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A: New Tools and Methods in Experiment and Theory #.zz
Reexamination of NICS ; Height Dependence, Off-Center Values and Integration Amnon Stanger J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.9b02083 • Publication Date (Web): 09 Apr 2019 Downloaded from http://pubs.acs.org on April 10, 2019
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Reexamination of NICS.zz; Height Dependence, Off-Center Values and Integration Amnon Stanger Schulich Department of Chemistry, Technion, Haifa 32000, Israel. E-mail:
[email protected] Abstract Applying fine grids of NICS probes (BQs) at different distances from the molecular plane of aromatic and antiaromatic molecules suggests that, at short distances, NICS,zz is maximal (absolute values) off the geometrical center of the systems. In non-symmetric systems the center of the induced ring current may be a little off the geometrical center, but the difference is negligible at distances 2 Å. At these distances, the change of NICS,zz with the distance from the ring follows a power relation. It is shown that the order of diatropicity and paratropicity within a group of molecules depends on the distance from the system (namely, the order of NICS(r),zz depends on r). It is thus suggested to use NICS,zz as a quantitative measure of aromaticity.
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Introduction. Aromaticity is one of the most fundamental concepts in chemistry. It has recently been reviewed.1,2 Nucleus Independent Chemical Shift (NICS) based methods are the most popular tools for identifying and quantifying aromaticity and antiaromaticity.3 The physics behind the idea is simple: A ghost-atom probe (BQ) senses the induced magnetic field4 and reports an NMR chemical shift, using one of the available methods for NMR calculations (in most cases, GIAO). The method has received serious criticism, mainly because it is over-interpreted, because it returns a single scalar number for the current (which is a vector field), and because the source of the NICS value cannot be identified, giving rise to the possibility that the NICS value results from effects that have nothing to do with aromaticity.5,6 Several variations of NICS have been developed over the years to compensate for the above-mentioned disadvantages: First, it was realized that only the ZZ component of the NMR tensor (resulting from a circular current in the XY plane, denoted as NICSzz) is relevant.7 Then, it was suggested that one NICS value may be misleading, and one-8 and three-dimensional9,10 scans were proposed. It was then realized that even the ZZ part of the tensor contains effects from the electrons, and NICS and NICS,zz were suggested as better means for determining aromaticity.11,12 These can be currently calculated using either localized molecular orbitals (LMO-NICS), the contribution of only the canonic molecular orbitals to NICS (CMO-NICS), or a model that mimics the system whose NICS values are subtracted from the NICS values of the molecule under study to yield the clean contribution of the electrons to NICS (the only model).13,14 It was extended for the study of polycyclic systems for predicting global, semi-global and local ring currents (NICS-XY-scan)15 and showed excellent agreement with current density studies. There were some attempts to correlate NICSzz (but not NICS,zz) to electron density properties,16,17 but these are not successful,18 mainly because the relation between NICS and electron density is not a simple straightforward one. The common feature of all these methods (except the 3D scans) is that the NICS values are calculated at and above the geometrical centers of the rings. The rationale for this is simple – the magnetic field, which results from the ring current, should be strongest at and above the middle of the current. Previous work suggested that the geometrical center of the ring is not necessarily the center of the induced ring current.19 In this study, we started by asking how different are the locations of the system’s geometrical centers and their respective centers of the induced current at different heights above the molecular plane. While studying this, we found that even in symmetric systems (e.g., benzene), at (relatively) short distances from the molecular plane, the most negative NICS,zz values are obtained off-2ACS Paragon Plus Environment
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center (geometrical and ring current). It was also noticed that the order of diatropicity of different systems depends on the height above the molecular plane at which NICS,zz is calculated. For example, at the molecular plane the order of diatropicity is cyclopentadienyl anion (2) > benzene (1) > tropylium cation (3). At 1 Å above the molecular plane the order is 1 > 2 > 3. At 2 Å above the molecular plane the order is 3 > 1 > 2. Thus, it is suggested to use integrated NICS,zz values for better quantitative assessment of aromaticity and antiaromaticity.
