756203000000 1480607000000 0110636000000 H 2292946460000 1392500770000

756203000000 1480607000000 0110636000000 h

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-1.756203000000 -1.480607000000 -0.110636000000 H -2.292946460000 1.392500770000 0.013851220000 H -2.211824870000 0.489597950000 -1.344402240000 H -0.878517500000 0.705429620000 -0.426592450000 C 0.939686306881 -0.620510570333 -0.380590381131 H 0.286405306881 -1.236880570333 0.242747618869 H 1.975207306881 -0.917323570333 -0.198589381131 H 0.709229306881 -0.790617570333 -1.435542381131 O 0.831296666881 0.764539269667 -0.041785681131 S14
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S2.2: Charged Water (CHW9) Table S2: Interaction energies in kcal/mol for the CHW9 data set. ID Complex E 1 1 Water ... 1 Hydronium -33.93 2 2 Water ... 1 Hydronium -57.42 3 2 Water ... 1 Hydronium -57.37 4 3 Water ... 1 Hydronium -77.14 5 3 Water ... 1 Hydronium -77.08 6 3 Water ... 1 Hydronium -73.06 7 3 Water ... 1 Hydronium -72.69 8 3 Water ... 1 Hydronium -73.13 S15
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CHW9/01: 1 Water, 1 Hydronium 7 O 1.6130818479 0.9577977382 3.8060481114 H 1.8692950753 1.4847112432 4.5750813314 H 1.6328918384 1.5223814517 3.0207483336 O 2.4646947897 -1.2462689662 3.4720602043 H 3.3581971853 -1.4875410872 3.7515926317 H 1.8574942836 -1.9568808991 3.7214197016 H 2.0873672799 -0.1322535806 3.6833121859 S16
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CHW9/02: 2 Water, 1 Hydronium 10 O 1.5291752404 -0.1470902635 1.5890245371 H 1.0588273488 0.5519950471 1.1220747256 H 1.9016793768 0.2549460675 2.3806251525 O 2.3463345459 -4.1370806378 0.4289564820 H 3.2950906265 -4.1728516787 0.5873288414 H 2.1964485260 -4.5106547429 -0.4459576100 O 0.7396795832 -2.4889330600 1.3457929899 H 1.4557977884 -3.1420618863 0.9718586951 H 0.3048362999 -2.8565130072 2.1258365085 H 1.0656783641 -1.5181567383 1.5041697778 S17
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CHW9/03: 2 Water, 1 Hydronium 10 O -3.3464825968 3.3313553677 2.4986072452 H -3.1294232785 4.2620714531 2.3834228523 H -3.0480138923 3.0794274674 3.3777687516 O -2.3622190435 0.0912093202 -0.2304965740 H -1.8868828394 0.1687275592 -1.0639480322 H -1.9313767498 -0.6041509528 0.2757610788 O -3.8741282780 1.8998087396 0.5424755697 H -3.2206470296 1.1436233814 0.2756008845 H -4.7822541990 1.5754736966 0.6003035790 H -3.6180350930 2.4529044676 1.3783525450 S18
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CHW9/04: 3 Water, 1 Hydronium 13 O 2.8748226451 -0.2572345142 -0.6795479135 H 3.2082739858 -1.1355973471 -0.4710768955 H 3.5915547668 0.3511201769 -0.4755761137 O -0.2003528751 1.8829551664 1.3557887524 H -0.6994014095 1.5869524947 2.1235804728 H -0.4295275027 2.8093541201 1.2346734430 O -0.7591761087 0.6889655650 -2.6990673014 H -1.4165323020 0.0711028281 -3.0341785228 H -0.3572384016 1.0913483560 -3.4749144238 O 0.3823289725 0.2138304976 -0.4747505796 H 0.1293253016 0.9067169620 0.2160096336 H -0.0241344149 0.4063184293 -1.3797299621 H 1.3809255428 0.0670041654 -0.5247418895 S19
