be found on page 478 of A Guide to Molecular Mechanics and Quantum Chemical Calculations.

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  • How can I calculate pH?
  • The pH of a compound should be related the energy (enthalpy) of the reaction described above

    BH+ + X -> B + XH+

    If you know the pH of a few standards you can use these in a regression fit (using regression tools in Spartan's spreadsheet). This will result in a simple linear relation correlating 'energy' with 'pH'.

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  • Spartan generates many different energies. I want the best one. Which one is the best energy?
  • Science is a series of approximations. The trick is to use the largest simplification one can and still get reasonably 'good' predictions. This said, we always feel more comfortable with a theory if a recipe exists to get the *exact* answer. In QM calculations this is so prohibitively time consuming as to be impossible, but it can be described. We describe this 'exact' calculation in the next section.

    One definition of the *best* energy is the energy which answers one's questions with enough accuracy, yet consumes the minimum amount of time and resources. As mentioned in the discussion on calculating heats of reactions, this is often achieved by writing a near-isodesmic reaction and calculating an energy difference. (The key here is the 'energy difference'. It allows cancellation of systematic errors.)

    In order to find what is *best* for your question, we suggest starting with a question/reaction in which you know the answer and that is similar to your reaction of interest. Try this reaction with HF/6-31G* or HF/3-21G*. If that isn't accurate enough then add the zero-point energy (ZPE) corrections. (scaled by .90 for HF or by .99 for DFT) If that fails, try MP2 or DFT energies with larger basis sets. If that fails attempt single point CCSD with ZPE corrections. Finally try the T1, G3(MP2), or G3 methods.

    Conversely, if HF/6-31G* is good enough, you may want to try faster methods to see if they are also acceptable. HF/3-21G* is a popular basis set and much faster than 6-31G*. Semi-empirical is the simplest method using quantum mechanics approaches while requiring an order of magnitude fewer resources and time. Molecular mechanics methods, while limited to ground states of common chemistry groups, is extremely quick and in the areas in which it is parameterized can be fairly accurate.

    If you are new to molecular modeling, Wavefunction's guide book, discusses many types of reactions and molecular properties, quantitatively comparing many different theory levels.

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  • How can I calculate the most precise/exact value for the energy?   or,
    18 steps to calculate the exact free energy of a molecule.
  • The complete Enthalpy (H) and the Gibb's Free Energy (G) of a given conformer of a molecule in the dilute gas phase can be written

    H = Ee + Zo + Hv + Ht + Hr + pV
    G = Ee + Zo + (Hv+Ht+Hr) - T*(Sv+St+Sr) + pV
    • Ee is the complete electronic energy including
      • an infinite basis set.
      • including all electron correlation (a full CI calculation)
      • accounting for spin-orbit coupling and relativistic effects.
    • Zo is the zero point energy of the nuclei.
    • Hv is the enthalpy due to vibrations (beyond the zero point energy).
    • Sv is the entropy due to vibrations.
    • Ht, Hr, St and Sr are the enthalpy and entropy due to rigid body rotation and translation.

    Calculating all of these terms is impossible for the foreseeable future for any real/non-trivial molecule. However a number of methods and recipes have been proposed that attempt to approach this limit. Below we describe such an algorithm using the G3 method. The G3 method is a specific thermo chemical recipe available in Spartan that attempts to produce accurate results in a relatively short amount of time. By studying it we can generalize it to imagine a method which should give the *exact* results even if such a recipe is impractical.

