Supporting Information Section for Pancake Bonding in ...

Supporting Information Section for

Pancake Bonding in Organic Radicals

CHAPTER V

Pancake Bond Orders of a Series of π-Stacked Triangulene Radicals*

Contents

S1. Tables and illustrations for π-stacked dimers of each radical/multiradical in Scheme 1.

S2. Degenerate or near-degenerate SOMO orbitals of 1 - 7.

S3. Additional information on geometry optimization.

S4. Convex vs. concave structures.

S5. CASSCF evaluation of the SOMO-SOMO energy.

S6. Basis set evaluation, comments on alternative density functionals and calculation of the approximate SOMO-SOMO energy.

S7. Cartesian coordinates of the converged geometries and the corresponding absolute energies (in Hartrees).

S8. References.

* Reproduced with permission from [Mou, Z.; Kertesz, M. Angew. Chem. Int. Ed. 2017, 129, 10322.] Copyright © 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

S1. Tables of π-stacked dimers of selected radical/multiradicals listed in Scheme 1.

Table 5.S1. Calculated properties of the optimized π-dimers of 12 and 22 at the (U)M05-2X/6-311G(d,p)a level.

aEnergies are in kcal/mol and distances in Å. cNumber of contact carbons with effective SOMO-SOMO orbital

overlap. dSum of Mulliken spin density of a monomer in the dimer. eShortest intermolecular distance.

12(stag) 22 (slip-6) 22 (slip-2)

22(twist-stag) 22 (ecl) 22 (Open-edge)

Figure 5.S1. Optimized geometries of 12 and 22 π-dimers. Selected intermolecular distance (d) are shown in Å.

In 22 (slip-6) there are 10 short contacts (d < 3.3 Å). In 22 (slip-2) there are 7 short contacts. In 22 (open-edge)

there are 3 short contacts.

22

(slip-6)

22

(slip-2)

22

(twist-stag)

22

(ecl)

22

(open-edge)

12

(stag)

Eint -19.58 -16.40 -18.71 -13.62 -8.28 -13.13

ESOMO -7.66 -4.48 -7.19 -10.19 -2.51 -15.24

# of SS sitesc 12 4 0 18 6 12

Spind 1.764 1.906 1.855 1.814 1.595 0.580

EvdW -11.92 -11.92 -11.53 -3.43 -5.77 2.11

Symmetry C2h C2h D3 D3h C2h D3h

Shortest de 3.120 3.130 3.286 3.360 3.080 3.051

Table 5.S2. Calculated properties of the optimized 32 dimers using (U)M05-2X/6-311G(d,p)

32

(π-dimer, staggered)

32

(π-dimer, eclipsed)

32

(π-dimer, open-edge)

32

(3σ-dimer)

Eint before ZPE -30.04 -21.83 -12.32 -32.27

Eint ZPE corr. -1.77 -5.22 -0.74 -9.53

Eint after ZPE -28.28 -16.60 -11.57 -22.75

ESOMO -12.76 -51.41 -6.13 NA

# of SS sitesa 12 36 8 NA

Spinb 2.447 0 2.8873 0

EvdW -17.28 29.58 -6.18 NA

Symmetry C2h D3h C2h C1

Shortest dc 3.101 2.908 2.970 1.621

aNumber of contact carbons with effective SOMO-SOMO orbital overlap. bSum of Mulliken spin density of a monomer in the dimer. cShortest intermolecular distance, in Å.

32 (eclipsed) 32(staggered)

32 (open-edge) 32 (3σ-dimer)

Figure 5.S2. Optimized geometries of 32 dimers. Selected intermolecular distances (d) are shown in Å. In 32 (eclipsed) there are 33 short contacts (d < 3.3 Å). In 32 (staggered) there are 14 short contacts. In 32 (open-edge) there are 4 short contact. Pancake bond to monomer angle (in degrees) is shown in 32 (open-edge).

Table 5.S3. Calculated properties of the optimized π-dimers of 62 using (U)M05-2X/6-311G(d,p)a

62

(staggered)

62

(eclipsed)

62

(slip-2)

Einta -33.67 -19.07 -23.35

ESOMOa -15.03 -5.04 -2.87

# of SS sitesb 12 24 4

Spin 0 0.834 0.898

EvdWa -18.65 -14.03 -20.47

Symmetry D3d D3h C2h

Shortest dc 3.174 3.511 3.190

aShown in kcal/mol without ZPE correction. bNumber of contact carbons with effective SOMO-SOMO orbital

overlap. cShortest intermolecular distance in Å.