Methods. Gaussian 0920 was used for all calculations. All of the structures were fully optimized (except the D4hcyclooctatetraene, which was optimized under D4h-symmetry constraints) at the B3LYP/6-311G(d) level of theory. NICS values were calculated at the GIAO-B3LYP/6-311+G(d) level. The values at and above the center of the rings were calculated as described above, using Aroma.21 The BQ grids were built around X=Y=0 (the geometric center) at a constant Z value with an interval of 0.1 Å between each BQ at all the values between -0.5X0.5 and -0.5Y0.5 (122 BQs for each Z value). These grids were put in heights (Z) from 0.8 to 2.0 Å above the molecular planes with a 0.1 Å step size (altogether 13 planes). CMONICS,zz were calculated using natural chemical shielding analysis (NCS)22 within NBO 6.0.23 Results and discussion. The studied systems are shown in scheme 1. -
These represent all the typical monocyclic
2+
+
systems needed for this study: different ring 2
1
3
sizes, different charges, different aromaticities
4
H H N
2-
(and a couple of antiaromatic examples) and
B
different symmetries with regard to the
N
B
geometrical center.
B N
H
H
N
H
First, the diatropic systems which should produce
H
6
5 H N
O
7 N
completely centrosymmetric circular currents
N N
due to their symmetrical structures are
N
presented: Benzene (1), cyclopentadienyl anion
N N
9
8
10
(2), tropylium cation (3), cyclooctatetraene
11
dication (4) and dianion (5) and borazine (6). -3ACS Paragon Plus Environment
Scheme 1: Systems studied in this paper. 12
13
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Physical considerations suggest that the induced magnetic field due to the ring current is maximal at and above the center of these molecules (X=Y=0). Figure 1 describes the NICS,zz values of the grids at 0.8, 1.0 and 1.4 Å above the molecular plane for benzene (1), as an representative examples for 1-6. The colors correspond to the percentage of the NICS values, where 100% reflects the highest value calculated on the respective plane. When the BQs are relatively close to the molecular plane, the more negative NICS,zz values are obtained off-center. For systems 1-5, the most negative NICS,zz values are obtained at the geometrical center only at distances larger than 1.2-1.3 Å, depending on the system. Furthermore, while the smallest absolute values at 0.8 Å are ca. 96% of the maximum values, they are only ca. 85% at 1.4 Å. Borazine (6) is even more problematic, and the most negative NICS,zz at X=Y=0 is found only at heights of ≥ 2.4 Å above the molecular plane. %NICS
In systems containing heteroatoms, the
100.0
1.40
99.22
1.35
98.44
1.30
97.66
1.25 1.20
96.88
1.15 1.10
95.32
z
96.10
1.05 1.00
94.54 93.76
0.95 0.90
92.98 92.20
0.85 0.80
0.6
0.2
-0 .4
geometrical center does not necessarily coincide with the center of the -electron density because of different electronegativities, orbital coefficients, etc. Thus, it may well be that the center of the ring current and the maximum induced magnetic field are not at the geometrical
0.4
-0.6
0 .0
-0 .2
0.0
center. We have thus studied pyridine (7), pyrrole
y
-0.2
0. 2
x
0. 6
0. 4
-0.4
-0.6
(8), furane (9), 1,2,3-triazine (10) and 1,2,4-triazine Figure 1: NICS,zz values (% of maximum value at each height) of benzene (1) at 0.8, 1.0 and 1.4 Å.