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CHW9/05: 3 Water, 1 Hydronium 13 O -0.0639189843 1.7390005297 0.6420588142 H -0.9131637363 1.4411209241 0.3041629172 H 0.0705259436 1.2861147397 1.4786773337 O 3.5329984427 2.1555018468 -1.7960610284 H 3.5944127384 2.0774958222 -2.7530464208 H 4.1317552246 1.4943368873 -1.4363193644 O 1.9619039550 5.4040659438 0.4995464184 H 2.7964270246 5.6774574718 0.8910548905 H 1.5273734683 6.2131287244 0.2115134384 O 1.4873545672 3.2245176198 -0.7186627650 H 2.2926038157 2.7610266404 -1.1096107630 H 0.9141474568 2.6162308896 -0.1547986024 H 1.7245930836 4.0824846603 -0.2386116682 S20
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CHW9/06: 3 Water, 1 Hydronium 13 O 0.0008745896 0.2552148196 -0.6190886732 H 0.1363742932 -0.2768320600 0.1742754767 H 0.1426801567 -0.3639458369 -1.3458634289 O -2.2714351623 1.9079576936 -0.9616827206 H -3.0787156897 1.8072939971 -0.4477307576 H -1.6880040268 1.1584824826 -0.7530614314 O 1.2675403985 2.7583486779 -0.9961859678 H 1.0922619929 1.8265438169 -0.7802109151 H 2.0417402369 3.0377032703 -0.4976307524 O -0.8922431476 3.9541546591 -1.0588194956 H -1.0205842522 4.4551727309 -1.8753176537 H -1.5607948650 3.1486077823 -1.0124574539 H 0.0700234758 3.5404744666 -1.0283439266 S21
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CHW9/07: 3 Water, 1 Hydronium 13 O -3.4884154492 3.0851398384 -2.0801865315 H -4.4192120446 3.1274547557 -1.8293663446 H -3.2579946641 3.9980856174 -2.2913085215 O -2.8434945504 0.9773999385 -3.8205121640 H -3.1531005206 1.8161365563 -3.4336150125 H -2.6700604582 1.1273630694 -4.7553223622 O -1.4777093138 1.7583568994 -0.5752587778 H -2.2352299225 2.3261475216 -0.7857785469 H -1.3269491999 1.7880008400 0.3734200839 O -1.2063414442 -0.0185151316 -2.2799954233 H -1.4352338763 -0.9205150768 -2.0206092098 H -1.8798707749 0.3465706759 -3.0068542936 H -1.2727922812 0.6284588960 -1.4725746962 S22
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CHW9/08: 3 Water, 1 Hydronium 13 O 2.1715892215 0.0668682826 1.0276979419 H 2.4300810064 0.3645249888 1.9044305156 H 1.9902778673 0.8646509967 0.5223571476 O 1.2709013232 -2.2321374320 0.2926696613 H 0.4749722602 -2.4693456668 0.7789932588 H 1.6015237968 -1.3459607549 0.6206131530 O 3.0598365465 -5.0631715010 -2.3207116496 H 3.8006353738 -4.9372190975 -2.9207845265 H 2.3464857399 -5.4270224446 -2.8523664639 O 2.9580698508 -3.8811424345 -0.0492524948 H 3.0859364642 -4.5496650483 0.6320392507 H 2.9520830828 -4.3292507795 -0.9481455571 H 2.1038402666 -3.1019529089 0.1596971630 S23
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CHW9/09: 1 Water 3 O 1.5983771345 1.0106524941 3.8250480251 H 1.8865611993 1.5638492471 4.5535887940 H 1.5803917662 1.6135116588 3.0793364809 S24
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CHW9/10: 1 Hydronium 4 O 2.4781953058 -1.2825558401 3.4277764063 H 3.3573087822 -1.4257622798 3.8321417449 H 1.8345452337 -1.9603189285 3.7162407697 H 2.1476428784 -0.3774304516 3.5961302791 S25