62(staggered) 62 (eclipsed)

62 (2OL)

Figure 5.S3. Optimized geometries of 12-TRL2 π-dimers. Selected intermolecular distances (d) are shown in Å. In 62(staggered) there are 19 short contacts (d < 3.3 Å). In 62(slip-2) there are 10 short contacts.

Table 5.S4. Calculated properties of the optimized 72 π-dimers using (U)M05-2X/6-311G(d,p)a and the

comparison with crystal configuration.

7a2(stag) 7a2(ecl) 7b2(stag) 7c2(stag)

Einta -23.03 -10.54 -23.75 -33.84

ESOMO -10.67 -3.33 -10.21 -9.47

# of SS sitesb 14 26 14 14

Spinc 0.679 0.924 0.329 0.707

EvdW -12.36 -7.21 -13.54 -24.37

Symmetry D3d D3h D3d D3

Shortest dd 3.007 3.420 3.002 3.042

In crystal 3.390(1D chain)e 2.979f

aAll energies are in kcal/mol and distances in without ZPE correction because ZPE correction very are similar

and negligible for these dimers. bNumber of contact carbons with direct effective SOMO-SOMO orbital overlaps.

cSum of Mulliken spin density of a monomer in the dimer dShortest intermolecular distance in Å. eShortest

intermolecular distance along the 1D chain from Ref.3d in main text, Cambridge Structural Database (CSD)

refcode: LEHYEE. fDimer structure, from Ref. 3d in main text CSD, refcode: LEHYAA.

7a2 (eclipsed) 7a2 (staggered)

7b2 (staggered) 7c2 (staggered)

Figure 5.S4. Optimized geometries of 72 π-dimers. Selected intermolecular distance are shown in Å. Carbons

are pink, hydrogens are blue, oxygens are red and bromines are burgundy. Hydrogens are omitted for

7c2(staggered) for clarity. In all 72 staggered dimers, there are 13 short contacts (d < 3.3 Å) including 6 carbon

to oxygen short contacts.

S2. Degenerate or near-degenerate SOMO orbitals of all (multi-)radicals in this study.

SOMO of 1

Degenerate SOMOs of 2

Near-degenerate SOMOs of 3.

Energy from left to right: -6.07 eV, -5.87 eV, -5.87 eV


Energy from left to right: -6.10 eV, -6.10 eV, -5.90 eV, -5.73 eV.


Energy from left to right: -6.19 eV, -6.10 eV, -6.10 eV, -5.73 eV, -5.73 eV.

SOMO of 6. SOMO of 7a.

Figure 5.S5. SOMO orbitals of all (multi-)radicals in this study at the UM052X/6-311G(d,p) level.

S3. Additional information on optimized geometries.

All geometry optimizations and frequency calculations were done using the Gaussian 09 package (revision D.01).

[i] The basis set used in this study is the Pople type 6-311G(d,p).[ii] Visualizations were done using Chemcraft.[iii]

S4. Convex vs. concave structures.

The eclipsed π-dimers for 12-62 are convex because the SOMOs bind the monomers and the SOMOs are largely

localized emphasis on peripheral carbons as shown in Figure 5.S5. The eclipsed π-dimer for 72 is concave because

the largest SOMO coefficient is at the central carbon. Therefore, the shortest contacts for 12-62 eclipsed π-dimers

are at the peripheral carbons while for the eclipsed π-dimer for 72 the shortest contact is between the central

carbons as illustrated in Figure 5.S6. (See also ref. [6] in the main text.)

Figure 5.S6. Side view of 32(ecl) (left) vs. 7a2(stag) (right) showing convex vs. concave shapes reflecting the

location of the SOMO coefficients that are localized at the periphery vs. the center, respectively.

S5. CASSCF evaluation of the SOMO-SOMO energy (ESOMO).

A post-HF method, Complete Active Space Self-Consistent Field (CASSCF, or CAS) was adopted to reevaluate

the ESOMO vs. PBO. Different active spaces are chosen based on the multi-radical nature of various triangulenes.