(11). Figure 2 shows the NICS,zz values at 0.8, 1.1 and 1.9 Å above the molecular plane of 1,2,3triazine, as a representative example for 7-11. As in the symmetric systems (1-6), the most negative %NICS
%NICS
100.0
2.10 1.12 1.10 1.08 1.06 1.04 1.02 1.00 0.98
100.0 99.17
2.00
97.50
1.95
95.84
0.92
0.90 0.88 0.86 0.84 0.82
96.94 95.41 93.88 92.35 90.82
1.90
89.29
95.00
1.85
94.17
1.80
93.34
87.76 86.23 84.70
1.75 0.6
0. 6
y
0 .0
-0.4
0. 6
0. 4
0. 2
0. 4
y
0 .0
-0.2
0. 2
-0 .4
-0.2
-0.4
0.2
0.0
x
0.0
x
0.4
-0 .4
0.4
0.2
.70.6 1-0
-0 .2
0.6
-0 .2
0.80 .78.6 0-0
98.34
96.67
0.96 0.94
98.47
2.05
z
z
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-0.6
-0.6
-4Figure 2: NICS,zz values (% of maximum value at each height) of 1,2,3-triazine (10) at 0.8, 1.1 (left) ACS Paragon Plus Environment and 1.9 Å (right).
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values are far off center at low heights (≤ 1.5 Å) above the molecular plane. For the less symmetric systems, the maximal induced magnetic field is off-center even at higher elevations. Like in the symmetric systems (1-6) the differences between the minimal and maximal (absolute) values become larger as the grid moves further away from the molecular plane. It is also noted that even for the most non-symmetric system (10) at large distances ( 1.8 Å) the differences between the NICS,zz values that are most negative (off-center) and those obtained for the geometrical center are minimal. For example, the most negative CMO-NICS,zz in 10 at a height of 1.9 Å is -12.76 ppm at X=0.1 and Y=-0.1. At the same height, the CMO-NICS,zz at the geometrical center (X=Y=0.0) is -12.74 ppm. For further details, please see the Supporting Information. Cyclobutadiene (12) is the only system that shows the maximal NICS,zz value at X=Y=0 already at a height of 0.8 Å above the molecular plane. However, D4h-cyclooctatetraene (13) behaves similarly to benzene, showing off-center maximal NICS,zz values at heights lower than 1.5 Å above the molecular surface. Why are the maximal (absolute) NICS,zz values obtained off-center when the probes are placed (relatively) close to the molecular plane, even in symmetric systems? Part of the answer to this question is given in a recently-published paper,24 but the reason for the induced field being larger off-center than at the center at lower elevations from the ring are unclear as yet.25
The immediate conclusion is that if (anti)aromaticity is of concern, the NICS,zz values have to be calculated at distances that are far enough to be beyond the influence of the “off-center” effects and at the center of the induced current, which does not always coincide with the geometrical center. Tables 1 and 2 show CMO-NICS,zz and -only model NICS,zz, respectively, calculated at different distances and by different methods: single point NICS,zz at the given distance, NICS,zz values obtained from the standard NICS-scan procedure (distances 1.0-3.9 Å), and NICS-scan procedures taking into consideration only values from heights at which the maximal (absolute) values are obtained at constant X and Y coordinates (assuring zero contribution from off-center effects), denoted as “Optimized scan”. Following the NICS,zz (r)= A + BCr
(1)
standard NICS-scan procedure, a 3rd degree polynomial fitting is used, and the reported values are the re-calculated
values according to the optimized fitting parameters. However, the physical decay of the -induced magnetic field at (relatively) large distances is of the form of Equation 1, where A, B and C are -5ACS Paragon Plus Environment
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parameters.26 The correlation coefficients that are obtained are larger than 0.9999. Thus, the numbers that are reported under the “Optimized scan” columns are inter- and extrapolated from this threeparameter fitting.27
Table 1: Different CMO-NICS,zz values (see text for details) at the molecular plane and at 1 Å and 2 Å above it.
Single value NICS(r),zz Comp.
