Supporting Information

© Copyright Wiley-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, 2005

Synthesis, Characterization and Corrosion Inhibitor Activity of Nano-Cap Shaped Tin Phthalocyanines.[*]

Hiram I. Beltrán,a,* Raquel Esquivel,a Marcelo Lozada-Cassou,a Marco A. Dominguez-

Aguilar,a Arturo Sosa-Sánchez,b Jose L. Sosa-Sánchez,b,** Herbert Höpfl,c Victor Barba,c

Rolando Luna-García,c Norberto Farfánd and Luis S. Zamudio-Riveraa,*.

[*], a) PIM-IMP, Eje Central Lázaro Cárdenas 152, Col. San Bartolo Atepehuacan, C. P. 07730, México, D. F. e-mail: hbeltran@imp.mx, lzamudio@imp.mx, Telephone: (+52)-55-9175-7399, Fax: (+52)-55-9175-6239. [**],

b) CIDS-IC-BUAP, Blvd. 14 Sur y Av. San Claudio, Ciudad Universitaria Puebla, Puebla, México. e-mail: jose.sosa@icbuap.buap.mx. c) CIQ-UAEM, Av. Universidad 1001, C. P. 62210 Cuernavaca, México. d) DQ-

CINVESTAV, Apdo. Postal 14-740, C. P. 07000 México, D.F. México.

Table A. 1 H NMR for compounds 3a-3h in CDCl3 at 200 MHz.

NN

N

NN

N NN

Sn O

OO

OR R

3

R

a -CH2-CH2-CH2-CH2-CH3

b -CH2-CH2-CH2-CH2-CH2-CH2-CH3

c -CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH3

d -CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH3

e -CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH3

f -CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH3

g -CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH3

h -CH2-CH2-CH2-CH2-CH2-CH2-CH2-cis-CH=CH-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH3