    Below is the edited result of a G3 run on a water molecule, used as a reference:

     Energy  HF/6-31G(d)             -76.009809  1
     Energy MP2/6-31G(d)             -76.196848  2
     Energy MP4/6-31G(d)             -76.207326  3
       perturbation correction        -0.000565  4
       polarization correction        -0.074488  5
       diffuse correction             -0.012979  6
       basis set correction           -0.081653  7
       spin-orbit correction           0.000000  8
       electron pair HLC              -0.025544  9
       ----------------------  ------------------ 
     G3 energy (Ee)                  -76.402556 
       HF/6-31G(d) zero point          0.020515  11
     G3 energy (Eo)                  -76.382040 
       HF/6-31G(d) Vibrational         0.020518  12
       HF/6-31G(d) Translation         0.001416  13
       HF/6-31G(d) Rotational          0.001416 
       RT constant                     0.000944 
     G3 kT energy (H298)             -76.378260 
       Atomic Energy                 -76.032990  14
     dH(298)                          -0.091381 
     dH(298)                         -57.34 kCal/mol

    A description of successive improvements to the energy is provided. The details of each step are not discussed here, as the main point is to provide an overview of what is required for an *exact* answer.

    1. First we start with the HF energy using the 6-31G(d) basis set. This is the total energy required to pull the 10 electrons, 2 protons, and 1 Oxygen nuclei apart.

    HF methods ignore electron correlation energy. The goal of DFT and other post HF methods is to account for this electron correlation energy.

    1. MP2 can often correct for 80% of this energy. (G3 minimizes the coordinates at the MP2 level. All further energies are done with this geometry.)
    2. MP4 is an improvement to MP2 collecting almost 95% of the total correlation energy.
    3. In an attempt to do better than 95% of the correlation energy (from MP4), another correction, the "perturbation correction", is made. (G3 theory uses a QCISD calculation for this term).

    One weakness in the approach described so far is the basis set. There are a number of possible improvements that can be made to the basis set:

    1. Adding polarization terms is often the easiest way to improve a basis set.
    2. Diffuse functions are sometimes useful, especially for negatively charged systems.
    3. We also need to make the core basis set more flexible with additional terms.
    4. We have so far totally neglected any spin-orbit contributions to the energy so we may want to add this energy term in.
    5. There are other systematic electronic errors. The G3 method lumps these into a "High Level Correction" (HLC) term.
    6. We could also add relativistic effects to the energy although this is not done in the G3 method.

    If we carry all the above corrections correctly to their infinite limit we should have the *exact* electronic energy. We label this energy Ee. But this would still not be good enough. We've made the assumption that the nuclei do not move. Quantum mechanics tells us that everything is moving, even at absolute zero; the so called "zero point" energy (Zo). By doing a normal mode analysis we can calculate this zero point energy.

    1. G3 calculates this zero point energy at the HF level with the 6-31G(d) basis set. If we had infinite computational resources we could improve this in the same way we discussed improving the electronic energy.

    The above energy would be correct at zero Kelvin, but chances are that the system we are studying exists at a non-zero temperature. We can make normal mode corrections to the energy, which we now call enthalpy and label it H298. (298.15 K being the most common temperature of interest.)

    1. G3 adds the enthalpy (Hv) due to normal mode vibrations.
    2. G3 also adds energy due to translating and rotating the entire molecule, as well as a pressure term from the ideal gas law equation (RT==pV).

    At this point we notice that the energy is in some "strange" units called Hartrees. In order to compare with other results it is useful to do a conversion.

    1. G3 does an energy conversion to kcals, attempting to define zero using the standard states of the constituent atoms. This finally is dH (delta-H). This is the final goal of the G3 theory.

      This final conversion step is not always necessary. What is necessary in QM calculations is to ensure that when comparing energies, the energies are not only in the same units, but define the same zero. (Typically that means the same basis set and theory level, and molecules with the exact same constituents and number of electrons.)

    Often, when examining reactions we require even more; the Gibbs free energy (G) which is calculated by subtracting entropy: G = H - TS + PV.

    1. A first approximation of the entropy (S) can be calculated using the same frequency data as Hv was previously.
    2. In our calculation of H298 and S we have used the normal mode approximation ignoring anharmonic terms. These actually become important at higher temperature, and are often most noticeable in the calculation of the entropy. Anharmonic cross terms may also become important. For low frequency vibrations the normal mode approximation may not be appropriate and other equations may need to be examined to model rigid rotors (such as methyl groups) or low frequency bending and folding modes.
    3. For flexible molecules it is necessary to look at multiple conformers of the same molecule. In a goal to get the *exact* answer one would need to apply all the previously discussed steps to each conformer and weight their contributions using a Boltzmann weighting scheme.