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S2.3: Water ions - (W2) Table S3: Interaction energies in kcal/mol for the W2 × 8 dataset as a function of displace- ment. ID Description E(0.90) E(0.95) E(1.00) E(1.05) E(1.10) E(1.25) E(1.50) E(2.00) 01 Hydronium (H3O+) ... Water (H2O) -35.95 -49.13 -52.13 -50.36 -46.48 -32.74 -17.34 -6.82 02 Hydroxide (OH-) ... Water (H2O) -35.47 -46.21 -48.84 -47.67 -44.76 -33.73 -19.74 -7.97 S26
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W2/01: 1 Water ... 1 Hydronium 7 O 2.463749936600 -1.248474117700 3.472682704300 H 3.361306187200 -1.487701840400 3.745796353200 H 1.858758547600 -1.960988341400 3.727563261100 H 2.084815376100 -0.129844211300 3.682921776900 O 1.610283063300 0.959261683100 3.803889099200 H 1.864030609400 1.482539350500 4.578171657000 H 1.640078579900 1.527153377300 3.019237648300 W2/02: 1 Water ... 1 Hydroxide 5 O -1.154095576700 0.207473003400 0.000000000000 H -1.483012527500 -0.694311688900 0.000000000000 O 1.250806942700 -0.204302672300 0.000000000000 H 1.579546804700 0.697542978000 0.000000000000 H 0.048444426800 0.001519499700 0.000000000000 S27
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S3: RMSD values Table S4: S22 error in interaction energy for various methods, compared to a CCSD(T) reference. All values are in kcal/mol, except r and r 2 which are unitless. *Reference energies are taken from Takatani et al. in Ref. S5. E Error ID Complex Ref.* PM6 PM6- D3H4 PBE/ 6-31G(d) PBE-D3/ 6-31G(d) PBE/ def2-QZVP PBE-D3/ def2-QZVP 1 Ammonia dimer -3.17 0.86 -0.61 -2.17 -2.76 0.18 -0.40 2 Water dimer -5.02 1.08 0.16 -2.89 -3.30 -0.28 -0.70 3 Formic acid dimer -18.61 7.48 0.44 -3.90 -5.44 0.13 -1.41 4 Formamide dimer -15.96 3.41 -0.88 -3.60 -5.24 0.94 -0.71 5 Uracil dimer h-bonded -20.47 7.15 2.00 -1.73 -3.97 1.75 -0.48 6 2-pyridoxine 2-aminopyridine -16.71 6.73 0.43 -2.91 -5.59 1.19 -1.48 7 Adenine thymine Watson-Crick -16.37 7.31 0.88 -2.60 -5.47 1.83 -1.04 8 Methane dimer -0.53 0.47 -0.13 0.28 -0.32 0.44 -0.16 9 Ethene dimer -1.51 1.11 0.51 0.27 -1.04 1.15 -0.17 10 Benzene - Methane complex -1.50 1.02 -0.02 1.02 -0.47 1.42 -0.06 11 Benzene dimer parallel displaced -2.73 2.85 -0.21 3.50 -0.95 4.46 0.02 12 Pyrazine dimer -4.42 2.61 -0.42 3.68 -0.76 5.04 0.59 13 Uracil dimer stack -9.88 5.42 0.74 4.57 -1.49 6.98 0.92 14 Indole benzene complex stack -5.22 5.29 1.14 6.02 -0.23 7.26 1.01 15 Adenine thymine complex stack -12.23 7.28 1.48 7.45 -1.04 10.53 2.05 16 Ethene ethyne complex -1.53 0.98 0.51 -0.54 -1.22 0.33 -0.35 17 Benzene water complex -3.28 1.00 -0.05 -0.03 -1.45 0.88 -0.54 18 Benzene ammonia complex -2.35 0.82 -0.26 0.58 -0.91 1.25 -0.24 19 Benzene HCN complex -4.46 2.47 1.63 0.63 -1.19 1.56 -0.26 20 Benzene dimer T-shaped -2.74 1.98 0.34 1.78 -0.76 2.54 0.01 21 Indole benzene T-shape complex -5.73 3.32 1.02 1.92 -1.49 3.52 0.11 22 Phenol dimer -7.05 3.67 -0.40 -0.01 -2.76 2.97
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