Theoretical investigation of the noble gas molecular anions XAuNgX− and HAuNgX− (X = F, Cl, Br; Ng = Xe, Kr, Ar)
Guoqun Liu* a,Yanli Zhang b, Xue Bai a, Fang He a, Xianxi Zhang* c, Zhixin Wang a, and Wangxi Zhang a
a School of Materials and Chemical Engineering, Zhongyuan University of Technology, Zhongyuan Road 41#, Zhengzhou 450007, P. R. China
Tel: +86-371-62506691 Fax: +86-371-62506687 E-mail:
b College of Chemistry and Chemical Engineering, HenanUniversity, Kaifeng 475001, P. R. China
c School of Chemistry and Chemical Engineering, LiaochengUniversity, Liaocheng 252059, P. R. China
E-mail:
The Supporting Information consists of the following two parts:
1) Results calculated with the smaller valence basis set of the gold atom, which are presented in the Tables S1~S18 and Figures S1~S6.
2) Computational difficulties of the investigated species, which are presented following the first part.
1
Table S1 Computed bond lengths (Å)and the T1 diagnostic of the equilibrium structure of XAuXeX− and HAuXeX− (X = F, Cl, Br)
Methods / r(X(H)−Au) / r(Au−Xe) / r(Xe−X) / T1 DiagnosticFAuXeF− / MP2 / 2.000 / 2.592 / 2.504 / 0.0204
CCSD(T) / 2.008 / 2.623 / 2.507 / 0.0207
HAuXeF− / MP2 / 1.559 / 2.733 / 2.625 / 0.0183
CCSD(T) / 1.570 / 2.769 / 2.627 / 0.0186
HAuXeCl− / MP2 / 1.552 / 2.761 / 3.328 / 0.0162
CCSD(T) / 1.561 / 2.804 / 3.357 / 0.0165
HAuXeBr− / MP2 / 1.551 / 2.769 / 3.518 / 0.0145
CCSD(T) / 1.559 / 2.812 / 3.559 / 0.0147
ClAuXeCl− / MP2 / 2.292 / 2.627 / 3.183 / 0.0164
CCSD(T) / 2.311 / 2.659 / 3.204 / 0.0167
BrAuXeBr− / MP2 / 2.420 / 2.641 / 3.370 / 0.0137
CCSD(T) / 2.444 / 2.674 / 3.401 / 0.0140
Table S2 Computed bond lengths (Å) and the T1 diagnostic of the equilibrium structure of XAuKrX− and HAuKrX− (X = F, Cl, Br)
Methods / r(X(H)−Au) / r(Au−Kr) / r(Kr−X) / T1 DiagnosticFAuKrF− / MP2 / 1.983 / 2.509 / 2.516 / 0.0187
CCSD(T) / 1.992 / 2.534 / 2.507 / 0.0189
HAuKrF− / MP2 / 1.544 / 2.655 / 2.638 / 0.0164
CCSD(T) / 1.554 / 2.684 / 2.633 / 0.0166
HAuKrCl− / MP2 / 1.539 / 2.695 / 3.287 / 0.0146
CCSD(T) / 1.548 / 2.730 / 3.309 / 0.0148
HAuKrBr− / MP2 / 1.539 / 2.705 / 3.467 / 0.0134
CCSD(T) / 1.548 / 2.740 / 3.498 / 0.0136
ClAuKrCl− / MP2 / 2.276 / 2.562 / 3.146 / 0.0151
CCSD(T) / 2.295 / 2.588 / 3.148 / 0.0153
BrAuKrBr−a / MP2 / 2.407 / 2.580 / 3.328 / 0.0130
a For the BrAuKrBr− molecule, the CCSD(T) calculations failed to locate a stationary point on the potential energy surface.
Table S3 Computed bond lengths (Å) and the T1 diagnostic of the equilibrium structure of XAuArX− and HAuArX− (X = F, Cl, Br)
Methods / r(X(H)−Au) / r(Au−Ar) / r(Ar−X) / T1 DiagnosticFAuArF− / MP2 / 1.974 / 2.403 / 2.526 / 0.0203
CCSD(T) / 1.982 / 2.425 / 2.514 / 0.0206
HAuArF− / MP2 / 1.535 / 2.562 / 2.655 / 0.0182
CCSD(T) / 1.544 / 2.591 / 2.651 / 0.0184
HAuArCl− / MP2 / 1.532 / 2.608 / 3.278 / 0.0164
CCSD(T) / 1.541 / 2.643 / 3.300 / 0.0166
HAuArBr− / MP2 / 1.532 / 2.619 / 3.455 / 0.0147
CCSD(T) / 1.541 / 2.648 / 3.474 / 0.0148
ClAuArCl− / MP2 / 2.267 / 2.470 / 3.140 / 0.0165
CCSD(T) / 2.285 / 2.495 / 3.153 / 0.0167
BrAuArBr−a / MP2 / 2.399 / 2.496 / 3.314 / 0.0138
a For the BrAuArBr− molecule, the CCSD(T) calculations failed to locate a stationary point on the potential energy surface.