Standard scan NICS(r),zz
Optimized scan NICS(r),zz
r=0.0 Å
r=1.0 Å
r=2.0 Å
r=0.0 Å
r=1.0 Å
r=2.0 Å
r=0.0 Å
r=1.0 Å
r=2.0 Å
1
-35.84
-29.19
-13.18
-57.33
-29.68
-13.31
-88.90
-33.35
-13.17
2
-35.16
-28.87
-12.33
-59.53
-29.30
-12.45
-87.38
-32.42
-12.30
3
-34.74
-28.47
-14.00
-51.88
-28.94
-14.12
-81.38
-33.45
-14.01
4
-32.76
-27.16
-14.62
-45.39
-27.57
-14.72
-71.66
-32.17
-14.66
5
-49.34
-41.65
-23.87
-65.46
-42.20
-23.99
-102.61
-49.29
-23.96
6
-8.06
-6.05
-3.88
-7.63
-6.14
-3.89
-17.42
-8.23
-3.92
7
-35.59
-28.4
-12.44
-57.26
-28.85
-12.57
-86.31
-32.38
-12.42
8
-32.22
-25.24
-10.08
-54.61
-25.57
-10.19
-78.47
-27.74
-10.05
9
-27.04
-20.44
-8.21
-44.06
-20.69
-8.30
-62.78
-22.40
-8.19
10
-36.06
-27.83
-11.55
-58.64
-28.21
-11.67
-84.38
-30.81
-11.52
11
-35.5
-27.3
-11.33
-57.57
-27.67
-11.43
-83.07
-30.26
-11.29
12
55.79
50.25
12.45
139.21
49.95
12.45
202.04
49.24
12.34
13
113.00
94.09
48.08
164.87
95.63
48.44
297.93
125.91
54.12
Table 2: Different -only-NICS,zz values (see text for details) at the molecular plane and at 1 Å and 2 Å above it.
Single value NICS(r),zz Comp.
r=0.0 Å
r=1.0 Å
Standard scan NICS(r),zz
r=2.0 Å
r=0.0 Å
r=1.0 Å
r=2.0 Å
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Optimized scan NICS(r),zz r=0.0 Å
r=1.0 Å
r=2.0 Å
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1 2 3 4 5 6 7 8 9 10 11 12 13
-34.17 3.14 -28.56 3.85 -30.23 3.24 -27.81 2.79 -46.34 3.89 -3.80 0.28 -32.87 3.78 -28.03 1.42 -23.14 2.17 -30.57 5.66 -30.92 5.19 56.73 7.48
-34.00 3.17 -27.14 0.69 -31.53 2.55 -28.88 1.59 -39.07 3.08 -6.96 3.10 -32.02 3.02 -25.03 2.41 -20.72 2.77 -30.22 3.76 -29.72 3.59 39.96 6.29
-14.77 1.74 -10.45 0.06 -16.17 2.40 -17.16 2.64 -21.33 1.69 -3.50 1.27 -13.75 1.84 -8.87 0.63 -7.51 0.90 -12.85 2.48 -12.64 2.39 11.09 1.39
-69.09 5.02 -61.04 2.91 -54.97 0.28 -42.36 3.76 -65.25 4.83 -12.02 6.18 -65.68 4.01 -58.79 6.66 -48.00 6.88 -62.68 4.51 -61.65 4.13 105.01 18.93
-34.76 3.51 -27.43 0.74 -32.37 2.91 -29.60 1.84 -39.67 3.02 -7.29 3.40 -32.76 3.41 -25.30 2.53 -21.04 2.99 -31.00 4.28 -30.45 4.08 39.94 6.31
-14.98 1.83 -10.55 0.08 -16.38 2.48 -17.32 2.69 -21.47 1.67 -3.58 1.35 -13.96 1.94 -8.96 0.67 -7.62 0.97 -13.07 2.61 -12.84 2.52 11.12 1.42
-107.91 14.53 -75.60 3.35 -94.21 10.88 -79.66 5.83 -97.05 8.07 -150.38 55.57 -102.04 14.73 -80.15 9.81 -67.89 13.14 -96.35 15.96 -93.78 15.88 170.67 9.18
-39.34 4.90 -27.64 0.62 -38.59 5.07 -36.70 4.20 -45.07 3.83 -20.83 7.40 -36.89 5.08 -26.17 2.45 -22.12 3.38 -33.82 6.01 -33.82 6.01 43.05 3.51
-14.72 1.72 -10.38 0.02 -16.00 2.33 -17.21 2.66 -21.32 1.76 -3.01 1.16 -13.70 1.82 -8.80 0.60 -7.45 0.87 -12.54 2.36 -12.54 2.39 11.09 1.31
116.81 0.12
94.73 1.22
48.11 1.32
167.28 0.51
96.11 1.37
48.44 1.35
296.67 4.73
128.83 2.52
54.25 1.32
A few observations and conclusions emerge from these tables. The first observation is that there are significant differences between the directly-calculated single-point values of NICS(0),zz and the values obtained at the same height with extrapolations from the standard and optimized scans. The data for the standard scan are taken at distances of 1.0-3.9 Å above the molecular plane. The data for the optimized scans are taken from the distance that the X and Y coordinates for the maximum (absolute) value of the NICS,zz stay constant (see above). The data from the “standard scan” are fitted to a 3rd degree polynomial equation (with a correlation coefficient > 0.999), and the data from the “optimized scans” are fitted to equation 1 (see above). The values in the tables are the values calculated from the fits. Thus, in both cases, the values at r = 0 are obtained by extrapolation. Obviously, the behavior of the magnetic field as a function of distance when proximate to the ring (< 1Å) is very different from the behavior at higher distances. Because of these “off-center” effects, NICS(0),zz should not be used as a measure of aromaticity, certainly not as a quantitative measure. -7ACS Paragon Plus Environment
