Volume Change Error manual

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We have used the difference between the computed volume after DFT relaxation and the volume reported experimentally as an indicator of a problem with a computation or entry. The problem can come from the experimental side (for instance atomic positions wrongly assigned in the ICSD) or from the approximation used in DFT.

Our analysis focused only on GGA (without U) results. Our strategy consist in first establishing a volume change distribution from our large data set. After establishing this distribution, outliers will be easily identified and tagged with a warning.

Volume Change Distribution in GGA

Our analysis focused on the GGA data in the database available on Friday September 23, 2011. In total, we considered 11579 entries. We report on volume changes by computing:

\Delta V=\frac{V_{GGA}-V_{exp}}{V_{exp}}

Where V_{GGA} is the unit cell volume obtained by GGA and V_{exp} the experimental volume given by the ICSD

The issue with high pressure phases

If the data is right away used, we would observe a longer tail on the positive values. This data is from the high pressure phase. Indeed, while our computations have been performed at 0 atm, compounds characterized at high-pressure will show a lower experimental than computed volume. This is not per se an error but instead a discrepancy between the experimental and computational conditions. To mitigate, this issue we removed from this analysis any entry likely to refer to a high-pressure phase according to the methodology presented in [1].

The fitting of the distribution

Figure 1: Histogram of the difference between computed (GGA) and experimental volume for 10,768 ICSD compounds

After exclusion of the possible high-pressure phases, we have 10768 points available to study the difference between experimental and computed volume. Figure 1 shows the histogram of volume difference. The distribution is symmetric but its median is positive (3.2%) indicating a tendency for GGA to overestimate the volume. This is in agreement with the know-how in the field established from previous studies on smaller set of compounds.

We obtained a very good fit to the data by using the a t-location scale distribution.[2] A normal distribution could not be fitted to this data because of the heavy tail observed. Using matlab and a maximum likelihood approach, we obtained maximum likelihood estimates as well as confidence intervals for the three parameters of the distribution. Figure 2 shows the good agreement between the raw data and the t-location scale probability density distribution.

Figure 2: Fitted t-location scale probability density (red curve) on the difference between computed (GGA) and experimental volume for 10,768 ICSD compounds

The tagging of the entries

After fitting the distribution, it is possible to tag the entries outlying the distribution. We assigned a warning tag to any entry in our database with a volume error higher than the 95th percentile (situated at 9.6% volume change) and lower than the 5th percentile (situated at -3,2% volume change). Figure 3 shows these boundaries on the cumulative t-location scale distribution.

Figure 3: Fitted t-location scale cumulative probability (red curve) on the difference between computed (GGA) and experimental volume for 10,768 ICSD compounds. The dashed black lines indicate the 5th and 95th percentiles

In total, 959 entries have been assigned a warning.

Some examples of outliers detected by the volume difference

Here, we analyze some of the largest outliers found in our analysis. Through these examples, we illustrate what kind of errors can be observed.

YZn and YbZn

Both compounds (task_id: 11577 and 179, icsd_id: 106232, 206226) show enormous volume differences: 370% and 350% ! Looking at the data present in the ICSD, we found that the paper reference mentioned CsCl structures, while the entry given by the ICSD is a fcc based alloy. The volume discrepancy comes therefore from an erroneous export of the experimental data in the paper to the ICSD.


55% volume difference task_id: 7162 and icsd_id: 52487. This entry refers to a high pressure structure our algorithm did not catch. It is not surprising to see the computed data reporting a much larger volume than the experimental obtained at high-pressure


-27% volume difference task_id: 7521, icsd_id: 15995 The icsd indicates already that the experimental data is dubious. There is a warning on the ICSD web site: "Unusual difference between calculated and measured density". The oxidation state reported for Ta: +2 is extremely rare.


18% volume difference task_id: 1434, icsd_id: 644257 This is most likely due to an inherent error from GGA. The MoS2 structure is layered and van der Waals interactions between the S atoms are essential to the geometry of the structure (c lattice parameter especially). However, it is known that GGA does not model well VDW interactions.


To cite the Materials Project, please reference the following work:

  • A. Jain, G. Hautier, C. J. Moore, S. P. Ong, C. C. Fischer, T. Mueller, K. A. Persson, and G. Ceder, A high-throughput infrastructure for density functional theory calculations, Computational Materials Science, vol. 50, 2011, pp. 2295-2310.


  1. Geoffroy Hautier