1234

5 6 7 8 9

5 6 7 8 9

5 6 7 8 9

5 6 7 8 9

5 6 7 8 9

5 6 7 8 9

10 11 12 13 14

10 11 12 13 14

10 11 12 13 14

10 11 12 13

10 11

15 16 17 18 19

15 16 17 18 19 20 21

5 6 7 8 9 10 11 12 13 14 15 16 17

15

5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

Compound H-3 H-4 H-5 H-6 H-7 H-8 Me

3a 8.05, dd, Jo=5.6

Jm=3.0, 8H 8.98, dd, Jo=5.6

Jm=3.0, 8H 0.14, t

J=7.4, 4H -0.22, q

J=7.4, 4H -0.02,q

J=7.4, 4H 0.45,sx

J=7.4, 4H 0.36, t

J=7.4, 6H

3b 8.28, dd, Jo=5.6

Jm=3.0, 8H 9.19, dd, Jo=5.6

Jm=3.0, 8H 0.39, t

J=7.4, 4H 0.02, q

J=7.4, 4H 0.25, q

J=7.4, 4H 0.68, q

J=7.4, 4H 0.94, t

J=7.4, 6H

3c 8.41, dd, Jo=5.6

Jm=3.0, 8H 9.37, dd, Jo=5.6

Jm=3.0, 8H 0.52, t

J=7.4, 4H 0.14, q

J=7.4, 4H 0.37, q

J=7.4, 4H 0.79, q

J=7.4, 4H 1.19, t

J=7.4, 6H

3d 8.41, dd, Jo=5.4

Jm=2.8, 8H 9.23, dd, Jo=5.4

Jm=2.8, 8H 0.39, t

J=7.2, 4H 0.01, q

J=7.2, 4H 0.24, q

J=7.2, 4H 0.67, q

J=7.2, 4H 1.14, t

J=7.2, 6H

3e 8.42, dd, Jo=5.4

Jm=2.8, 8H 9.38, dd, Jo=5.4

Jm=2.8, 8H 0.52, t

J=7.4, 4H 0.14, q

J=7.4, 4H 0.36, q

J=7.4, 4H 0.79, q

J=7.4, 4H 1.25, t

J=7.4, 6H

3f 8.42, dd, Jo=5.4

Jm=2.8, 8H 9.38, dd, Jo=5.4

Jm=2.8, 8H 0.15, t

J=7.4, 4H -0.25, q

J=7.4, 4H 0.00, q

J=7.4, 4H 0.42, q

J=7.4, 4H 0.92, t

J=7.4, 6H

3g 8.19, dd, Jo=5.8

Jm=3.0, 8H 9.14, dd, Jo=5.8

Jm=3.0, 8H 0.38, bs

4H 0.00, bs

4H 0.23, bs

4H 0.61, bs

4H 1.03, t

J=6.5, 6H

3h 8.21, dd, Jo=5.8

Jm=3.0, 8H 9.18, dd, Jo=5.8

Jm=3.0, 8H 0.35, bs

4H 0.00, bs

4H 0.23, bs

4H 0.63, bs

4H 1.02, t

J=6.5, 6H 3b: H-9, 0.94, q, J=7.4, 4H; H10, 1.19, sx, J=7.4, 4H. 3c: H-9, 1.05, q, J=7.4, 4H; H-10, 1.32, m, 4H; H-11, 1.16, m, 4H; H-12, H-13, 1.62-1.37, m, 8H. 3 d: H-9, 0.94, q, J=7.2, 4H; H-10, 1.10, m, 4H; H-11, 1.23, m, 4H; H-12, 1.32, m, 4H; H-13, 1.45, m, 4H; H-14, 1.50, m, 4H. 3e: H-9, 1.05, q, J=7.4, 4H; H-10, 1.28, m, 4H; H-11, 1.34, m, 4H; H-12, 1.47, m, 4H; H-13, H-14, H-15, H-16, 1.70-1.50, m, 16H. 3f: H-9, 0.69, q, J=7.4, 4H; H-10, 0.94, m, 4H; H-11, 1.02, m, 4H; H-12, 1.07, m, 4H; H-13, H-14, H-15, H-16, H-17, H-18, 1.70-1.50, m, 24H. 3g: H-9, 0.91, bs, 4H; H-10, H-11, H-12, H-13, H-14, H-15, H-16, H-17, H-18, H-19, H-20, 1.50-1.10, m, 44H. 3h: H-9, 0.90, q. J=7.2, 4H; H-10, 1.16, q, J=7.2, 4H; H-11, 1.96, dd, J=7.2, 6.6, 4H; H-12, H-13, 5.51-5.31, m, 8H; H-14, 2.09, c, J=6.6, 4H; H-15, H-16, H-17, H-18, H-19, H-20 1.53-1.28, m, 24H. Signal acronyms: bs, broad signal; dd, double of doublets; t, triplet; q, quintuplet; sx, sextuplet.

Table B. 13C and 119Sn NMR for compounds 3a-3h in CDCl3.

NN

N

NN

N NN

Sn O

OO

OR R

3

R

a -CH2-CH2-CH2-CH2-CH3

b -CH2-CH2-CH2-CH2-CH2-CH2-CH3

c -CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH3

d -CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH3

e -CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH3

f -CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH3

g -CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH3

h -CH2-CH2-CH2-CH2-CH2-CH2-CH2-cis-CH=CH-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH3

1234

5 6 7 8 9

5 6 7 8 9

5 6 7 8 9

5 6 7 8 9

5 6 7 8 9

5 6 7 8 9

10 11 12 13 14

10 11 12 13 14

10 11 12 13 14

10 11 12 13

10 11

15 16 17 18 19

15 16 17 18 19 20 21

5 6 7 8 9 10 11 12 13 14 15 16 17

15

5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

Compound COOSn C-1 C-2 C-3 C-4 C-5 C-6 C-7 C-8 Me 119Sn

3a 176.5 152.6 135.6 122.7 129.8 31.9, bs 24.6 30.7 22.1 13.9 -846.1 3b 176.5 152.6 135.6 122.7 129.8 32.0, bs 24.9 28.5 28.8 14.5 -846.3 3c 176.6 152.7 135.7 123.0 130.1 31.7, bs 24.6 28.3 28.8 14.3 -845.9 3d 176.9 152.9 135.9 123.3 130.4 32.0, bs 25.0 28.6 29.1 14.7 -845.6 3e 176.9 153.0 136.0 123.4 130.4 32.0, bs 25.0 28.6 29.1 14.7 -846.4 3f 176.5 152.6 135.6 123.0 130.0 31.7, bs 24.6 28.3 28.8 14.4 -846.1 3g 176.7 152.7 135.7 123.1 130.1 31.8, bs 24.7 28.4 28.9 14.4 -846.1 3h 177.0 153.1 136.0 123.4 130.4 32.1, bs 25.0 28.7 29.1 14.7 -848.8