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The second conclusion is that the standard NICS-scan procedure yields numbers that are not so different from those obtained by the optimized scans for NICS(1),zz and NICS(2),zz. This is because most of the data of the standard scans is obtained from distances > 2Å. At these distances, even for systems in which the geometrical center does not coincide with the center of the current, the offset is minimal. Thus, they can be safely used for qualitative and quantitative comparisons. Finally, it may seem that there are large discrepancies between CMO- NICS,zz and “-only model” NICS,zz values. Figure S1 shows all the NICS,zz values of Tables 1 and 2, and suggests that in the vast majority of the cases, CMO- NICS,zz values are within the uncertainly of the “-only model” NICS,zz. Many studies use the NICS value as a measure for (anti)aromaticity. Therefore, it is bothersome that the order of aromaticity, if judged by the magnitude of the NICS,zz value, depends on the distance from the molecular plane. For example, according to Table 1, the order of aromaticity according to the “optimized scan” procedure is 1>2>3 at the molecular plane, 3>1>2 at 1Å above the molecular plane, and 3>1>2 at 2Å above the molecular plane. Similar phenomena are observed using the -only model (Table 2). Obviously, this is a problem if accurate quantification of aromaticity by NICS is desired. The change of the magnetic field with the distance depends on the exact shape (e.g., location, width) of the induced current.28 Thus, sampling the magnetic field at differing distances from the molecular plane may result in contradictions, as demonstrated above. Therefore, it is suggested here to take the integrated values of NICS,zz instead of the value at a certain point. This is also scientifically justified. Aromaticity is a molecular property. As such, the total induced magnetic field, which considers contributions from the whole compound, is a more suitable representation of aromaticity than a value, which is sampled at an arbitrary height above the molecular plane. As mentioned above, the behavior of the induced magnetic field at large distances is described by Equation 1. Assuming that this is the true behavior of the -current induced field (at shorter distances “off-center” effects change the apparent behavior), the equation that should describe the field as a NICS,zz (r)= BCr
(2)
function of distance r should be Equation 2, where B and C are parameters, i.e., Equation 1 with A = 0. Physically, A is the value at infinite
distance (i.e., NICS()), which should be zero. Indeed, the correlations to Equation 1 give A values of -0.3 to -1.2 for 1-11 and 0.1 to 2.7 for 12 and 13, respectively, namely, very small values compared to the NICS,zz values at short distances from the ring. B represents the NICS,zz value which results only from the circular induced current, and C is the system-specific sensitivity of the decay of the induced -8ACS Paragon Plus Environment
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magnetic field with the distance from the molecular plane. Thus, despite the fact that the correlation coefficients for Equation 2 are somewhat inferior (R≥0.998) relative to the correlation coefficients obtained for Equation 1, Equation 2 rests on a more solid physical foundation. NICS,zz (r)= BCr /lan(C) – B/ln(C) (4) NICS,zz (r)= BC /lan(C) + constant (3)
Integration of Equation 2 gives Equation 3. When limits are 0 to , the NICS,zz gets the form of Equation 4 . Table 3 detail the results for CMO-NICS,zz and the -
only model, as well as the percent of the value, relative to benzene.