Table S4 Computed bond lengths (Å) of the equilibrium structure of X(H)AuXe and AuXeX (X = F, Cl, Br)
Methods / r(X(H)−Au) / r(Au−Xe) a / r(Au−Xe) b / r(Xe−X)FAuXe + AuXeF / MP2 / 1.962 / 2.641 / 2.605 / 2.180
CCSD(T) / 1.969 / 2.676 / 2.645 / 2.214
HAuXe + AuXeF / MP2 / 1.538 / 2.871 / 2.605 / 2.180
CCSD(T) / 1.546 / 2.935 / 2.645 / 2.214
HAuXe + AuXeCl / MP2 / 1.538 / 2.871 / 2.643 / 2.685
CCSD(T) / 1.546 / 2.935 / 2.717 / 2.766
HAuXe + AuXeBr / MP2 / 1.538 / 2.871 / 2.665 / 2.852
CCSD(T) / 1.546 / 2.935 / - c / - c
ClAuXe + AuXeCl / MP2 / 2.261 / 2.683 / 2.643 / 2.685
CCSD(T) / 2.279 / 2.722 / 2.717 / 2.766
BrAuXe + AuXeBr / MP2 / 2.392 / 2.700 / 2.665 / 2.852
CCSD(T) / 2.411 / 2.741 / - c / - c
a The Au−Xe bond length of the X(H)AuXe molecule.
b The Au−Xe bond length of the AuXeX molecule.
c For AuXeBr, the CCSD(T) calculations failed to locate a stationary point within the default 23 optimization steps.
Table S5 Computed bond lengths (Å) of the equilibrium structure of X(H)AuKr and AuKrX (X = F, Cl, Br)
Methods / r(X(H)−Au) / r(Au−Kr) a / r(Au−Kr) b / r(Kr−X)FAuKr + AuKrF / MP2 / 1.955 / 2.605 / 2.522 / 2.153
CCSD(T) / 1.963 / 2.635 / - c / - c
HAuKr + AuKrF / MP2 / 1.529 / 2.845 / 2.522 / 2.153
CCSD(T) / 1.539 / 2.904 / - c / - c
HAuKr + AuKrCl / MP2 / 1.529 / 2.845 / 2.594 / 2.634
CCSD(T) / 1.539 / 2.904 / - c / - c
HAuKr + AuKrBr / MP2 / 1.529 / 2.845 / 2.645 / 2.780
CCSD(T) / 1.539 / 2.904 / - c / - c
ClAuKr + AuKrCl / MP2 / 2.255 / 2.661 / 2.594 / 2.634
CCSD(T) / 2.272 / 2.694 / - c / - c
BrAuKr + AuKrBr / MP2 / 2.386 / 2.685 / 2.645 / 2.780
CCSD(T) / 2.405 / 2.714 / - c / - c
a The Au−Kr bond length of the X(H)AuKr molecule.
b The Au−Kr bond length of the AuKrX molecule.
c At the CCSD(T) level of theory, the AuKrF, AuKrCl, and AuKrBr molecules dissociate into atomic fragments during the geometry optimizations.
Table S6 Computed bond lengths (Å) of the equilibrium structure of X(H)AuAr and AuArX (X = F, Cl, Br)
Methods / r(X(H)−Au) / r(Au−Ar) a / r(Au−Ar) b / r(Ar−X)FAuAr + AuArF / MP2 / 1.954 / 2.536 / 2.424 / 2.137
CCSD(T) / 1.961 / 2.568 / - c / - c
HAuAr + AuArF / MP2 / 1.525 / 2.801 / 2.424 / 2.137
CCSD(T) / 1.534 / 2.871 / - c / - c
HAuAr + AuArCl / MP2 / 1.525 / 2.801 / 2.554 / 2.598
CCSD(T) / 1.534 / 2.871 / - c / - c
HAuAr + AuArBr / MP2 / 1.525 / 2.801 / 2.659 / 2.741
CCSD(T) / 1.534 / 2.871 / - c / - c
ClAuAr + AuArCl / MP2 / 2.251 / 2.609 / 2.554 / 2.598
CCSD(T) / 2.267 / 2.647 / - c / - c
BrAuAr + AuArBr / MP2 / 2.383 / 2.648 / 2.659 / 2.741
CCSD(T) / 2.403 / 2.679 / - c / - c
a The Au−Ar bond length of the X(H)AuAr molecule.
b The Au−Ar bond length of the AuArX molecule.
c At the CCSD(T) level of theory, the AuArF, AuArCl, and AuArBr molecules dissociate into atomic fragments during the geometry optimizations.