3a: C-1, 2J(119/117Sn-13C)=8.0 Hz; C-2, 3J(119/117Sn-13C)=20.2 Hz. 3 b: C-2, 3J(119/117Sn-13C)=20.6 Hz; C-9, 31.6; C-10, 22.9. 3c: C-1, 2J(119/117Sn-13C)=8.6 Hz; C-2, 3J(119/117Sn-13C)=20.5 Hz; C-9, 29.0; C-10, 29.2; C-11, 29.0; C-12, 31.9; C-13, 22.8. 3 d: C-2, 3J(119/117Sn-13C)=20.6 Hz; C-9, 29.4; C-10, 29.8; C-11, 29.9; C-12, 30.0; C-13, 32.4; C-14, 23.2. 3e : C-2, 3J(119/117Sn-13C)=20.6 Hz; C-9, 29.4; C-10, 29.8; C-11, 29.9; C-12, 30.0; C-13, 30.1; C-14, 30.1; C-15, 32.4; C-16, 23.2. 3f: C-1, 2J(119/117Sn-13C)=8.0 Hz; C-2, 3J(119/117Sn-13C)=20.6 Hz; C-9, 29.1; C-10, 29.5; C-11, 29.7; C-12, 29.8; C-13, 29.9; C-14, 29.9; C-15, 29.9; C-16, 29.9; C-17, 32.0; C-18, 22.9. 3g: C-2, 3J(119/117Sn-13C)=21.2 Hz; C-9, 29.2; C-10, 29.5; C-11, C-12, C-13, C-14, 29.9; C-15, 29.9; C-16, 29.9; C-17, 29.9; C-18, 29.9; C-19, 32.1; C-20, 22.9. 3h: C-2, 3J(119/117Sn-13C)=20.6 Hz; C-9, 29.1; C-10, 27.6; C-11, C-16, C-17, C-18, C-20, 29.8, 30.2; C-12, C-15, 30.3; C-13, C-14, 129.9, 129.8; C-19, 23.2. Signal acronyms: bs= broad signal. The 13C NMR was measured at 50.29 MHz. The 119Sn NMR was measured at 74.53 MHz.

a) Crystals of 3a·CHCl3. b) Crystals of 3b.

c) Magnification for 3b crystals. d) Crystals of 3c-A.

Chart I. SEM micrographs for a) 3a·CHCl3, b), c)3b and d)3c-A.

Periodic DFT Calculations of 3-cA and 3c-B Allotropes

Since for many Pc systems there exist different kinds of molecular packing arrangements

within specific energetic stabilities (e.g. a, ß, ?, d, etc. packing allotropes), compound 3c

leads, trough two different crystal growth techniques, to two different crystalline states or

polymorphs. The former is related to the relaxed hydrocarbon chains packing in 3c-A

“Polymorph A”, whereas the latter is related to other different packed molecule with a

hindered hydrocarbon chain 3c-B “Polymorph B”. Herein, the use of theoretical chemistry

approache was used to elucidate the more stable polymorph of 3c. A set of DFT plane wave

calculations at the PW91/GGA1-3 level of theory was performed for the two different

crystalline structures with the CASTEP program (ACCELRYS, Inc.).4 According to the

prerequisite for the lattice cell symmetry (periodic calculation), both cells were transformed

from the original P -1 space group, with equivalent inversion center symmetry: 1) x, y, z

and 2) –x, -y, -z, to the less symmetric P 1 space group, with identity symmetry

equivalents: 1) x, y, z. For the two different crystalline lattices, integrations over the

