Correction of the PM7 method for predicting band gaps of
semi-conductors
Xiang Liu and Dr. Karl Sohlberg
Department of Chemistry, Drexel University, Philadelphia, PA
Introduction
Tertiary transition-metal oxide
Predicting ABOx band gaps
PM7 calculations of binary transition-metal oxide MxOy have been
carried out. A comparison between uncorrected PM7 band gaps
and experimental band gaps is shown below.
PM7 calculations of tertiary transition-metal oxide ABOx have
been carried out. The comparison between uncorrected PM7
band gaps and experimental band gaps are shown as below. It
can be seen the PM7 method still tends to overestimate the band
gaps.
The above correction term has been applied to some other ABOx
oxides.
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Experimental band gaps (eV)
The PM7 method has been successfully applied in predicting the
structures of organic molecules and their heat of formations [1-3].
It can also yield reliable results for the densities and heats of
formation for solid materials. These benefits together with the fast
calculations make PM7 method a very useful modelling tool for
chemists.
RMS = 3.15 eV
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RMS = 2.89 eV
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Species
PM7 band
gaps(eV)
Exp. band
gaps (eV)
Error (eV)
Corrected
PM7 band
gaps (eV)
Errors (eV)
PBTiO3
9.40
3.40
-6.00
5.35
-1.95
MnTiO3
3.40
3.18
-0.22
3.02
0.16
Mg2TiO4
5.39
4.00
-1.39
3.75
0.25
MgTiO3
5.79
3.07
-2.72
4.21
-1.14
Rms.
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Experimental band gaps(eV)
Semi-empirical methods were developed as simplified versions of
Hartree-Fock methods by using empirical and experimental data
to parameterize the one- and two-centered integrals in the
Hartree-Fock secular equations, which can greatly reduce the
computation time. The semi-empirical PM7 method has been
developed as a re-parameterization of the Neglect of Differential
Diatomic Overlap (NDDO) method, in which all two-electron
integrals involving two-center charge distributions are neglected.
Binary transition-metal oxide
3.37
1.14
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With this correction, the errors have been reduced by 3 times.
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Conclusion
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[4]
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PM7 band gaps (eV)
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PM7 band gaps (eV)
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In this work, we have developed a post-calculation correction for
PM7 band gaps of transition-metal semi-conductor oxides. This
correction utilizes a parameter evolved from the atomic charge of
the metal cations in the oxides. The rms of the errors of band
gaps for binary oxides is thereby reduced from 3.15 eV to 1.03 eV.
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With a certain modification, this method can also be applied to
tertiary transition-metal oxides. The modified correction term
includes contributions from both A-site and B-site cations. The rms
of the errors is reduced from 2.89 eV to 1.10 eV. Applying this
correction to other oxides also reduces the errors by a similar
factor.
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In contrast, the PM7 method has very poor performance in
predicting band gaps of semi-conductors due to the limitation of
Hartree-Fock method itself (in which the correlation is completely
ignored) and the NDDO approximations. In this work, we present
a convenient post-calculation method to correct the PM7 bandgap errors for transition-metal oxides.
Calculation method
PM7 band gaps
Band-gap errors
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Correction parameter
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A correction parameter is introduced as
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Pm7 band gaps (eV)
𝑃 = 𝑚𝑖𝑛𝑖𝑚𝑢𝑚 𝑆 , 𝑆 − 5 , 𝑆 − 10
𝑆 =𝑑−𝐶
Where d is the number of d electrons of the free transition-metal
atoms, and C is the atomic charge of metal cations in the oxides
obtained from PM7 calculations.
Corrected PM7 band gaps for binary oxides
The PM7 calculations are performed with MOPAC2012 semiempirical quantum chemistry program. Supercells of transitionmetal oxides, containing several unit cells, are fully relaxed
instead of single unit cell in order to reduce the single-gamma
error from MOPAC2012 calculations.
For binary transition-metal oxides, the correction terms is found to
be
𝐸𝑐𝑜𝑟𝑟 = −1.22 − 1.71 ∗ 𝑃
The corrected band gaps are
𝑐𝑜𝑟𝑟
𝑃𝑀7
𝐸𝑏𝑔
= 𝐸𝑏𝑔
+ 𝐸𝑐𝑜𝑟𝑟
Errors (eV)
Different from the binary transition-metal oxides, tertiary transitionmetal oxides have two different metal cations, which both
contributes to the electronic structures and the band gaps.
Therefore the correction term has been modified to include the
contribution from both two metal cations.
𝐸𝑐𝑜𝑟𝑟 = 3.83 − 3.48 ∗ 𝐶𝐴 − 1.65𝑃𝐵
Where 𝐶𝐴 is the atomic charge of A-site cation from MOPAC
calculation and 𝑃𝐵 is the correction parameter for B-site cation as
described before. The corrected PM7 band gaps are as below.
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RMS = 1.03 eV
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Lastly, I would like to thank all the graduate and undergraduate students in the lab;
thank you for all your guidance, advice, support, and cooperation.
Experimental band gaps (eV)
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(2*2*2) MnO supercell
The band gaps are evaluated from the highest occupied
molecular orbital (HOMO) and the lowest unoccupied molecular
orbital (LUMO) of which the energies are obtained from MOPAC
results.
Experimental bans gaps (eV0
MnO unit cell
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References
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1. Stewart, J. J. P. (1989). J. Comp. Chem. 10(2): 209-220; 221-264.
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2. Stewart, J. J. P. (2004). J. Mol. Modelling 10: 6-12.
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3. Stewart, J. J. P. (2004). J. Phys. Chem. Ref. Data 33(3): 713-724.
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𝐸𝑏𝑔 = 𝐸𝐿𝑈𝑀𝑂 − 𝐸𝐻𝑂𝑀𝑂
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Corrected PM7 band gaps (eV)
TEMPLATE DESIGN © 2008
www.PosterPresentations.com
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Corrected PM7 band gaps (eV)
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(1) Extend this method to oxides other than transition metals.
(2) Build a theoretical scheme for this correction. This can make
us better understand and utilize the semi-empirical methods.
I would like to thank my mentor Dr. Sohlberg for all his guidance and
encouragement and for giving me a chance to work in his lab.
RMS = 1.01 eV
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Future Work
Acknowledgements
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With this method, we can effectively reduce the errors in the PM7
band gaps. Hence it renders the PM7 method more valuable and
useful for investigations of semi-conductors.
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4. Stewart, J. J. P. (2013). J. Mol. Modelling 19: 1-32.