    The above steps should cover all the physics of a completely isolated molecule. (i.e. In a vacuum or a dilute gas.) Adding a real environment (such as a solvent or a crystal lattice) is vastly more difficult.

    1. Calculating this environment could be attempted by adding all a shell of the environment's atoms surrounding the molecule and performing all of the previous steps on this larger system.

    Combining all of these corrections terms "correctly" (for which there is currently no 'good' systematic procedure) one should arrive at the "exact" answer.

    Thankfully, a careful examination of the types of chemistry questions one typically asks shows that one does not need to do all this work. (See our guide book for a thorough discussion of this.) Surprisingly, in many cases, HF/6-31G(d) is a good approximation to reality. This happy accident makes quantum chemistry possible on today's computers.

    Spartan gives users the ability to choose from a number of advanced correlated methods, and implements the G3 recipe, which is a standard approach for improving the accuracy of calculated energies.

    Spartan also provides the flexibility to work with a wide variety of theoretical models:.

    • Steps 2-4: A number of post HF methods are available, including
      • DFT: BP, SVWN, EDF1, BLYP, B3LYP, M06, wB97X-D
      • MP2, RI-MP2, LMP2, and MP3
      • MP4SDQ, MP4
      • QCISD(T), CCSD(T), OD(T)
      • VQCCD(2), VOD(2), QCCD(2), CCSD(2), CCD(2), OD(2)
    • Steps 5-7 Spartan has a full range of basis sets available, and allows the input of external basis sets. These include:
      • STO-3G,3-21G(*)
      • 6-31G with flexible polarization and diffuse options.
      • 6-311G with flexible polarization and diffuse options.
      • cc-pVDZ, cc-pVTZ, cc-pVQZ, cc-pV5Z
      • the G3 basis sets; G3MP2large, G3large
      • ECP basis sets including LACVP and LANL2DZ
      • and the ability to add user basis sets.
    • Steps 11-15 The ability to calculate frequencies and other thermodynamic data allows for the calculation of free energy due to vibrations using the normal mode approximation.
    • Step 17 Spartan's conformation module makes it easy to generate and work with multiple conformers.
    • Step 18 Spartan has a number of solvation methods which can be used to approximate a solvent.

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  • Why do molecular mechanics, semi-empirical, and ab initio energies look so different?
  • All three approaches have a different definition of zero, and use different units (by convention).

    • Molecular Mechanics calculates a "strain" energy. The zero of this system is one in which all bond angles and lengths are at their 'ideal' values. This 'zero' may not be attainable. For example the water molecule has a 'zero' energy at the global minimum, however, methane does not (in MMFF). This is because in methane the 'unstrained' angle is not 104.9 even though the 3-dimensional interactions of the 6 angles cause the minimized structure to have bond angles of 104.9.

      Given this definition one cannot compare molecular mechanics energies of different molecules. This restriction holds true even for different isomers. One can compare energies of different conformations. In fact this is one of the most popular and appropriate uses of molecular mechanics.

    • Semi-Empirical methods use the same definition as ab initio, but a constant is subtracted for each atom in the molecule. The goal of this 'shift' is to approximate a heat of formation (HOF). In reality, this approximation is not very accurate and should only be used as a first guess at the HOF. Semi-empirical methods are most useful for predicting rough geometries and transition states quickly.
    • Ab initio methods (including HF and DFT) compare the energy of the combined molecule with the energy required to remove every electron, and separate every nuclei. While this reaction is not a very realistic experiment, it is theoretically simple and can be used to calculate energy differences of conformers, isomers, and entirely different molecules. See the discussion on calculating the heat of formation for a more detailed description o using this energy.

      By convention ab initio results are returned in units of Hartrees. See the units section to convert from Hartrees to more common units

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  • How is the solvation energy calculated?