Brillouin zone were performed using one k-point generated via the Monkhurst-Pack

scheme.5 Hence, for both crystal lattices, single point SCF calculations were computed to

observe difference in the energetic contribution at the supramolecular level. The single

point calculations for both systems indicate that the form 3c-A (ET=-13004.5316 eV) is

more stable by 1.8 Kcal·mol-1 than the 3c-B (ET=-13004.4535 eV). In addition, a

simultaneous optimization of crystal lattice parameters and atomic relaxation were

performed. By the full minimization procedure (relaxation of the crystal packing and

crystal lattice), the energy between both allotropes is diminished to 0.1 Kcal·mol-1, which

confirms that the 3c-A (ET=-13019.9237 eV) is more stable than the 3c-B (ET=-13019.9270

eV). However, the energetic difference indicates that the allotropes are essent ially

isoenergetic (Table C). It is important to mention that according to the tail-tail interactions,

the energetic preference is not as simply viewed by theoretical calculations as in previous

disordered crystal structure of plumbocene molecule6 (the investigated conformers were the

staggered and eclipsed calculated with the CASTEP package). For the plumbocene case,

the studied conformers are stabilized through strong p···p and s ···p forces as well as charge

transfer present trough.

Computational Details

Each CASTEP run was performed in an Origin 3000 SGI multitask computer provided

with 48 processors. The SCF as well as minimization were computed with parallel

executions using MPI on 2 processors with the selected distribution as a G-vector. All runs

were carried out with the Cerius2 program set. The global setup definitions were as follows,

Task: Geometry Optimization, Material type: Insulator, Theory level: GGA-PW91, Total

charge (electrons): 0, Kinetic energy cut-off for plane waves: 340.000 (eV), Fourier

transform grid: 72x72x75 for 3c-B, 72x72x80 for 3c-A, Electronic minimization method:

Density Mixing, Pseudopotential representation: Reciprocal space. The setup variables for

the run were as follows, SCF convergence criterion per atom: 0.2000E-05 (eV), Electronic

CG steps at each SCF loop: 5, Internal coordinates optimization: BFGS algorithm,

Table C. DFT (PW91/GGA) energetic for single point and minimized 3c-A and 3c-B allotropes.

Properties 3c-A 3c-B SCF data Energy [eV] -13004.5316 -13004.4535 Cell lattice parameters a [Å] 13.176 12.808 b [Å] 13.418 12.833 c [Å] 14.929 13.947 a [°] 65.399 87.761 ß [°] 71.356 85.840 ? [°] 78.930 78.093 Volume [Å3] 2268.72 2236.47 Minimized data Energy [eV] -13019.9237 -13019.9270 Cell lattice parameters a [Å] 13.218 12.853 b [Å] 13.469 12.864 c [Å] 14.983 13.991 a [°] 66.300 87.152 ß [°] 71.500 86.199 ? [°] 78.975 78.280 Volume [Å3] 2310.00 2258.46

Tolerance for total energy: 0.2000E-04 (eV·atom-1), Tolerance for RMS displacement of

atoms: 0.00100 (Å), Tolerance for RMS force on atoms: 0.05000 (eV·Å-1), Tolerance for

RMS stress tensor: 0.10000 (GPa), Unit cell optimization: BFGS algorithm, subspace

rotation of wavefunctions. The density mixing scheme with the conjugate gradient solver

was started with the following variables, Density mixing scheme used: Pulay, Amplitude

for charge density mixing: 0.80000, Qmax cut-off for charge density mixing: 1.50000,

History length for density mixing: 20, Starting charge density was generated from atomic

orbitals in the form of random wavefunctions, Timer information was included in the

logfile, Wavefunctions are stored in memory with a backup frequency of 5 iterations. The

finite basis set correction was calculated automatically. The cell optimization was

performed with 6 cell parameters free to vary. The current used FFT grid was sufficient for

this cut-off due to the used grid pass. The used potentials were ultrasoft for all atoms.

Corrosion rate of AISI 1018 in sour brine with and without inhibitor.

The corrosion rates obtained after applying the 3a-h inhibitors are indicated below. The

time indicated in each column of the tables is referred to the period of time in which the

open circuit potential was left to reach the corresponding equilibrium potential. Inhibitor

efficiency was calculated taking into account the blank material in sour brine after 3 min

and the system (carbon steel-sour brine- inhibitor) after 5 h without inducing any change in

potential or current.