Table S7 Mulliken (NBO) atomic charges of the equilibrium structure of XAuXeX− and HAuXeX− (X = F, Cl, Br) computed at the MP2 level of theory a
q(X(H)) / q(Au) / q(Xe) / q(X) / μ/DFAuXeF− / -0.554
(-0.746) / 0.020
(0.325) / 0.356
(0.366) / -0.821
(-0.945) / 6.11
HAuXeF− / -0.388
(-0.295) / -0.013
(-0.014) / 0.263
(0.276) / -0.862
(-0.968) / 10.13
HAuXeCl− / -0.349
(-0.270) / 0.029
(0.017) / 0.252
(0.234) / -0.931
(-0.982) / 13.63
HAuXeBr− / -0.342
(-0.265) / 0.025
(0.023) / 0.280
(0.224) / -0.963
(-0.983) / 12.35
ClAuXeCl− / -0.769
(-0.584) / 0.383
(0.218) / 0.289
(0.328) / -0.903
(-0.962) / 10.21
BrAuXeBr− / -0.591
(-0.539) / 0.196
(0.183) / 0.336
(0.323) / -0.941
(-0.967) / 10.75
a The MP2 rather than the SCF density was used to compute the properties.
Table S8 Mulliken (NBO) atomic charges of the equilibrium structure of XAuKrX− and HAuKrX− (X = F, Cl, Br) computed at the MP2 level of theory a
q(X(H)) / q(Au) / q(Kr) / q(X) / μ/DFAuKrF− / -0.536
(-0.735) / 0.305
(0.456) / 0.112
(0.248) / -0.881
(-0.968) / 9.08
HAuKrF− / -0.316
(-0.267) / 0.147
(0.072) / 0.081
(0.178) / -0.912
(-0.983) / 12.93
HAuKrCl− / -0.283
(-0.246) / 0.132
(0.086) / 0.101
(0.149) / -0.951
(-0.990) / 15.55
HAuKrBr− / -0.275
(-0.241) / 0.129
(0.089) / 0.130
(0.142) / -0.985
(-0.991) / 13.84
ClAuKrCl− / -0.651
(-0.581) / 0.472
(0.343) / 0.106
(0.217) / -0.928
(-0.978) / 12.57
BrAuKrBr− / -0.563
(-0.534) / 0.386
(0.306) / 0.144
(0.208) / -0.968
(-0.980) / 12.92
a The MP2 rather than the SCF density was used to compute the properties.
Table S9 Mulliken (NBO) atomic charges of the equilibrium structure of XAuArX− and HAuArX− (X = F, Cl, Br) computed at the MP2 level of theory a
q(X(H)) / q(Au) / q(Ar) / q(X) / μ/DFAuArF− / -0.535
(-0.729) / 0.256
(0.528) / 0.196
(0.184) / -0.918
(-0.984) / 11.46
HAuArF− / -0.323
(-0.251) / 0.121
(0.114) / 0.142
(0.130) / -0.940
(-0.994) / 15.23
HAuArCl− / -0.294
(-0.232) / 0.109
(0.120) / 0.167
(0.107) / -0.982
(-0.995) / 17.17
HAuArBr− / -0.287
(-0.228) / 0.118
(0.121) / 0.157
(0.102) / -0.988
(-0.996) / 14.93
ClAuArCl− / -0.751
(-0.579) / 0.538
(0.409) / 0.183
(0.158) / -0.969
(-0.989) / 14.55
BrAuArBr− / -0.588
(-0.536) / 0.376
(0.377) / 0.185
(0.149) / -0.973
(-0.990) / 14.60
a The MP2 rather than the SCF density was used to compute the properties.