In order to reflect the important orbitals with occupancies significantly different from 0 and 2, we chose CAS(2,2)

for 12, CAS(4,4) for 22, CAS(6,6) for 32, CAS(8,8) for 42. A CAS(10,10) computation for 52 was not conducted

due to computational limitations of the large size of the system. The geometries at the UM05-2X/6-311G(d,p)

level were used. ESOMO was calculated the same way using equation (3) in the main text where the Etot (dimer

singlet) was calculated by CAS/(6-311G(d,p)) and Etot (dimer high spin @ min. singlet) is calculated at the

ROHF/(6-311G(d,p)) level.

Figure 5.S7. ESOMO vs PBO using CAS/6-311G(d,p)//UM05-2X/6-311G(d,p) level. Full symbols indicate

optimized geometries. Empty symbol refers to the 22(ecl) at 3 Å structure listed in Tables 1 and S5.

12

3

4

y = ‐24.449xR² = 0.9743

‐140

‐120

‐100

‐80

‐60

‐40

‐20

0

0 1 2 3 4 5

E / kcal m

ol‐1

PBO

Table 5.S5. Detailed CAS calculation result for selected systems as shown in Figure 5.S7.

12(stag) 22(ecl)

at 3 Å 32(ecl) 42(ecl)

CAS active space 2,2 4,4 6,6 8,8

PBO 1 2 3 4

ni of CAS orbitalsa 1.85;

0.15

1.84, 1.84;

0.16.0.16

1.86,1.86, 1.86;

0.14, 0.14 ,0.14

1.94, 1.92, 1.91, 1.90;

0.10, 0.09, 0.08,0.05

ESOMOb -24.50 -43.92 -68.24 -104.11

anatural orbital occupancies bin kcal/mol

As shown in Figure 5.S7 the CAS-based calculation reproduced and accentuates the linear correlation between

SOMO-SOMO energy and the formal pancake bond order. We mentioned that previous high-level MR-AQCC/6-

31g(d) calculation predicted ˗17.2 kcal/mol SOMO energy for phenalenyl (1) with a single pancake bond (See

Ref. 1e in the main text). The DFT predicted correlation presented in Figure 5.4 (˗15.91 kcal/mol per bond) being

much closer to MR-AQCC value is more accurate than the CAS predicted one in Figure 5.S7 (˗24.5 kcal/mol per

bond), therefore we presented the DFT-based value in the main text. The reason for this overestimation of the

ESOMO by CAS is due to the different way electron correlation is included in the two methodologies. In CAS the

orbital relaxation includes some electron correlation for the singlet state that is absent in the high spin state,

leading to a relatively larger stabilization of the singlet and thus a larger SOMO-SOMO energy term. Note that

the trends are very similar, and this is the key point of this work.

S6. Basis set evaluation, comments on alternative density functionals and the calculation of the

approximate SOMO-SOMO energy.

Basis set evaluation: The basis set superposition error (BSSE) in intermolecular computations is widely

recognized. However, in order to treat large systems compromises are needed. One is the use of form of density

functional (DF), the other is to use practically useful basis sets. An important point in this respect is that on the

potential energy surfaces that include both σ- bonded and π-stacking dimers, the use of methods such as the Boys–

Bernardi counterpoise approach are not applicable because interactions that are intermolecular at one end of the

potential energy surface become intramolecular as the contact distances change. We have used a reasonably

accurate basis set for rather large systems with complex potential energy surfaces. While computations would be

difficult to do with much larger basis sets, we present below a comparison with full geometry optimizations for

the phenalenyl dimer, 12(stag) providing validation for the use of the 6-311G(d,p) basis.

Table 5.S6. Comparison between different basis set for 12(stag) using UM05-2X.

Basis set comparison for 12(stag) Eint (kcal mol-1) α-α distance (Å)a c-c distance (Å)a

6-31g(d) -10.71 3.085 3.137

6-31g(d,p) -10.77 3.082 3.136

6-31g+(d,p) -10.74 3.114 3.154

6-311G(d,p) -13.13 3.051 3.101

6-311+G(d,p) -13.17 3.059 3.107

6-311++G(2d,2p) -10.26 3.101 3.147

6-311++G(3df,3pd) -12.71 3.050 3.107

aRefer to Figure 5.S1 for the definition of α-α and central-central (c-c) carbon distances in 12(stag). In Figure

5.S1 we used 6-311G(d,p) and obtained 3.051 Å for α-α distance and for 3.101 for c-c distance.

