Supplementary Materials

Radiation-induced defects in quartz. III. Single-crystal

EPR, ENDOR and ESEEM study of a peroxy radical

Mark J. Nilges, Yuanming Pan and Rudolf I. Mashkovtsev

Figure 1s. Plot of field positions vs. angle for the plane of data collected on crystal #2. Arrows point to the values of the B field set in obtaining the ENDOR and ESEEM spectra shown in Figures 8 and 10.


Figure 2s a) Angular plot of the ten ΔmI = ±1 ENDOR transitions for site 1.

Figure 2s b) Angular plot of the ten ΔmI = ±1 ENDOR transitions for site 2.

Figure 2s c) Angular plot of the ten ΔmI = ±1 ENDOR transitions for site 3.

Figure 2s d) Angular plot of the ten ΔmI = ±1 ENDOR transitions for site 4.

Figure 2s e) Angular plot of the ten ΔmI = ±1 ENDOR transitions for site 5.

Figure 2s f) Angular plot of the ten ΔmI = ±1 ENDOR transitions for site 6.

Figure 3s. Echo decay/modulation as a function of time for the three-pulse ESEEM experiment recorded for the rotation angle of 90º for crystal #2.

DFT Calculations

Unrestricted Hartree–Fock DFT calculations were performed with the software package GAMESS (Schmidt et al. 1993). Geometry optimization used a triple zeta valence basis set with two d polarization function with the B3LYP hybrid density functional. Isotropic (Fermi contact) and anisotropic (spin dipolar) hyperfine terms were calculated using the DFT wavefunction calculated using a triple zeta valence basis set with two d polarization function.

Calculations of the g-tensor used the DFT optimized geometry (except for adjustment of the Si-O-O and/or Al-O-O angles) using a full CIS (Maurice and Head-Gordon 1996) wavefunction based upon the natural orbitals of the UHF wavefunction calculated using a triple zeta valence basis set with two d polarization functions. It should be noted that the standard CIS implementation includes simple hole and electron single electron excitations and as such is not applicable to open shell systems. In order to obtain the full CIS wavefunction, which is an Eigenfunction of S2, a symmetry adapted set of single excitations involving promotion of either an α or β electron from a double occupied orbital to a empty valance orbital must be included. This gives rise to three Fock-like matrices instead of the conventional two Fock-like matrices (Foresman et al. 1992) that are used in the standard CIS method. The resulting CIS equations are solved using the standard iterative quasi-Newton-Raphson method coupled with Pulay’s DIIS accelerator.

The spin-orbit coupling operator is then applied as a finite perturbation to the CIS wavefunction for directions x, y, and z. The atomic spin-orbit coupling integrals are calculated using the built-in spin-orbit coupling routines in Gamess. The three resultant iteratively solved complex (imaginary) wavefunctions for x, y and z are then factored against the orbital angular momentum operators, lx, ly, and lz to give the resultant 3X3 tensor. The relatively small diamagnetic and relativistic contributions are also included.

Table 1s. Bond angles and bond lengths for the geometry optimized structures

[(OH)3Si-O-O-Si(OH)3]+ / (OH)3Al-O-O-Si(OH)3
O-O / 1.32 Å / 1.34 Å
Si-O2 / 1.83 Å / 1.75 Å
Si-O-O / 112.7º / 107.5 º
Si-Si / 4.34 Å / -
Si-Al / - / 4.43 Å
Al-O2 / - / 2.00 Å
Al-O-O / - / 117.9º
Si-O-O-Si / 173.4º / -
Si-O-O-Al / - / 174.8º

Table 2s. Calculated values of g and Aa using optimized geometry

[(OH)3Si-O-O-Si(OH)3]+ / (OH)3Al-O-O-Si(OH)3
g3 / 2.00201 / 2.00202
g2 / 2.00724 / 2.00694
g1 / 2.02378 / 2.02960
Aiso (29Si) / 12.52 / 10.76
T3 (29Si) / -0.75 / -0.88
T2 (29Si) / 0.12 / 0.22
T1 (29Si) / 0.63 / 0.66
Aiso(27Al) / - / -12.85
T3 (27Al) / - / 1.35
T2 (27Al) / - / -0.45
T1 (27Al) / - / -0.90
Aiso(17O) / -42.2 / -45.9
T3 (17O) / -167.9 / -201.9
T2 (17O) / 82.1 / 100.0
T1 (17O) / 85.8 / 101.9
Aiso(17O)b / - / -30.1
T3 (17O)b / - / -117.5
T2 (17O)b / - / 56.8
T1 (17O)b / - / 60.7

a) Principal Hyperfine values are in MHz. The T matrix is the anisotropic (traceless) part of the hyperfine matrix.

b) Hyperfine for the O atom (of the O2-) adjacent to the Al atom.