Table S10 Computed harmonic vibrational frequencies (cm-1) and infrared intensities (km/mol) of the equilibrium structure of XAuXeX− and HAuXeX− (X = F, Cl, Br)
Methods / ν(X(H)−Au) / ν(Au−Xe) / ν(Xe−X)FAuXeF− / MP2 / 508.9/107 / 159.3/19 / 247.4/193
CCSD(T) / 499.3 / 151.5 / 247.2
HAuXeF− / MP2 / 2237.7/255 / 123.8/28 / 212.0/134
CCSD(T) / 2158.0 / 118.0 / 211.8
HAuXeCl− / MP2 / 2267.9/205 / 142.2/11 / 89.0/43
CCSD(T) / 2193.8 / 135.6 / 85.2
HAuXeBr− / MP2 / 2269.5/202 / 131.5/1 / 61.9/21
CCSD(T) / 2198.5 / 123.9 / 59.3
ClAuXeCl− / MP2 / 346.2/44 / 170.6/24 / 107.9/54
CCSD(T) / 334.3 / 163.2 / 105.2
BrAuXeBr− / MP2 / 246.8/20 / 152.5/9 / 72.2/26
CCSD(T) / 236.1 / 144.7 / 70.2
Table S11 Computed harmonic vibrational frequencies (cm-1) and infrared intensities (km/mol) of the equilibrium structure of XAuKrX− and HAuKrX− (X = F, Cl, Br)
Methods / ν(X(H)−Au) / ν(Au−Kr) / ν(Kr−X)FAuKrF− / MP2 / 526.1/93 / 155.6/52 / 251.0/94
CCSD(T) / 514.9 / 152.5 / 250.4
HAuKrF− / MP2 / 2290.9/164 / 120.6/51 / 210.5/61
CCSD(T) / 2215.1 / 117.8 / 210.6
HAuKrCl− / MP2 / 2307.1/136 / 151.8/3 / 79.7/40
CCSD(T) / 2234.1 / 146.0 / 77.0
HAuKrBr− / MP2 / 2309.4/135 / 141.6/0 / 54.7/17
CCSD(T) / 2235.9 / 135.2 / 52.8
ClAuKrCl− / MP2 / 355.5/37 / 185.5/9 / 96.8/47
CCSD(T) / 343.6 / 180.6 / 96.8
BrAuKrBr− a / MP2 / 253.0/19 / 166.0/3 / 63.9/21
a For the BrAuKrBr− molecule, the CCSD(T) calculations failed to locate a stationary point on the potential energy surface.
Table S12 Computed harmonic vibrational frequencies (cm-1) and infrared intensities (km/mol) of the equilibrium structure of XAuArX− and HAuArX− (X = F, Cl, Br)
Methods / ν(X(H)−Au) / ν(Au−Ar) / ν(Ar−X)FAuArF− / MP2 / 534.1/83 / 288.4/28 / 145.9/73
CCSD(T) / 524.71 / 284.0 / 146.4
HAuArF− / MP2 / 2327.9/118 / 233.3/13 / 115.0/69
CCSD(T) / 2254.4 / 229.6 / 112.9
HAuArCl− / MP2 / 2334.7/103 / 184.5/0 / 71.0/36
CCSD(T) / 2262.8 / 176.8 / 68.6
HAuArBr− / MP2 / 2334.4/102 / 173.9/1 / 47.9/14
CCSD(T) / 2263.6 / 168.7 / 47.2
ClAuArCl− / MP2 / 361.3/33 / 226.7/2 / 86.4/40
CCSD(T) / 349.4 / 220.2 / 85.5
BrAuArBr− a / MP2 / 258.5/18 / 202.6/1 / 56.2/17
a For the BrAuArBr− molecule, the CCSD(T) calculations failed to locate a stationary point on the potential energy surface.
1
Table S13Computed bond lengths (Å) and angles (º) and the T1 diagnostic of the bending transition state of XAuXeX− and HAuXeX− (X = F, Cl, Br)
Methods / r(X(H)−Au) / r(Au−Xe) / r(Xe−X) / (AuXeX) / (X(H)AuXe) / T1 diagnosticFAuXeF− / MP2 / 2.008 / 2.664 / 2.735 / 78.0 / 158.6 / 0.0204
CCSD(T) / 2.000 / 2.650 / 2.722 / 87.4 / 180.0 / 0.0203
HAuXeF− / MP2 / 1.548 / 2.829 / 2.790 / 82.9 / 166.4 / 0.0186
CCSD(T) / 1.557 / 2.839 / 2.785 / 87.5 / 180.0 / 0.0187
HAuXeCl− a / MP2 / 1.546 / 2.903 / 3.467 / 79.7 / 161.3 / 0.0169
HAuXeBr− / MP2 / 1.545 / 2.914 / 3.647 / 79.0 / 161.1 / 0.0152
CCSD(T) / 1.553 / 2.890 / 3.691 / 80.5 / 180.0 / 0.0152
ClAuXeCl− a / MP2 / 2.297 / 2.703 / 3.384 / 81.1 / 161.1 / 0.0160
BrAuXeBr−a / MP2 / 2.425 / 2.715 / 3.569 / 82.7 / 161.4 / 0.0133
aThe CCSD(T) calculations failed to locate the bending transition structure.