  • Spartan automatically calculates the solvation energy (whenever possible) using the SM5.4 solvation method:

    "Energy of Solvation" = E[AM1] - E[SM5.4A]

    The "energy(aq)" displayed in the properties dialogue is the sum of the base energy and this Energy of Solvation:

    "Energy(aq)" = E[Base-method] + E[AM1] - E[SM5.4A]

    The SM5.4 solvation method is a modification to the semi-empirical methods used to model a molecules interaction with water. There is a parameterization for both AM1 (the default) and PM3. These parameterizations are labeled SM5.4A and SM5.4P respectively.

    A number of other solvation models are available in Spartan. Whenever one of these models the solvation energy and "energy(aq)" is calculated using these methods replacing the above equations

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  • How many parameters are there in each method

  • Each method is different, but an overly short answer would be:

    • no parameters for ab initio methods (HF, MP2, MP4, CCSD, ...)
    • about a dozen parameters for DFT methods (SVWN, B3LYP, wB97X-D, ...)
    • dozens for semi-empirical methods (AM1, PM3, ...)
    • hundreds for molecular mechanics methods (SYBYL, MMFF, ...)

    For an exact number one will need to examine the primary literature on these methods. However, slightly more detailed discussion of these methods presented below. More details can be found in Spartan's documentation.

    • The HF,MP2, MP4, CISD, CISD(T) can be thought of as keeping more terms in a "Taylor-like" series expansion of the full/exact quantum mechanical calculation. They are called 'ab initio' because there are no parameters other than where to/how to stop the expansion.
    • The basis sets (3-21G*, 6-31G* ...) can be thought of as a "Taylor-like" series expansions of the exact electron density. The smallest have ~10 terms per atom ... and more are added as the sets get bigger. The authors of these basis sets would not call them free parameters, but defend that most of these parameters are derived and claim there are only a few free parameters that describe how the expansion is terminated. (In QM parlance; splitting and polarization.)
    • DFT methods can be considered an extension to HF methods, with a few parameters added to attempt to go from HF to the exact quantum mechanical solution. In reality these approximations appear to improve the base HF to MP2 level or better.
    • Semi-empirical, is a radically abbreviated "Taylor-like" expansion of the exact quantum mechanical solution. To compensate for how bad this early termination is, about 20 parameters per atom are added.
    • Mechanical force fields are purely empirical; roughly 5 parameters per "atom type", many more for each bond, (including torsional, bond bending, cross terms). In modern forcefields there are more "atom types" than one might initially guess. For example, MMFF94 has 8 different kinds of oxygen. Using the PRINTLEV=4 keyword will dump the parameters for a given molecule. (Only available for the mechanics module).

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  • Can I add other DFT functionals?

    Spartan understands a large number of DFT functionals. Only the most popular and well tested are available from the "Density functional" pull-down menu of the setup panel. For example Truhlar group's M06-2x function while not available by default from the pull-down can be typed in the "Option" line as M062x. When the return key is struck the M062x will disappear from the option line and now show as selected in the "Density Functional" pull-down menu.

    It is possible to define your own functionals with the EXCHANGE= and CORRELLATION= keywords. Each functional must be followed a colon (':') and then it's weighting. Different functionals are then separated by commas. For example a functional consisting of 9 parts "Slater" exchange and 1 part "Becke" exchange would look like:


    If any correlation functionals are required one would use the CORRELATION keyword. For example:


    The values allowed exchange functionals are

    • HF Fock exchange
    • Slater Slater (Dirac 1930)
    • Becke Becke (1988)
    • GILL96 Gill (1996)
    • GG99 Gilbert and Gill (1999)
    • B(EDF1) Becke (uses EDF1 parameters)
    • PW91 Perdew
    • PBE Perdew-Burke-Ernzerhof (1996)
    • BR89
    • B97 Becke97 XC hybrid (1997)
    • B97-1 Becke97 re-optimized by Hamprecht et. al. (1998)
    • B97-2 Becke97-1 optimzed by Wilson et. al. (2001)
    • B3PW91
    • B3LYP the popular hybrid of Vosko, Wilk and Nusair
    • B3LYP5 #5 hybrid of Vosko, Wilk, and Nusair (Gaussian's version of B3LYP)
    • EDF1 also EDF2
    • BMK BMK hybrid
    • M05 also M052X,
    • M06 also M06HF, M062X,
    The correlation functionals available are
    • VWN Vasko-Wilk-Nusair #5
    • VWN1RPA
    • LYP Lee-Yang-Parr
    • PW91 GGA91, Perdew
    • PW92
    • LYP(EDF1)
    • BNLC
    • PK06
    • B94
    • P86 Perdew (1986)
    • PZ81 Perdew-Zungner (1981)
    • PBE Perdew-Burke-Ernzerhof (1996)
    • WIGNER Wigner
    • wB97,wB97X,wB97X-D the correlation part of the B97 series
    • LP Liu-Parr (1996)
    • HF HF exchange (K), (required for hybrid density functionals)

    For those who are familiar with the Q-Chem Exchange/Correlation notation; using EXCHANGE or CORRELATION without any colons set the appropriate "REM" values. If they include the colons, an "XC_FUNCTIONAL" section is built.

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  • The B3LYP coefficients look different; are they correct?

    We implement the main equation of the Vosko, Wilk, and Nusair paper. Sometimes, people will use equation #5 of this paper, which, in Spartan is called B3LYP5.

    In some references the coefficients are written differently. For example we write the B3LYP functional as

    EB3LYP = 0.20*ExHF + 0.08*ExSlater + 0.72*ExBecke + 0.19*EcVWN + 0.81*EcLYP
    Some literature might have it written (equivilantly) as
    EB3LYP = (ExSlater + EcVWN ) + 0.20*(ExHF - ExSlater ) + 0.72*(ExBecke - ExSlater ) + 0.81*(EcLYP - EcVWN )
    in order to highlight the "correction to SVWN". Another example is:
    EB3LYP = 0.20*ExHF + 0.80*ExSlater + 0.72*(ExBecke - ExSlater ) + 1.00*EcVWN + 0.81*(EcLYP - EcVWN )

    Another subtle difference between different B3LYP calculations can be the selection of the numerical grid used to calculate the density. See "What size grid does Spartan use for DFT calculations?" for a discussion of this.

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  • What size grid does Spartan use for DFT calculations?

    For most functionals, Spartan employs a hybrid SG-0 and SG-1 grid as follows: SG-0 for H,N,C, and O, SG-1 for all other atoms. For some functionals we use a larger grid. Specifically, we use the "BIGGRID" (70,302) for the Truhlar functionals and Head-Gordon functionals:

    Following are some keywords which can be typed into the Options line of Spartan's Calculations dialogue to change the grid:

    • SG-1 and SG-0, small grids tuned for the 6-31G* basis sets.
    • SMALLGRID(Spartan's default, an SG-0/SG1 Hybrid. SG-0 for H,C,N, and O and SG-1 for all other atoms)
    • EMLGRID (50,194)
    • BIGGRID (70,302)
    • VERYBIGGRID (100,434)

    In the above notation the first number is the number of shells in the radial direction, the second number (i.e. 194, 434 etc.) is the number of Lebedev radial points.

    One can also use the BIGGIRD keyword with an equal sign, to enter a Q-Chem like grid notation. Specifically a 12 digit number with the first six (counting leading/implied zeros) defining the number of shells in the radial direction and the next 6 defining the number of Lebedev radial points. i.e., BIGGRID and BIGGRID=70000302 both refer to (70,302)

    Valid values for Lebedev grids are:
    6, 18, 26, 38, 50, 74, 86, 110, 146, 170, 194, 230, 266, 302, 350, 434, 590, 770, 974, 1202, 1454, 1730, 2030, 2354, 2702, 3074, 3470, 3890, 4334, 4802, 5294.

    If you want to use Gauss-Legendre angular points (a=2N^2) instead of Lebedev numbers use BIGGRID=-rrraaaaaa (i.e. use a negative number).