Table 3s. Atom positions (Å) for the optimized [(OH)3Si-O-O-Si(OH)3]+ cluster

FINAL U-B3LYP ENERGY IS -1184.3056068317

COORDINATES OF ALL ATOMS ARE (ANGS)

ATOM CHARGE X Y Z

------

O 8.0 -0.4263616692 0.5066387221 -0.0810111819

O 8.0 0.4263616692 -0.5066387221 -0.0810111819

SI 14.0 2.1704851838 0.0390526795 0.0164711935

SI 14.0 -2.1704851838 -0.0390526795 0.0164711935

O 8.0 2.2955526180 0.5131141716 1.5412651994

O 8.0 -2.2955526180 -0.5131141716 1.5412651994

O 8.0 2.2804949894 1.2044478265 -1.0719718150

O 8.0 -2.2804949894 -1.2044478265 -1.0719718150

O 8.0 2.8722282357 -1.3515555951 -0.3401994993

O 8.0 -2.8722282357 1.3515555951 -0.3401994993

H 1.0 2.7151780330 -0.0397803792 2.2145712033

H 1.0 -2.7151780330 0.0397803792 2.2145712033

H 1.0 2.4060835607 2.1281511455 -0.8164327403

H 1.0 -2.4060835607 -2.1281511455 -0.8164327403

H 1.0 3.3148271008 -1.5068914951 -1.1852916927

H 1.0 -3.3148271008 1.5068914951 -1.1852916927

Table 4s. Atom positions (Å) for the optimized (OH)3Al-O-O-Si(OH)3 cluster

FINAL U-B3LYP ENERGY IS -1137.5152029884

COORDINATES OF ALL ATOMS ARE (ANGS)

ATOM CHARGE X Y Z

------

O 8.0 0.5152809237 -0.6447799727 -0.1166390961

O 8.0 -0.3503626922 0.3796829816 -0.0506038666

AL 13.0 -2.2997640271 -0.0467251941 0.0041236452

SI 14.0 2.1330253068 0.0226065858 -0.0018923998

O 8.0 -2.4351244309 0.1106248881 1.7166985463

O 8.0 -2.4522443060 -1.6115471321 -0.6767652560

O 8.0 -2.7898497641 1.2897735703 -0.9644696214

O 8.0 2.3633379859 0.4647726314 1.5340224121

O 8.0 2.2534480735 1.2622539750 -1.0264086290

O 8.0 3.0826726884 -1.2127601082 -0.4262344326

H 1.0 -2.7140497495 0.9453618362 2.1074814966

H 1.0 -2.5525747827 -2.3842256250 -0.1133269695

H 1.0 -3.0876608702 1.1279739100 -1.8651246841

H 1.0 2.2309770421 -0.1899711025 2.2306725501

H 1.0 1.6485728243 2.0067638754 -0.9112652060

H 1.0 3.1066236847 -1.4878502457 -1.3511868260

References:

Schmidt MW, Baldridge KK, Boatz JA, Elbert ST, Gordon MS, Jensen MS, Koseki S, Matsunaga N, Nguyen KA, Su SJ, Windus TL, Dupuis M, Montgomery JA, (1993) General atomic and molecular electronic structure system. J Comput Chem 14: 1347-1363.

Maurice D, and Head-Gordon M, (1996) On the nature of electronic transitions in radicals: An extended single excitation configuration interaction method. J Phys Chem 100: 6131-6137.

Foresman JB, Head-Gordon M, Pople J A, Frisch MJ, (1992) Toward a Systematic Molecular Orbital Theory for Excited States. J Phys Chem 96: 135-149.

Table 5s. Spin Hamiltonian parameters of Centers B and B’ in citrine quartz at 110 and 298 K

Center / Matrix Y / k / Principal
value / Principal direction / DP
RMSD
(mT)
Yk / θk (°) / φk (°)
B
110 K / G / 2.00299(1) / 0.00063(1) / –0.00435(1) / 1 / 2.03447(1) / 21.3(2) / 248.1(2) / 372
0.156
2.01086(1) / –0.00845(1) / 2 / 2.00790(1) / 71.6(2) / 99.7(2)
2.03077(2) / 3 / 2.00226(1) / 79.5(2) / 6.2(2)
27Al
A/geβe
(mT) / –0.27(1) / –0.019(9) / –0.02(1) / 1 / –0.24(1) / 62(11) / 269(15)
–0.29(1) / 0.01(1) / 2 / –0.30(1) / 75(26) / 6(19)
–0.30(1) / 3 / –0.31(1) / 31(18) / 121(51)
B
298 K / G / 2.00319(1) / 0.00077(1) / –0.00469(1) / 1 / 2.03505(1) / 22.1(2) / 247.4(2) / 576
0.161
2.01097(1) / –0.00893(1) / 2 / 2.00773(1) / 71.1(2) / 100.7(2)
2.03095(1) / 3 / 2.00234(1) / 78.6(2) / 6.8(2)
27Al
A/geβe
(mT) / –0.29(1) / 0.005(9) / –0.002(8) / 1 / –0.226(9) / 67(7) / 265(8)
–0.23(1) / –0.026(7) / 2 / –0.299(8) / 82(57) / 358(65)
–0.289(9) / 3 / –0.300(8) / 23(62) / 106(43)
B'
298 K / G / 2.00282(2) / 0.00042(2) / –0.00348(1) / 1 / 2.03555(2) / 22.5(2) / 254.5(2) / 322
0.213
2.01142(2) / –0.00960(1) / 2 / 2.00771(2) / 69.5(2) / 100.5(2)
2.03131(2) / 3 / 2.00231(2) / 80.9(2) / 7.1(2)
27Al
A/geβe
(mT) / –0.34(2) / 0.01(1) / –0.00(1) / 1 / –0.27(2) / 62(10) / 264(9)
–0.29(2) / –0.03(1) / 2 / –0.35(1) / 73(9) / 3(20)
–0.34(1) / 3 / –0.36(2) / 33(9) / 120(9)

Spin Hamiltonian parameters are for a set related to those in part II (Pan et al. 2008) by a rotation of φ=120º. θk and φk (or equivalent 180 θk and 180+ φk) are tilting angles relative to crystallographic c and a axes, respectively. DP is the number of line-position data points used in optimization. RMSD is the root-mean-sum of squares of the weighted difference between the calculated and observed line-position data.