Table S14 Computed bond lengths (Å) and angles (º) and the T1 diagnostic of the bending transition state of XAuKrX− and HAuKrX− (X = F, Cl, Br)
Methods / r(X(H)−Au) / r(Au−Kr) / r(Kr−X) / (AuKrX) / (X(H)AuKr) / T1 diagnosticFAuKrF− a / MP2 / 1.984 / 2.560 / 2.706 / 95.5 / 175.5 / 0.0183
HAuKrF− a / MP2 / 1.538 / 2.732 / 2.774 / 97.8 / 174.7 / 0.0165
HAuKrCl− a / MP2 / 1.536 / 2.772 / 3.393 / 96.3 / 173.5 / 0.0149
HAuKrBr− a / MP2 / 1.536 / 2.782 / 3.567 / 95.4 / 173.3 / 0.0137
ClAuKrCl− a / MP2 / 2.278 / 2.614 / 3.302 / 99.7 / 173.6 / 0.0147
BrAuKrBr− b / MP2 / 2.408 / 2.632 / 3.473 / 100.8 / 173.1 / 0.0127
a The CCSD(T) calculations failed to locate the bending transition structure.
b The transition structure search was not performed at the CCSD(T) level.
Table S15 Computed bond lengths (Å) and angles (º) and the T1 diagnostic of the bending transition state of XAuArX− and HAuArX− (X = F, Cl, Br)
Methods / r(X(H)−Au) / r(Au−Ar) / r(Ar−X) / (AuArX) / (X(H)AuAr) / T1 diagnosticFAuArF− / MP2 / 1.979 / 2.453 / 2.655 / 106.1 / 175.7 / 0.0201
CCSD(T) / 1.985 / 2.472 / 2.646 / 104.7 / 180.0 / 0.0203
HAuArF− a / MP2 / 1.533 / 2.629 / 2.741 / 107.5 / 174.9 / 0.0184
HAuArCl− a / MP2 / 1.531 / 2.676 / 3.338 / 106.7 / 173.9 / 0.0167
HAuArBr− a / MP2 / 1.531 / 2.689 / 3.511 / 105.7 / 173.7 / 0.0150
ClAuArCl− a / MP2 / 2.270 / 2.517 / 3.228 / 111.1 / 174.5 / 0.0163
BrAuArBr− b / MP2 / 2.402 / 2.543 / 3.398 / 112.7 / 174.1 / 0.0136
a The CCSD(T) calculations failed to locate the bending transition structure.
b The transition structure search was not performed at the CCSD(T) level.
1
Table S16ZPE-corrected relative energies (kcal/mol)of XAuXeX− and HAuXeX− (X = F, Cl, Br)a
Methods / X(H)AuX− + Xe / X(H)AuXe + X− / X(H)− + AuXeX / X(H) + Au + Xe + X− / X(H)− + Au + Xe + X / Dissociation barrierFAuXeF− / MP2 / -34.57 / 36.88 / 98.03 / 125.77 / 125.77 / 12.92
CCSD(T) / -35.18 / 37.26 / 94.89 / 118.73 / 118.73 / 12.19
HAuXeF− / MP2 / -32.23 / 25.25 / 139.89 / 95.17 / 167.63 / 7.64
CCSD(T) / -32.47 / 24.99 / 133.12 / 98.56 / 156.96 / 7.56
HAuXeCl− / MP2 / -28.44 / 16.39 / 151.61 / 86.31 / 160.27 / 5.35
CCSD(T) / -28.22 / 15.70 / 143.66 / 89.27 / 153.19 / - b
HAuXeBr− / MP2 / -26.25 / 14.75 / 153.06 / 84.67 / 156.76 / 5.03
CCSD(T) / -26.09 / 13.94 / - c / 87.51 / 150.80 / 4.94
ClAuXeCl− / MP2 / -35.74 / 24.53 / 94.79 / 103.45 / 103.45 / 7.80
CCSD(T) / -35.92 / 24.11 / 89.29 / 98.81 / 98.81 / - b
BrAuXeBr− / MP2 / -34.49 / 22.13 / 91.77 / 95.47 / 95.47 / 7.02
CCSD(T) / -34.69 / - c / - c / 91.79 / 91.79 / -b
aRelative energies of the dissociation limits X(H)AuX− + Xe, X(H)AuXe + X−, X(H)− + AuXeX, X(H) + Au + Xe + X−, X(H)− + Au + Xe + X, and the bending transition state with respect to the molecular anions X(H)AuXeX−.
bThe CCSD(T) calculations failed to locate the bending transition structure.
c For AuXeBr and BrAuXe, the CCSD(T) calculations failed to locate a stationary point.