Table 3: Integrated NICS,zz values. The 5* is the normalized (according to the number of electrons) NICS value. 100 Å was taken as the infinity value for r.
1 2 3 4 5 6 7 8 9 10 11 12 13 5*
CMO- NICS,zz -82.18 -77.86 -84.10 -84.68 -135.05 -22.6 -78.07 -65.37 -52.98 -73.27 -71.84 110.11 321.56 -81.03
% of benzene 100 94.74 102.34 103.04 164.33 27.50 95.00 79.54 64.47 89.16 87.42 -133.99 -391.29 98.60
-only NICS ,zz -92.5410.15 -65.103.96 -95.6912.66 -97.6813.34 -119.6011.54 -55.4515.47 -86.3810.83 -59.114.06 -49.405.70 -80.1613.50 -78.6913.46 103.610.06 322.616.51 -71.766.92
% of benzene 100 70.35 103.40 105.55 129.24 59.92 93.34 63.88 53.38 86.62 85.03 -111.96 -348.62 77.54
The values for CMO-NICS,zz look quite different from those of the -only model, however, as can be observed in Figure S2, the correlation is good. The %NICS of benzene for both methods are different, however, it should be noted that these values do not include the error bars provided with the -only
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model. Most importantly, both methods yield the same order of NICS,zz, which is crucial for meaningful comparisons How good are NICS(0),zz, NICS(1),zz, and NICS(0),zz in comparison with NICS,zz? Correlations between the data in Table 1 and Table 3 suggest that best is the optimized NICS(1),zz (R2=0.99738). The standard NICS(1),zz, obtained with the 3rd degree polynomial yields a correlation coefficient of R2=0.98061. The full correlations are given in the Supporting Information.
Summary and conclusions. It has been shown that when NICS,zz values are calculated at small distances from a system, they are not reliable and should not be used for assessment of aromaticity. However, NICS-scan methods are quite dependable for qualitative and semi-quantitative results. For quantitative NICS,zz values one has to scan at larger distances – in most cases starting at 2.0 Å above the molecular plane is high enough.29 For systems containing heteroatoms, a grid of BQs at different heights is needed to determine at which X and Y coordinates the BQs should be places to construct an accurate Z-scan. Nevertheless, at large distances ( 2.0 Å) the scan can be carried out above the geometrical centers, as the differences from the maximal (absolute) values are minimal. Finally, it is suggested to use integrated values of NICS,zz (denoted as NICS,zz) for quantitative comparisons when aromaticity is of concern. Supporting information: Coordinates of the BQ grids, optimized geometries of 1-13 and their -only model, plots of various NICS,zz methods and a complete list of all the NICS,zz values. References and footnotes 1.
Aromaticity themed issue: Chem. Soc. Rev. 2015, 44, issue 18.
2.
Aromaticity Themed issue: Phys. Chem. Chem. Phys. 2016, 18, issue 17.
3.
Gershoni-Poranne, R.; Stanger, A. “Magnetic criteria of aromaticity” Chem. Soc. Rev. 2015, 44, 6597-6615.
