Surface Area Calculations

About

This describes the surface area calculations that we have done in a number of papers. Our first uses of this (and hence the references to the various literature articles, and a more complete description of the assumptions and utilization are described in

  • H. S. Casalongue, S. J. Choyke, A. N. Sarjeant, J. Schrier, A. J. Norquist, "Charge density matching in templated molybdates" J. Solid State Chem. 182, 1297 (2009)
  • K. B. Chang, D. J. Hubbard, M. Zeller, J. Schrier, and A. J. Norquist, "The Role of Stereoactive Lone Pairs in Templated Vanadium Tellurite Charge Density Matching" Inorg. Chem. 49, 5167 (2010)

DMS

Calculations performed using dms, which you can download from the author

(1) Create the "radii" file. A typical file looks like (all units in Angstroms). For some reason, AN and JS got into the habit of using "U" to denote lone pairs.

jschrier@ws5:~/anorquis/VTeOX_surf$ less radii
O       1.52
V       2.00
Te      2.00
U       1.50
C       1.70
N       1.55
H       1.09

(2) Run dms on the pdb coordinate input file. We typically use a probe radius of 1.5 A and a highest density SA = 10.0. This program is installed in your path on the ws* machines. Alternatively it is located in /packages/dms/bin/dms

dms input.pdb -a -d 10.0 -w 1.5 -o output.file

(3) Collect output. The part that we are most concerned with gets printed on STDOUT; we care about the surface area (which below is 439.13 square Angstroms). For our purposes, the output file that is generated (named "out") below is not important.

jschrier@ws5:~/anorquis/VTeOX_surf$ dms mz10-083\ MSA\ 1\ 1.pdb -a -d 10.0 -w 1.5 -o out
34 atoms
22732 points    (9346 contact, 13386 reentrant)
439.13 sq. A    (190.36 contact, 248.77 reentrant)
51.77 pts/sq.A    (49.10 contact, 53.81 reentrant)

Triangular surface decomposition

This uses a home-made perl code to compute these. It requires the Math::Matrix module to be installed.

(1) The input file is a CSV file of the format shown below. The first column is arbitrary and is thrown away (i.e., it is usually the atom number from the program AN uses), the next 3 columns are x, y,z coordinates, and then the remaining columns are letters describing which vertices are part of which triangle. E.g., in the example below, the first vertex belongs to triangles "l" and "o". Vertices can belong to an arbitrary number of triangles, and can have arbitrary letter names.

jschrier@ws5:~/anorquis/VTeOX_surf$ less mz10-083\ GD.csv 
26,6.82073,-1.55528,-1.92714,l,o,,,
27,13.56933,-1.55528,-1.92714,i,,,,
29,7.37929,5.58009,-1.92714,m,p,,,
30,14.12789,5.58009,-1.92714,k,,,,
35,-0.07213,1.55528,1.92714,a,,,,
36,6.67647,1.55528,1.92714,e,g,,,
38,0.48643,8.69065,1.92714,c,,,,
39,7.23503,8.69065,1.92714,f,h,,,
44,7.15904,1.71928,-0.7868,o,p,,,
45,13.90764,1.71928,-0.7868,i,j,k,,
52,0.14812,5.41609,0.7868,a,b,c,,
53,6.89672,5.41609,0.7868,g,h,,,
90,9.50532,1.52937,-2.18967,l,m,n,o,p
95,4.55044,5.606,2.18967,d,e,f,g,h
98,11.00598,-1.71835,-0.52346,i,j,l,n,
100,11.56454,5.41702,-0.52346,k,j,m,n,
101,2.49122,1.71835,0.52346,a,b,d,,
103,3.04978,8.85372,0.52346,b,c,d,e,f

(2) Run the perl script.

jschrier@ws1:~/anorquis/VTeOX_surf$ perl -w surface_area.pl <mz10-083\ GD.csv 
nAt = 17
a -->  4 10 16 
d -->  13 16 17 
j -->  9 14 15 
h -->  7 11 13 
k -->  3 9 15 
g -->  5 11 13 
f -->  7 13 17 
i -->  1 9 14 
e -->  5 13 17 
n -->  12 14 15 
m -->  2 12 15 
l -->  0 12 14 
p -->  2 8 12 
c -->  6 10 17 
b -->  10 16 17 
o -->  0 8 12 
a --> (4,10,16) --> 5.73267377989287
d --> (13,16,17) --> 8.64596466921981
j --> (9,14,15) --> 9.43930778396267
h --> (7,11,13) --> 4.71974496781504
k --> (3,9,15) --> 5.73267377989288
g --> (5,11,13) --> 5.48054656687296
f --> (7,13,17) --> 7.42009151394578
i --> (1,9,14) --> 5.09781695617559
e --> (5,13,17) --> 4.30021435253958
n --> (12,14,15) --> 8.64596466921982
m --> (2,12,15) --> 9.01759364577896
l --> (0,12,14) --> 7.42009151394578
p --> (2,8,12) --> 5.48054656687296
c --> (6,10,17) --> 5.09781695617558
b --> (10,16,17) --> 9.43930778396267
o --> (0,8,12) --> 4.71974496781504
total surface area = 106.390100474088

the output first reports which triangles (a,d,j) are defined by which vertices (4, 10, 16). Then it reports the area of each triangle, and finally it reports the total surface area at the end of the file.

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