Table S17ZPE-corrected relative energies (kcal/mol) of XAuKrX− and HAuKrX− (X = F, Cl, Br)a
Methods / X(H)AuX− + Kr / X(H)AuKr + X− / X(H)− + AuKrX / X(H) + Au + Kr + X− / X(H)− + Au + Kr + X / Dissociation barrierFAuKrF− / MP2 / -48.41 / 29.60 / 109.93 / 111.92 / 111.92 / 7.24
CCSD(T) / -48.21 / 30.15 / - b / 105.70 / 105.70 / -c
HAuKrF− / MP2 / -41.25 / 19.04 / 156.62 / 86.16 / 158.62 / 4.31
CCSD(T) / -40.86 / 18.88 / - b / 90.16 / 148.56 / -c
HAuKrCl− / MP2 / -34.95 / 12.68 / 164.86 / 79.80 / 153.76 / 2.80
CCSD(T) / -34.07 / 12.14 / - b / 83.42 / 147.34 / -c
HAuKrBr− / MP2 / -32.42 / 11.39 / 164.66 / 78.51 / 150.59 / 2.60
CCSD(T) / -31.56 / 10.76 / - b / 82.04 / 145.32 / -c
ClAuKrCl− / MP2 / -46.19 / 19.94 / 104.10 / 93.00 / 93.00 / 3.97
CCSD(T) / -45.52 / 19.70 / - b / 89.21 / 89.21 / -c
BrAuKrBr− / MP2 / -44.39 / 17.83 / 99.63 / 85.56 / 85.56 / 3.44
a Relative energies of the dissociation limits X(H)AuX− + Kr, X(H)AuKr + X−, X(H)− + AuKrX, X(H) + Au + Kr + X−, X(H)− + Au + Kr + X, and the bending transition state with respect to the molecular anions X(H)AuKrX−.
bAt the CCSD(T) level of theory, the AuKrF, AuKrCl, and AuKrBr molecules dissociate into atomic fragments during the geometry optimizations.
c The CCSD(T) calculations failed to locate the bending transition structure.
Table S18 ZPE-corrected relative energies (kcal/mol) of XAuArX− and HAuArX− (X = F, Cl, Br)a
Methods / X(H)AuX− + Ar / X(H)AuAr + X− / X(H)− + AuArX / X(H) + Au + Ar + X− / X(H)− + Au + Ar + X / Dissociation barrierFAuArF− / MP2 / -57.47 / 24.48 / 118.33 / 102.87 / 102.87 / 3.73
CCSD(T) / -57.37 / 24.77 / - b / 96.53 / 96.53 / 3.97
HAuArF− / MP2 / -47.43 / 14.76 / 167.90 / 79.97 / 152.43 / 2.13
CCSD(T) / -47.05 / 14.36 / - b / 83.98 / 142.38 / - c
HAuArCl− / MP2 / -39.31 / 10.23 / 173.39 / 75.44 / 149.40 / 1.39
CCSD(T) / -38.26 / 9.62 / - b / 79.23 / 143.15 / - c
HAuArBr− / MP2 / -36.55 / 9.16 / 171.61 / 74.38 / 146.46 / 1.30
CCSD(T) / -35.50 / 8.49 / - b / 78.10 / 141.39 / - c
ClAuArCl− / MP2 / -52.77 / 16.92 / 110.41 / 86.42 / 86.42 / 1.91
CCSD(T) / -51.98 / 16.61 / - b / 82.75 / 82.75 / - c
BrAuArBr− / MP2 / -50.68 / 15.00 / 104.43 / 79.28 / 79.28 / 1.59
a Relative energies of the dissociation limits X(H)AuX− + Ar, X(H)AuAr + X−, X(H)− + AuArX, X(H) + Au + Ar + X−, X(H)− + Au + Ar + X, and the bending transition state with respect to the molecular anions X(H)AuArX−.
b At the CCSD(T) level of theory, the AuArF, AuArCl, and AuArBr molecules dissociate into atomic fragments during the geometry optimizations.
c The CCSD(T) calculations failed to locate the bending transition structure.
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Figure S1 Relative energies (kcal/mol) of the dissociation limits FAuF− + Ng, FAuNg + F−, F− + AuNgF, F + Au + Ng + F−, and the bending transition state with respect to FAuNgF−(Ng = Xe, Kr, Ar). Both the MP2 values and the CCSD(T) values (in parentheses) were corrected for the ZPE.
Figure S2 Relative energies (kcal/mol) of the dissociation limits HAuF− + Ng, HAuNg + F−, H− + AuNgF, H + Au + Ng + F−, H− + Au + Ng + F,and the bending transition state with respect to HAuNgF−(Ng = Xe, Kr, Ar). Both the MP2 values and the CCSD(T) values (in parentheses) were corrected for the ZPE.
Figure S3 Relative energies (kcal/mol) of the dissociation limits HAuCl− + Ng, HAuNg + Cl−, H− + AuNgCl, H + Au + Ng + Cl−, H− + Au + Ng + Cl,and the bending transition state with respect to HAuNgCl−(Ng = Xe, Kr, Ar). Both the MP2 values and the CCSD(T) values (in parentheses) were corrected for the ZPE.
Figure S4 Relative energies (kcal/mol) of the dissociation limits HAuBr− + Ng, HAuNg + Br−, H− + AuNgBr, H + Au + Ng + Br−, H− + Au + Ng + Br,and the bending transition state with respect to HAuNgBr−(Ng = Xe, Kr, Ar). Both the MP2 values and the CCSD(T) values (in parentheses) were corrected for the ZPE.