Comments on alternative density functionals

The number of available density functionals (DFs) for intermolecular interactions is quite large. We have tested

over 50 DFs for their quality to adequately describe pancake bonding in phenalenyl, a system for which both

experiments and high level data are available (see main text for references). M05-2X was clearly superior to all

others, including +D methods when the following parameters were monitored: direct CC contact distances,

interaction energy and the SOMO-SOMO energy component as defined in this article.

SOMO-SOMO energy elaboration: It is desirable to obtain a separation of the SOMO-SOMO contribution and

the rest of the interaction energy.[9a] This SOMO-SOMO contribution is not dominated by dispersion in this case.

Equation (2) in the main text is an approximation that provides consistent data and is generally applicable across

various approaches including DFT or wave function methods for pancake bonded systems. The approximate

nature of this decomposition is mentioned below equations (1) and (2) in the manuscript. It has its limitations as

discussed for instance in ref.[1e] in the main text. Using this approximate energy decomposition, we arrive at a

surprisingly clear correlation between the formal bond order and the SOMO-SOMO binding energy (Figure 5.4),

which turns out to be quite substantial for the larger members of the series providing a relatively large driving

force for π-stacking as compared to vdW interactions. (See references [1c, 1e, 6, 9] of the main text for the

discussion in this paragraph.

S7. Cartesian coordinates of the converged geometries and the corresponding absolute energies (in hartrees).

2(monomer): UM052x/6-311G(d,p), -845.723662853 H C -1.408188000 -2.439023000 0.000000000 C -2.127367000 -1.233792000 0.000000000 C -3.541795000 -1.205432000 0.000000000 C -0.004795000 -2.459331000 0.000000000 C -1.416317000 0.000000000 0.000000000 C 0.000022000 0.000000000 0.000000000 C 0.708119000 -1.226595000 0.000000000 C 0.708119000 1.226595000 0.000000000 C -0.004795000 2.459331000 0.000000000 C -1.408188000 2.439023000 0.000000000 C -2.127367000 1.233792000 0.000000000 C -3.541795000 1.205432000 0.000000000 C -4.226280000 0.000000000 0.000000000 H -4.082784000 2.141656000 0.000000000 H -1.949607000 3.376086000 0.000000000 C 0.727052000 -3.670082000 0.000000000 C 2.113367000 -3.660246000 0.000000000 C 2.814719000 -2.464539000 0.000000000 C 2.132191000 -1.225505000 0.000000000 H 3.896023000 -2.464496000 0.000000000 C 2.132191000 1.225505000 0.000000000 C 2.816114000 0.000000000 0.000000000 H 3.898351000 0.000000000 0.000000000 C 2.814719000 2.464539000 0.000000000 C 2.113367000 3.660246000 0.000000000 C 0.727052000 3.670082000 0.000000000 H 3.896023000 2.464496000 0.000000000 H 0.186369000 4.606487000 0.000000000 H 2.654114000 4.596444000 0.000000000 H -5.307464000 0.000000000 0.000000000 H -4.082784000 -2.141656000 0.000000000 H -1.949607000 -3.376086000 0.000000000 H 0.186369000 -4.606487000 0.000000000 H 2.654114000 -4.596444000 0.000000000 22(slip-6): UM052x/6-311G(d,p), -1691.47853152 H C 1.599387000 0.001818000 -2.093321000 C 0.937035000 -1.221876000 -1.922684000 C 1.597151000 -2.463245000 -2.102016000 C 0.935560000 1.224646000 -1.922282000 C -0.431299000 -1.224359000 -1.529949000 C -1.112572000 0.000039000 -1.333545000 C -0.432802000 1.225323000 -1.529646000 C -2.465580000 -0.000849000 -0.906629000 C -3.143038000 -1.234917000 -0.694043000 C -2.449583000 -2.440258000 -0.898891000 C -1.112535000 -2.459847000 -1.322042000

