Example: Meta-GGA energy functionals: OH¶
First two calculations on OH are performed which use, respectively, the hybrid meta-GGA TPSSh and the meta-GGA TPPS during the SCF. They require, respectively, the following XC input:
XC
MetaHybrid TPSSh
END
XC
MetaGGA TPSS
END
Next large even-tempered basis sets are used in the calculation of the atomization energy of OH using various modern GGA, meta-GGA and hybrid post-SCF energy expressions.
In the Create runs, a large even-tempered basis set is selected for O and H, which should give results closer to the basis set limit than the regular ADF basis sets. For both atoms, a second atomic calculation follows the Create run, in order to enable a comparison to the true atoms, rather than the artificial spherically symmetric atom from the Create run. This is achieved by specifying the keywords
unrestricted
charge 0 2
symmetry C(lin)
occupations
sigma 3 // 3
pi 2 // 0
end
in the case of oxygen. This fixes the proper occupations. The result files of both the Create runs and the atomic correction runs are stored.
In the molecular calculation, the symmetry of the molecule is explicitly broken and the occupations are specified in order to avoid the fractional occupations that ADF would otherwise choose. Although it is not said that such a solution would be inferior, the integer occupation solution is the one which allows direct comparison to literature results obtained with other programs.
One of the new GGA potentials has been specified for the xc potential and the keyword METAGGA implies that a series of GGA and meta-GGA xc energies is to be calculated and compared to those energies from the atomic calculations. Specifying HARTREEFOCK also enables calculation of PostSCF energies using hybrid functionals.
METAGGA
symmetry C(lin)
xc
GGA PBE
end
HARTREEFOCK
A fairly high numerical quality has been specified. For meta-GGA calculations we do recommend this, for example, Quality Good for the time being, as the numerical stability of the results tends to be somewhat lower than for regular GGA calculations.
The block key ENERGYFRAG
ENERGYFRAG
O t21.unr.O
H t21.unr.H
END
implies that the meta-GGA result must not only be compared to the spherically symmetric results from the Create runs, but also to the non-spherical atoms.
The molecular output file prints the PBE Total Bonding energy as usual (in various energy units).
Then a prints a list of ‘Total Bonding Energies’ for many different Exc functionals, including PBE. Because the numerical approach to obtain the two PBE results is somewhat different, small differences may occur between the two numbers. You now have an overview of the bonding energies of all (meta)GGA functionals currently implemented in ADF. This should give a good indication of the theoretical error bar or the uncertainty in the xc approximation.
Total Bonding Energy: -0.285869458939526 -7.7789 -179.39 -750.55
Correction terms (incorporated in energies above; only for test purposes):
1. Indication of fit-quality: 1st-order fit-correction used in the energy (hartree): 0.0000009773
2. Electrostatic (Fit correction): 0.0000000000
TOTAL BONDING ENERGIES FROM VARIOUS XC FUNCTIONALS
with respect to fragments in FRAGMENTS input block
hartree eV kcal/mol kJ/mol
Total Bonding Energy with respect to FRAGMENTS
XC Energy Functional
====================
FR: KCIS-modified [1] = -0.2755562529 -7.4982671559 -172.9141775210 -723.4728395652
FR: KCIS-original [2] = -0.2777926755 -7.5591233119 -174.3175540544 -729.3445663384
FR: PKZB [3] = -0.2815583042 -7.6615912811 -176.6805219563 -739.2312229576
FR: VS98 [4] = -0.3017930412 -8.2122064916 -189.3780124939 -792.3575175526
FR: LDA(VWN) [5] = -0.2887549829 -7.8574228734 -181.1965065198 -758.1261003036
FR: PW91 [6] = -0.2876886802 -7.8284073001 -180.5273913915 -755.3265229132
FR: BLYP [7] = -0.2770694652 -7.5394437569 -173.8637326580 -727.4457778237
FR: BP [8] = -0.2855207088 -7.7694137958 -179.1669686327 -749.6345147134
FR: PBE [9] = -0.2858693788 -7.7789015896 -179.3857623932 -750.5499477071
The same energy comparison is done with respect to the fragments (which most currently be atomic) in the ENERGYFRAG block. These are the numbers which should be comparable to experimental numbers.
Finally, the references for the various Exc functionals are printed in the output file.
XC Energy Functional
====================
EF: KCIS-modified [1] = -0.1713864911 -4.6636637112 -107.5466581930 -449.9751686305
EF: KCIS-original [2] = -0.1703788432 -4.6362442179 -106.9143495501 -447.3295895582
EF: PKZB [3] = -0.1717979877 -4.6748611039 -107.8048762475 -451.0555528525
EF: VS98 [4] = -0.1706480210 -4.6435689175 -107.0832611655 -448.0363156796
EF: LDA(VWN) [5] = -0.1980802920 -5.3900389935 -124.2972729569 -520.0597331321
EF: PW91 [6] = -0.1759718553 -4.7884378208 -110.4240180000 -462.0140407454
EF: BLYP [7] = -0.1748781607 -4.7586768767 -109.7377142099 -459.1425460020
EF: BP [8] = -0.1786134359 -4.8603188858 -112.0816350167 -468.9495095841
EF: PBE [9] = -0.1751555912 -4.7662261426 -109.9118044460 -459.8709394702
Similar calculations can be done to obtain energy differences between different molecules. In that case the ENERGYFRAG keyword is not operational though. No detailed breakdown of the bonding energy is currently available for these new energy functionals. Experience shows that the energy values depend only mildly on the chosen xc functional for the xc potential.