4.
Pople, J. A. “Molecular orbital theory of aromatic ring currents” Mol. Phys. 1958, 1, 175-180.
5.
See, for example, Islas, R.; Martinez-Guajardo, G.; Jimenez-Halla, J. O. C.; Solả, M.; Merino, G. “Not All That Has a Negative NICS Is Aromatic: The Case of the H-Bonded Cyclic Trimer of HF” J. Chem. Theor. Comput. 2010, 6, 1131-1135. -10ACS Paragon Plus Environment
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6.
Van Damme, S.; Acke, G.; Havenith, R. W. A.; Bultinck, P “Can the current density map topology be extracted from the nucleus independent chemical shifts?”. Phys. Chem. Chem. Phys. 2016, 18, 11746-11755.
7.
Schleyer, P. v. R.; Jiao, H.; van Eikema Hommes, N. J. R.; Malkin, V. G.; Malkina, O. “An Evaluation of the Aromaticity of Inorganic Rings: Refined Evidence from Magnetic Properties” J. Am. Chem. Soc. 1997, 119, 12669-12670.
8.
Stanger, A. “Nucleus-Independent Chemical Shifts (NICS): Distance Dependence and Revised Criteria for Aromaticity and Antiaromaticity” J. Org. Chem. 2006, 71, 883-893.
9.
Klod, S.; Kleinpeter, E. “Ab initio calculation of the anisotropy effect of multiple bonds and the ring current effect of arenes—application in conformational and configurational analysis” J. Chem. Soc. Perkin Trans. 2, 2001, 1893-1898.
10 .
Kleinpeter, E.; Klod, S.; Koch, A. “Visualization of through space NMR shieldings of aromatic and anti-aromatic molecules and a simple means to compare and estimate aromaticity” THEOCHEM 2007, 811, 45-60.
11.
Corminboeuf, C.; Heine, T.; Seifert, G.; Schleyer, P. V. R.; Weber, J. “Induced magnetic fields in aromatic [n]-annulenes—interpretation of NICS tensor components” Phys. Chem. Chem. Phys. 2004, 6, 273-276.
12.
Fallah-Bagher-Shaidaei, H.; Wannere, C. S.; Corminboeuf, C.; Puchta, R.; Schleyer, P. V. R. “Which NICS Aromaticity Index for Planar π Rings Is Best?” Org. Lett. 2006, 8, 863-866.
13.
Stanger, A. “Obtaining Relative Induced Ring Currents Quantitatively from NICS” J. Org. Chem. 2010, 75, 2281-2288.
14.
Jimenez-Halla, J. O. C.; Matito, E.; Robles, J.; Solá, M. “Nucleus-independent chemical shift (NICS) profiles in a series of monocyclic planar inorganic c”mpounds" J. Organomet. Chem. 2006, 691, 4359-4366.
15.
Gershoni-Poranne, R.; Stanger, A. “The NICS-XY-Scan: Identification of Local and Global Ring Currents in Multi-Ring Systems” Chem. Eur. J., 2014, 20, 5673-5688.
16.
Foroutan-Nejad, C.; Shahbazian, S.; Rashidi-Ranjbar, P. “The electron density vs. NICS scan: a new approach to assess aromaticity in molecules with different ring sizes” Phys. Chem. Chem. Phys. 2010, 12, 12630-12637.
17.
Foroutan-Nejad, C.; Shahbazian, S.; Rashidi-Ranjbar, P. “Reply to the ‘Comment on “The electron density vs. NICS scan: a new approach to assess aromaticity in molecules with different ring sizes”’ by A. Stanger, Phys. Chem. Chem. Phys., 2011, 13, DOI: 10.1039/c0cp02407d” Phys. Chem. Chem. Phys. 2011, 13, 12655-12658.
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18.