C -0.406763000 -3.667661000 -1.519963000 C 0.921252000 -3.657664000 -1.924232000 H -0.925049000 -4.604357000 -1.366152000 H -2.962499000 -3.378644000 -0.732053000 C 1.594215000 2.466900000 -2.100908000 C 0.916896000 3.660442000 -1.922548000 C -0.411235000 3.668650000 -1.518631000 C -1.115599000 2.459887000 -1.321462000 H -0.930664000 4.604642000 -1.364421000 C -3.144628000 1.232282000 -0.693891000 C -2.452652000 2.438524000 -0.898485000 H -2.966691000 3.376257000 -0.731455000 C -4.484883000 1.203820000 -0.248253000 C -5.133489000 -0.002642000 -0.029789000 C -4.483316000 -1.208250000 -0.248368000 H -4.999911000 2.140290000 -0.081348000 H -4.997154000 -2.145404000 -0.081616000 H -6.160202000 -0.003331000 0.310181000 H 1.439640000 -4.594371000 -2.078381000 H 2.638636000 -2.457675000 -2.395253000 H 2.647847000 0.002487000 -2.365699000 H 2.635759000 2.462727000 -2.393964000 H 1.434238000 4.597833000 -2.076071000 C -1.599285000 -0.002575000 2.093586000 C -0.937300000 1.221317000 1.922930000 C -1.597651000 2.462496000 2.102684000 C -0.935174000 -1.225219000 1.922388000 C 0.431003000 1.224177000 1.530092000 C 1.112622000 -0.000033000 1.333690000 C 0.433166000 -1.225521000 1.529645000 C 2.465585000 0.001247000 0.906654000 C 3.142727000 1.235472000 0.694063000 C 2.448991000 2.440626000 0.899095000 C 1.111958000 2.459834000 1.322277000 C 0.405879000 3.667465000 1.520327000 C -0.922054000 3.657099000 1.924834000 H 0.923927000 4.604298000 1.366542000 H 2.961666000 3.379152000 0.732303000 C -1.593578000 -2.467609000 2.100916000 C -0.916000000 -3.660977000 1.922351000 C 0.412077000 -3.668824000 1.518260000 C 1.116199000 -2.459896000 1.321170000 H 0.931685000 -4.604690000 1.363872000 C 3.144858000 -1.231710000 0.693546000 C 2.453196000 -2.438159000 0.897996000 H 2.967460000 -3.375713000 0.730656000 C 4.485015000 -1.202892000 0.247644000 C 5.133318000 0.003745000 0.029232000

C 4.482921000 1.209174000 0.248128000 H 5.000210000 -2.139225000 0.080481000 H 4.996503000 2.146470000 0.081375000 H 6.159958000 0.004713000 -0.310955000 H -1.440604000 4.593660000 2.079318000 H -2.638884000 2.456614000 2.396798000 H -2.647633000 -0.003541000 2.366399000 H -2.635094000 -2.463692000 2.394065000 H -1.433100000 -4.598512000 2.075808000 22(slip-2): UM052x/6-311G(d,p), -1691.47346154 H C -0.591228000 2.437772000 -1.448810000 C 0.064634000 1.232373000 -1.747063000 C 1.383158000 1.204169000 -2.255330000 C -1.898087000 2.458636000 -0.937945000 C -0.602195000 -0.000435000 -1.495857000 C -1.918885000 -0.000004000 -0.973709000 C -2.569708000 1.226614000 -0.696278000 C -2.570486000 -1.226191000 -0.696217000 C -1.899571000 -2.458649000 -0.937637000 C -0.592676000 -2.438618000 -1.448433000 C 0.063874000 -1.233672000 -1.746973000 C 1.382325000 -1.206369000 -2.255452000 C 2.016602000 -0.001301000 -2.515116000 H 1.895866000 -2.143251000 -2.426570000 H -0.076498000 -3.374313000 -1.621818000 C -2.561081000 3.668579000 -0.625038000 C -3.846410000 3.659571000 -0.105776000 C -4.513613000 2.463938000 0.118598000 C -3.893515000 1.226513000 -0.167362000 H -5.518099000 2.465127000 0.519275000 C -3.894288000 -1.225219000 -0.167292000 C -4.532071000 0.000857000 0.078600000 H -5.537513000 0.001189000 0.479886000 C -4.515162000 -2.462236000 0.118752000 C -3.848673000 -3.658300000 -0.105451000 C -2.563306000 -3.668154000 -0.624601000 H -5.519667000 -2.462756000 0.519384000 H -2.052527000 -4.604711000 -0.803512000 H -4.340366000 -4.594049000 0.122210000 H 3.028963000 -0.001637000 -2.894179000 H 1.897396000 2.140710000 -2.426227000 H -0.074556000 3.373157000 -1.622409000 H -2.049772000 4.604806000 -0.804162000 H -4.337516000 4.595646000 0.121811000 C 0.591263000 -2.437734000 1.449207000 C -0.064645000 -1.232276000 1.747193000 C -1.383093000 -1.204007000 2.255641000