Sour brine (@ pH=4) + Oleic derivative (3h) at 500 ppm

Blank (3 min.) System (3 min.) System (1 h) System(5 h) 62.48 41.93 35.58 10.94 60.71 34.20 27.68 11.81 53.23 31.81 27.80 9.84 45.75 31.27

X = 55.54 X = 34.80 X = 30.35 X =10.86 81.75-11.73/81.75

=86.7%

Sour brine (@ pH=4) + Oleic derivative (3h) at 1000 ppm

Blank (3 min.) System (3 min.) System (1 h) System (5 h) 75.16 41.85 23.57 17.03 72.99 44.64 25.05 15.60 68.35 41.38 26.70 19.68 60.67 37.27

X =69.30 X = 41.28 X = 25.11 X = 17.44 81.75-17.44/81.75

=78.7%

Sour brine (@ pH=4) + Oleic derivative (3h) at 300 ppm

Blank (3 min.) System (3 min.) System (1 h) System (5 h) 65.60 45.47 47.24 22.05 71.80 41.10 46.45 26.10 60.10 36.60 42.44 38.50 50.43 44.68 42.12

X = 61.98 X = 41.96 X =44.56 X = 28.88 81.75-28.88/81.75

=64.7%

Sour brine (@ pH=4) + Octadecanoic derivative (3g) at 1000 ppm

Blank (3 min.) System (3 min.) System (1 h) System (5 h) 59.41 47.59 35.35 32.68 56.10 43.30 34.35 29.50 48.42 40.15 36.01 26.57

X = 54.64 X = 43.68 X = 35.23 X = 29.37 81.75-29.37/81.75

=64.1%

Sour brine (@ pH=4) + Octadecanoic derivative (3g) at 500 ppm

Blank (3 min.) System (3 min.) System (1 h) System (5 h) 78.74 49.21 44.10 26.38 67.32 47.24 41.26 24.41 66.34 44.29 39.25 27.95

X = 70.80 X = 46.91 X = 41.54 X = 26.25 81.75-26.25/81.75

=67.9%

Sour brine (@ pH=4) + Hexadecanoic derivative (3f) at 1000 ppm Blank (3 min.) System (3 min.) System (1 h) System (5 h)

61.42 46.85 32.53 27.50 54.84 43.22 31.49 26.40 51.20 40.00 34.25 25.60

X = 55.82 X = 43.36 X = 32.76 X = 26.50 81.75-26.50/81.75

=67.6%

Sour brine (@ pH=4) + Hexadecanoic derivative (3f) at 500 ppm Blank (3 min.) System (3 min.) System (1 h) System (5 h)

61.42 40.23 34.25 35.43 56.40 41.30 29.92 26.80 69.30 39.40 27.95 22.44

X = 62.37 X = 40.31 X = 30.71 X = 28.23 81.75-28.23/81.75

=65.5%

Sour brine (@ pH=4) + Tetradecanoic derivative (3e) at 1000 ppm Blank (3 min.) System (3 min.) System (1 h) System (5 h)

43.31 22.83 11.20 12.47 40.55 28.74 25.17 12.20 47.64 27.55 19.29 10.53

23.62 X = 43.83 X = 25.68 X = 18.55 X = 11.73

81.75-11.73/81.75 =85.7%

Sour brine (@ pH=4) + Tetradecanoic derivative (3e) at 500 ppm

Blank (3 min.) System (3 min.) System (1 h) System (5 h) 45.15 25.59 20.53 16.37 40.91 26.61 19.97 11.81 42.22 23.63 20.87 7.87

24.41

24.97 X = 42.76 X = 25.04 X = 20.46. X = 12.02

81.75-12.02/81.75 =85.3%

Sour brine (@ pH=4) + Dodecanoic derivative (3d) at 1000 ppm

Blank (3 min.) System (3 min.) System (1 h) System (5 h) 55.31 44.88 38.58 25.59 58.66 42.56 35.82 22.57 54.17 41.77 37.00 19.76