Stanger, A. “Comment on “The electron density vs. NICS scan: a new approach to assess aromaticity in molecules with different ring sizes” by C. Foroutan-Nejad, S. Shahbazian and P. RashidiRanjbar, Phys. Chem. Chem. Phys., 2010, 12, 12630: is there a connection between electron densities at the ring critical points and NICS?” Phys. Chem. Chem. Phys. 2011, 13, 12652-12654.
19.
Morao, I.; Cossío, F. P. “A Simple Ring Current Model for Describing In-Plane Aromaticity in Pericyclic Reactions” J. Org. Chem. 1999, 64, 1868-1874.
20.
Gaussian 09, Revision D.01, Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, et. Al, Gaussian, Inc., Wallingford CT, 2009.
21.
Rahalkar, A.; Stanger, A. “Aroma” package; https://chemistry.technion.ac.il/members/amnonstanger/
22.
Bohmann. J. A.; Weinhold, F.; Farrar, T. C. “Natural chemical shielding analysis of nuclear magnetic resonance shielding tensors from gauge- including atomic orbital calculations” J. Chem. Phys. 1997, 107 1173-1184.
23.
Glendening, E. D.; Badenhoop, A. K.; Reed, A. E.; Carpenter, J. E.; Bohmann, J. A.; Morales, C. M.; Landis, C. R.; Weinhold, F. Theoretical Chemistry Institute, University of Wisconsin, Madison (2013).
24.
Acke, G.; Van Damme, S.; Havenith, R. W. A.; Bultinck, P. “Interpreting the behavior of the NICSzz by resolving in orbitals, sign, and positions” J. Comp. Chem. 2018, 39, 511-519.
25.
Clearly, not all the electrons are delocalized; otherwise, all the systems with the same number of electrons would produce the same ring current, which is not the case. A feasible speculation is that these localized electrons produce localized induced currents, which, in turn, produce induced magnetic fields that are observed by the NICS,zz. These induced fields are relatively small and fade relatively fast with the distance. Thus, at short distances from the molecular plane the induced magnetic field is produced by the ring currents and local currents. Only at higher elevations the induced magnetic field (as read by NICS,zz) is a product of the pure ring current.
26.
A logarithmic form of this equation was used before. See, for example, reference 13 and Jesélius, J.; Sundholm, D. “Ab initio determination of the induced ring current in aromatic molecules” Phys. Chem. Chem. Phys. 1999, 1, 3429-3435.
27.
A quantitative relation of the induced field as a function of distance is given in Foroutan-Nejad, C.; Shahbazian, S.; Feixas, F.; Rashidi-Ranjbar, P.; Solà, M. “A dissected ring current model for assessing magnetic aromaticity: A general approach for both organic and inorganic rings” J. Comp. Chem. 2011, 32, 2422-2431. However, this model is based on infinite thin current loop, and local currents, if exist, are not considered.
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28.
Monaco, G.; Zanasi, R. “Assessment of Ring Current Models for Monocycles” J. Phys. Chem. A. 2014, 118, 1673-1683.
29.
Please note that “Aroma” utility (reference 14) can be easily modified to carry out the NICS-scan procedures within any desired range (starting height, ending height) and interval distance between BQs.
TOC graphics
%NICS 100.0
1.40
99.22
1.35
98.44
1.30
97.66
1.25
96.88
1.20
96.10
1.15
z
1.10
95.32
1.05 1.00
94.54 93.76
0.95 0.90
92.98 92.20
0.85 0.80
0.6
0.4
-0.6
-0 .4
0.2
0 .0
-0.2
0. 2
x
y
0.0
-0 .2
0. 4
-0.4
0. 6
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-0.6
TOC text An XY grid of BQs at different distances (Z) from the molecular plane suggests that the maximum induced magnetic filed is off-center at distances < 1.2 Å even in symmetric systems (left – benzene). It is also found that the order of diatropicity (according to NICS,zz) depends on the height at which it is calculated. A new method which is based on scanning NICS at distances ≥ 2 Å and integrate all NICS,zz (NICS) is proposed.
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