Figure S5 Relative energies (kcal/mol) of the dissociation limits ClAuCl− + Ng, ClAuNg + Cl−, Cl− + AuNgCl, Cl + Au + Ng + Cl−, and the bending transition state with respect to ClAuNgCl−(Ng = Xe, Kr, Ar). Both the MP2 values and the CCSD(T) values (in parentheses) were corrected for the ZPE.
FigureS6 Relative energies (kcal/mol) of the dissociation limits BrAuBr− + Ng, BrAuNg + Br−, Br− + AuNgBr, Br + Au + Ng + Br−, and the bending transition state with respect to BrAuNgBr−(Ng = Xe, Kr, Ar). Both the MP2 values and the CCSD(T) values (in parentheses) were corrected for the ZPE.
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Computational difficulties
At the MP2 level of theory, for all of the eighteen molecular anions, whether the smaller or the larger valence basis set of the gold atom was applied, the equilibrium structure was always optimized smoothly to a stationary point with the default GEDIIS (Geometry optimization using Energy-represented Direct Inversion in the Iterative Subspace, [1]) algorithm. At first, when the smaller valence basis set of the gold atom was applied, at the MP2 level of theory, the transition structure of FAuXeF− was optimized using the QST3 (Quadratic Synchronous Transit 3, searching for a transition structure using the STQN (Synchronous Transit-guided Quasi-Newton) method [2,3], requiring the reactant, product, and initial transition structures as input) method. However, the optimizations did not converge into a stationary point within the default 20 optimization steps. It should be pointed out that the initial transition structure of the QST3 optimizations is already a bending structure, which should not depart far from the true transition structure. When the "NoSymmetry" keyword was added in the Route section of the GJF (Gaussian Job File) file, the geometry optimizations converged into a stationary point within 17 steps. Under the "NoSymmetry" constraint, the QST3 optimizations of HAuXeBr−, HAuXeCl−, ClAuXeCl−, and HAuXeF− converged into a stationary point within 9, 17, 19, and 20 steps, respectively, while BrAuXeBr− was eventually optimized into a stationary point within 50 steps! Under such circumstances, it was realized that using the "NoSymmetry" constraint and increasing the maximum number of optimization steps are not the key to overcoming the convergence difficulties.
On the other hand, from the Gaussian 09 Help documentation of the "Opt" keyword, it was learned that, for the optimizations to transition states, some knowledge of the curvature around the saddle point is essential, and the default approximate Hessian must always be improved. Some options have been presented in the Gaussian 09 programs for providing the improved Hessian or force constants. One of the options is "CalcFC", which computes the force constants at the first point. At the MP2 level of theory, when the smaller valence basis set of the gold atom was applied, the transition structure optimizations of all the twelve krypton and argon molecular anions converged smoothly into a stationary point with the "CalcFC" option. At the MP2 level of theory, when the larger valence basis set of the gold atom was applied, the transition structure optimizations of all the eighteen anions converged smoothly into a stationary point with the "CalcFC" option.
At the CCSD(T) level of theory, whether the smaller or the larger valence basis set of the gold atom was applied, the geometry optimizations of the equilibrium structure were performed with the default rational function optimization (RFO) algorithm [4]. When the smaller valence basis set of the gold atom was adopted, sixteen of the eighteen anions (except BrAuKrBr− and BrAuArBr−, see Table S19 for the description of the failure) were optimized successfully to a stationary point within 3~22 steps (Table S19, Column 2). It should be pointed out that, for most of the cases, the geometrical parameters optimized at the MP2 level were taken as the starting point of the CCSD(T) geometry optimizations. For these sixteen molecular anions, in general, when the number of optimization steps is greater than 10, the optimization process will have a common problem, i.e. oscillation. For example, for the optimizations of BrAuXeBr−, from "ITERATION 1" (Step number 1) to "ITERATION 5" (Step number 5), the calculated values of MAXIMUM FORCE, RMSFORCE, MAXIMUMDISPLACEMENT, and RMS DISPLACEMENT become gradually approaching the convergence thresholds (0.000450, 0.000300, 0.001800, and 0.001200, respectively). At the step number 5, the calculated values of the four items are 0.000493, 0.000293, 0.003153, and 0.002098, respectively. However, at the step number 6, the calculated values of the four items are 0.000648, 0.000437, 0.295812, and 0.173205, respectively. Obviously, both the Maximum and RMS displacements become relatively very large suddenly. And then from "ITERATION 6" to "ITERATION 9", the calculated values of the four items become gradually approaching the convergence thresholds. At "ITERATION 10", the four convergence criteria were satisfied and the optimizations terminated successfully. Thus the oscillation appears once in the optimizations of the equilibrium structure of BrAuXeBr−. Similarly, the oscillation appears three times in the optimizations of HAuKrBr−.