X = 56.05 X = 43.07 X = 37.13 X = 22.64

81.75-22.64/81.75 =72.30%

Sour brine (@ pH=4) + Dodecanoic derivative (3d) at 500 ppm

Blank (3 min.) System (3 min.) System (1 h) System (5 h) 62.87 44.00 39.10 34.40 62.59 41.73 38.41 32.70 46.73 39.10 37.00 29.90 44.72 38.18

X = 54.23 X = 40.75 X = 38.17 X = 32.33 81.75-32.33/81.75

=60.5%

Sour brine (@ pH=4) + Decanoic derivative (3c) at 1000 ppm Blank (3 min.) System (3 min.) System (1 h) System (5 h)

50.83 37.00 38.20 30.31 66.93 46.85 36.61 35.40 54.80 42.10 37.20 35.40

X = 57.52 X = 41.98 X = 37.34 X = 33.70

81.75-33.70/81.75 =58.8%

Sour brine (@ pH=4) + Decanoic derivative (3c) at 500 ppm

Blank (3 min.) System (3 min.) System (1 h) System (5 h) 49.20 39.70 37.79 20.10 48.80 40.16 38.20 21.21 54.30 39.72 37.14 22.13

37.80

X = 50.77 X = 39.34 X = 37.71 X = 21.15 81.75-21.15/81.75

=74.1%

Sour brine (@ pH=4) + Octanoic derivative (3b) at 1000 ppm Blank (3 min.) System (3 min.) System (1 h) System (5 h)

43.31 39.11 25.79 19.68 42.68 28.74 23.03 20.40 44.01 34.64 27.10 19.29

X = 43.33 X = 34.16 X = 25.31 X = 19.79

81.75-19.79/81.75 =75.8%

Sour brine (@ pH=4) + Octanoic derivative (3b) at 500 ppm

Blank (3 min.) System (3 min.) System (1 h) System (5 h) 42.21 37.54 27.16 19.32 44.11 32.74 27.81 20.17 43.98 33.82 26.90 21.12

X =43.43 X =34.70 X = 27.29 X = 20.20 81.75-20.20/81.75

=75.3%

Sour brine (@ pH=4) + Hexanoic derivative (3a) at 1000 ppm Blank (3 min.) System (3 min.) System (1 h) System (5 h)

44.36 30.33 23.55 22.00 40.20 30.77 25.05 20.87 42.32 27.55 26.70 19.70

X = 42.29 X = 29.55 X = 25.10 X = 20.86 81.75-20.86/81.75

=74.5%

Sour brine (@ pH=4) + Hexanoic derivative (3a) at 500 ppm

Blank (3 min.) System (3 min.) System (1 h) System (5 h) 58.07 51.18 44.68 19.75 68.89 55.11 44.72 21.26 60.12 49.86 47.24 21.96 60.83 57.08 22.42

X =61.98 X =53.31 X = 45.55 X = 21.35 81.75-21.35/81.75

=73.9%

References [1] J.P. Perdew, Phys. Rev. B 1986, 33, 8822-3824. [2] A.D. Becke, Phys. Rev. A 1988, 38, 3098-3100. [3] J.P. Perdew, J.A. Chevary, S.H. Vosko, K.A. Jackson, D.J. Singh, C. Fiolhais, Phys. Rev. B 1992, 46, 6671-6687. 4. CASTEP: CAmbridge Serial Total Energy Package, Ab initio Molecular Dynamics Program with Conjugate Gradient Minimisation (CG) for the Electronic Energy, Version 4.6, Release 1 June 2001. Accelrys Inc., CASTEP Users Guide, San Diego: Accelrys Inc., 2001. V. Milman, B. Winkler, J.A. White, C.J. Pickard, M.C. Payne, E.V. Akhmatskaya, R.H. Nobes, Int. J. Quant. Chem. 2000, 77, 895-910. 5. H.J. Monkhurst, J.D. Pack, Phys. Rev. B 1976, 13, 5188-5192. 6. C.A. Morrison, D.S. Wright, R.A. Layfield, J. Am. Chem. Soc. 2002, 124, 6775-6780.