C 1.898096000 -2.458643000 0.938289000 C 0.602163000 0.000508000 1.495788000 C 1.918856000 0.000013000 0.973648000 C 2.569672000 -1.226635000 0.696373000 C 2.570436000 1.226160000 0.695931000 C 1.899587000 2.458655000 0.937360000 C 0.592750000 2.438706000 1.448307000 C -0.063848000 1.233782000 1.746872000 C -1.382341000 1.206523000 2.255242000 C -2.016567000 0.001495000 2.515198000 H -1.895962000 2.143422000 2.426025000 H 0.076659000 3.374449000 1.621720000 C 2.561152000 -3.668627000 0.625661000 C 3.846468000 -3.659678000 0.106364000 C 4.513605000 -2.464066000 -0.118300000 C 3.893466000 -1.226604000 0.167424000 H 5.518080000 -2.465291000 -0.519004000 C 3.894224000 1.225124000 0.166967000 C 4.532002000 -0.000984000 -0.078764000 H 5.537433000 -0.001375000 -0.480077000 C 4.515082000 2.462102000 -0.119269000 C 3.848631000 3.658200000 0.104875000 C 2.563322000 3.668121000 0.624168000 H 5.519556000 2.462571000 -0.519981000 H 2.052598000 4.604705000 0.803096000 H 4.340312000 4.593917000 -0.122936000 H -3.028935000 0.001873000 2.894240000 H -1.897313000 -2.140522000 2.426740000 H 0.074872000 -3.373089000 1.623792000 H 2.049879000 -4.604835000 0.804983000 H 4.337610000 -4.595784000 -0.121017000 22(ecl): UM052x/6-311G(d,p), -1691.46902350 H C 1.259150000 2.428490000 1.748168000 C -0.142186000 2.460470000 1.688025000 C -0.862948000 3.676583000 1.644328000 C 1.967003000 1.218584000 1.805125000 C -0.864289000 1.233664000 1.656142000 C -0.167269000 0.001724000 1.699754000 C 1.247030000 -0.009287000 1.772723000 C -0.883483000 -1.219190000 1.656697000 C -2.304957000 -1.207133000 1.573421000 C -2.976662000 0.023571000 1.520730000 C -2.285765000 1.243650000 1.573472000 C -2.956360000 2.488146000 1.532402000 C -2.247163000 3.677643000 1.581896000 H -4.036448000 2.496847000 1.472898000 H -4.057443000 0.032022000 1.454953000

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H 3.881993000000 -5.048822000000 0.894839000000 C 3.014282000000 -5.663617000000 0.657102000000 H 3.337216000000 -6.705994000000 0.669827000000 C 1.880425000000 -5.473603000000 1.676117000000 S8. References.

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Barone, B. Men-nucci, G. A. Petersson, H. Nakatsuji, M. Caricato, X. Li, H. P. Hratchian, A. F. Izmaylov, J.

Bloino, G. Zheng, J. L. Sonnenberg, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T.

Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, J. A. Montgomery, Jr. ,J. E. Peralta, F. Ogliaro, M. Bearpark,

J. J. Heyd, E. Brothers, K. N. Kudin, V. N. Staroverov, R. Ko-bayashi, J. Normand, K. Raghavachari, A. Rendell,

J. C. Burant, S. S. Iyen-gar, J. Tomasi, M. Cossi, N. Rega, J. M. Millam, M. Klene, J. E. Knox, J. B. Cross, V.

Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli,

J. W. Ochterski, R. L. Martin,K. Morokuma, V. G. Zakrzewski, G. A. Voth, P. Salvador, J.J.Dannenberg, S.

Dapprich, A. D. Daniels, Farkas, J. B. Foresman, J. V. Ortiz, J. Cio-slowski, D. J. Fox, Gaussian 09, Revision

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R. Krishnan, J. S. Binkley, R. Seeger, J. A. Pople, J. Chem. Phys. 1980, 72, 650.

[iii] G. A. Zhurko, D. A. Zhurko, Chemcraft, Version 1.8, http://chemcraftprog.com [4] See e.g. Grimme, S., Hansen, A., Brandenburg, J. G., Bannwarth, C. Chem. Rev. 2016, 116, 5105-5154.

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