When the larger valence basis set of the gold atom was adopted, the most distinct difference from the results obtained with the smaller basis set is that BrAuArBr− was successfully optimized to a stationary point within 21 steps. However, BrAuKrBr− was still unable to be optimized. The problem is similar to that encountered for the smaller valence basis set. Within 2 steps, the optimizations of BrAuKrBr− terminated abnormally with the error message as "UNABLE TO DETERMINE LAMDA IN FmD114". This problem was solved by replacing the defaultRFO algorithm with the Newton-Raphson algorithm during the Berny optimizations.
At the CCSD(T) level of theory, geometry optimizations of the transition structure were performed with the default partitioned-rational function optimization (P-RFO) algorithm [4]. As shown in Table S19 (Columns 4 and 5), whether the smaller or the larger valence basis set of the gold atom was applied, for many of the eighteen anions, the geometry optimizations have encountered difficulties. When the smaller valence basis set of the gold atom was applied, only four of the eighteen anions (i.e. FAuXeF−, HAuXeF−, HAuXeBr−, and FAuArF−) were optimized successfully to a stationary point. When the larger valence basis set was adopted, at least six of the eighteen anions (i.e. FAuXeF−, HAuXeF−, HAuXeCl−, HAuXeBr−, ClAuXeCl−, and HAuArF−) were optimized to a stationary point. In particular, HAuXeCl−, ClAuXeCl−, and HAuArF− were also optimized to a stationary point. However, FAuArF− was not optimized to a stationary point within the default 25 steps.
At the CCSD(T) level of theory, why do the geometry optimizations of the transition structure, irrespective of the application of the smaller or the larger valence basis set of the gold atom, have so many convergence difficulties (see Table S19)? If the equilibrium and, in particular, the transition structure of the molecular anions have considerable multi-configuration character, the geometry optimizations will probably encounter convergence difficulties. In order to verify this conjecture, the T1 diagnostics [5] of the equilibrium and transition structure of the molecular anions have been calculated. The T1 diagnostics of the structures optimized with the larger valence basis set of the gold atom are presented in Figures 1~6. The T1 diagnostics of the structures optimized with the smaller valence basis set of the gold atom are presented in the Supporting Information (Tables S1~S3 and S13~S15).
As shown in Figures 1~6, at the CCSD(T) level of theory, the equilibrium structure of FAuXeF− has the largest T1 diagnostic (0.0202), while the equilibrium structure of HAuKrBr− has the smallest T1 diagnostic (0.0138). For the same molecular anion, the T1 diagnostic is always larger for the structure optimized at the CCSD(T) level than for that optimized at the MP2 level. For example, the T1 diagnostic of the equilibrium structure of FAuXeF− optimized at the CCSD(T) level is 0.0202, while the T1 diagnostic of the structure optimized at the MP2 level is 0.0194. These indicate that both the MP2 and CCSD(T) methods are probably adequate to describe the equilibrium and transition structure of the investigated molecular anions. As shown in Tables S1~S3 and S13~S15, this is also the case when the smaller valence basis set of the gold atom was applied.
It should be pointed out that the T1 diagnostics presented in Figures 1~6 and Tables S1~S3 and S13~S15 were calculated from the optimized stationary points. What the T1 diagnostic is if the CCSD(T) optimizations are not converged to a stationary point? In order to find the answer to this question, at the CCSD(T) level of theory, when the larger valence basis set of the gold atom was applied, the T1 diagnostic has been calculated after every optimization step for all of the molecular anions investigated. It was found that all the calculated T1 diagnostics are not greater than 0.0202. For example, the T1 diagnostic of the transition structure of FAuArF− was calculated to range from 0.0190 to 0.0198 within the default 25 optimization steps.
Tentatively, the convergence difficulties may be due to the weak intramolecular interaction nature of the investigated anions. As will be shown in Section 3, in X(H)AuNgX−, X(H)AuNg is interacting weakly with X−; meanwhile, in X(H)AuNg, X(H)Au is also interacting weakly with Ng. In other words, the anion X(H)AuNgX− is generally a weak-interaction system. As we know, the geometry optimizations of a weak-interaction system or a system with low-frequency vibrational modes are usually not smooth. At the MP2 level of theory, the convergence difficulties of the transition structure optimizations were overcome by using the "CalcFC" option. Unfortunately, the "CalcFC" option is available for the MP2 method but not available for the CCSD(T) method. In addition, the "ReadFC" option of the "Opt" keyword, which can extract force constants from a checkpoint file of an MP2 frequency calculations, is also not successful in combination with the CCSD(T) method.