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  • "6-31G* Basis Set for Third-Row Atoms", V. Rassolov, J. A. Pople, M. Ratner, P. C. Redfern, and L. A. Curtiss, J. Comp Chem., 22 (9) 976-984

  • "Gaussian-3 (G3) theory for molecules containing first and second-row atoms" J. Chem. Phys. Vol. 109, No. 18, (Nov. 8 1998) pp 7764-7776

  • "Gaussian-3 theory using reduced Moller-Plesset order" J. Chem. Phys. Vol 110, No. 10, (Mar. 8 1999) pp 4703-4709

  • "A Brief Guide to Molecular Mechanics and Quantum Chemical Calculations" W.J. Hehre, J. Yu, P.E. Klunzinger, L. Lou; Wavefunction Inc.

  • "A Guide to Molecular Mechanics and Quantum Chemical Calculations" W.J. Hehre; Wavefunction Inc. (2003)
    As of June 2008 this books ships with all versions of Spartan and Spartan Essential as a pdf file.

  • "Ab Initio Molecule Orbital Theory", Warren J. Hehre, Leo Radom, Paul v.R. Schleyer, John A. Pople; John Wiley & Sons, Inc. (1986)

  • "Efficient Calculation of Heats of Formation" W.S. Ohlinger, P.E. Klunzinger, B.J. Deppmeier, W.J. Hehre, J. Phys. Chem. A 2009 113 (10), 2165-2175

  • "1998 CODATA Recommended Values of the Fundamental Physical Constants"
    which derives the "..values of the basic constants and conversion factors of physics and chemistry resulting from the 1998 least-squares adjustment of the fundamental physical constants as ... published by the CODATA Task Group on Fundamental Constants and as recommended for international use by CODATA. The new, 1998 CODATA set of recommended values replaces its predecessor published by the Task Group and recommended for international use by CODATA in 1986..." and prior to that in 1973.

  • Yan Zhao, Nathan E. Schultz, and Donald G. Truhlar (2006). "Design of Density Functionals by Combining the Method of Constraint Satisfaction with Parameterization for Thermochemistry, Thermochemical Kinetics, and Noncovalent Interactions". The Journal of Chemical Theory and Computation (ACS Publications) 2 (2): 364-382. doi: 10.1021/ct0502763.

  • Yan Zhao and Donald G. Truhlar (2008). "The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals". Theoretical Chemistry Accounts (Springer Berlin / Heidelberg) 120 (1-3): 215-241. doi: 10.1007/s00214-007-0310-x.

  • Yan Zhao and Donald G. Truhlar (2008). "A new local density functional for main-group thermochemistry, transition metal bonding, thermochemical kinetics, and noncovalent interactions". The Journal of Chemical Physics (American Institute of Physics) 125 (8): 194101-194119. doi:10.1063/1.2370993. doi: 10.1063/1.2370993.

  • Yan Zhao and Donald G. Truhlar (2008). "Density Functional for Spectroscopy: No Long-Range Self-Interaction Error, Good Performance for Rydberg and Charge-Transfer States, and Better Performance on Average than B3LYP for Ground States". The Journal of Physical Chemistry A (ACS Publications) 110 (49): 13126´┐ŻE3130. doi: 10.1021/jp066479k.

  • Jeng-Da Chai and Martin Head-Gordon (2006). "Systematic optimization of long-range corrected hybrid density functionals". The Journal of Chemical Physics (American Institute of Physics) 128 (8):084106-084121. doi:10.1063/1.2834918. doi: 10.1063/1.2834918.

  • J. D. Chai and Martin Head-Gordon (2008). "Long-range corrected hybrid density functionals with damped atom-atom dispersion corrections". Physical Chemistry Chemical Physics (RSC Publishing) 10 (44): 6615-66120. doi: 10.1039/b810189b.

  • S.-H. Chien and P. M. W. Gill, "SG-0: A Small Standard Grid for DFT Quadrature on Large Systems" J. Comput. Chem., 27, 730, (2006)

  • P. M. W. Gill, B. G. Johnson and J. A. Pople, "A standard grid for density functional calculations" Chem. Phys. Lett. , 209, 506, (1993) doi: 10.1016/0009-2614(93)80125-9.

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