Atropisomers with no heavy elements
The Parity Violation Energy Difference (PVED) depends on the fourth power of Z. In the first part of our work we considered chiral molecules known in literature showing atropisomerism but containing instead no heavy elements. This should facilitate the screening of molecules having the most interesting (larger PVED) backbone structures and in second instance our findings could be applied in the search of similar molecular architectures with heavy elements. Our search starts from helicenes, organic compounds having an exceptionally high optical rotatory power.
Atoms are colored by the PVED contribution of single atoms. Red and green color indicate, respectively, a positive and a negative effect (Figure 1). The total PVED effect is given by the summation of the atomic contributions (Table 1).
Table 1 Total PVED calculated with the different basis set. *:for the compound 3 it was calculated the opposite enantiomer
Molecule
|
PVED (Ha)
|
STO-6G
|
cc-pVDZ
|
Hexahelicene (1)
|
-4.5x10-20
|
/
|
Heptahelicene (2)
|
-6.4x10-20
|
-4.8x10-20
|
Diazahelicene (3)*
|
2.6x10-20
|
1.7x10-20
|
Paracyclophane (4)
|
/
|
-9.1x10-21
|
Twisted pentacene (5)
|
-2.4x10-19
|
-2.2x10-19
|
The modulus of PVED effect of helicenes 1-3 is inversely proportional to the distance from the center of the molecule. However, the sign changes alternatively leading ultimately to a low value of PVED. Values are almost insensitive by the substitution of carbon with nitrogen (see 3 vs. 1). For diazahelicene, the lower PVED value was due to the conformation change with respect to 1. In fact, as it is visible in figure XC, carbon atoms of the terminal benzene rings give a low effect on PVED. PVED slightly increases with the increase of atoms in the structure (2 vs. 1).
The effect of the basis set was explored with compound 3. Total PVED calculated with STO-6G, 6-31G(d) and cc-pVDZ are, respectively: -6.4x10-20, -4.2x10-20 and -4.8x10-20 Ha. Unfortunately calculations did not converge on all basis sets. Paracyclophane 4 (figure 2) has a scarcely predictable behavior that depends on the low symmetry. The best molecular structure from the point of view of cooperative PVED effect is the twisted pentacene 5 (Figure 2). This reflects on the highest PVED calculated among molecules 1-5 (see table 1).
The PVED effect of molecules having a phenylene repeating unit (Figure 3) was then investigated. Phenylenes have a low rotation barrier for the conversion between R and S. Usually at ambient temperature the rotation is free. However, ring substitutions might increase the rotational barrier. PVED of phenylenes shows a cooperative effect for atoms lying on the main axis, while the contribution of other atoms is almost negligible (figure 4).
Table 2 Calculated PVED for phenylenes and total value of PVED divided by the number of repeating units (See text)
Molecule
|
PVED (Ha)
|
PVED/n (Ha x1021)
|
Biphenyl (n=2)
|
1.7x10-21
|
0.85
|
Triphenyl (n=3)
|
3.4x10-21
|
1.13
|
Tetraphenyl (n=4)
|
5.1x10-21
|
1.28
|
Pentaphenyl (n=5)
|
6.8x10-21
|
1.36
|
The PVED of (poly)phenylenes is proportional to the number of phenylene repeating units (table 2). As it is visible from the last column of table 2, the total PVED divided by the number of repeating units shows an increment with a value that tends to 1.4.
Cinnabar crystals
Cinnabar (HgS) is a good candidate for the investigation of PVED since it can crystallize giving a helical structure (see figure 5). Calculations were effectuated on portions of HgS chains containing from 1 to 3 mercury atoms. Chains are capped with hydrogen atoms, however, the contribution of hydrogen to the total PVED is negligible. The highest calculated PVED is about 10-15 Ha for the HgS2H2 fragment. However, the PVED does not increase with the number of mercury atoms (See table 3).
Table 3 Total PVED calculated for cinnabar chains
Formula
|
Total PVED (Ha)
|
HgS2H2
|
-2.09x10-15
|
Hg2S3H2
|
-7.91x10-16
|
Hg3S4H2
|
-4.92x10-16
|
Table 4 PVED contribution of single mercury atoms for the cinnabar-like structures calculated
Structure
|
Contribution of mercury atom(s) on total PVED (Ha)
|
HgS2H2
|
-2.09x10-15
|
Hg2S3H2
|
-3.93x10-16
|
-3.93x10-16
|
Hg3S4H2
|
-3.57x10-16
|
2.32x10-16
|
-3.57x10-16
|
Analyzing more in detail the structures (Fig. 6), it is visible how in the structure having three mercury atoms, one mercury atom has a PVED of a different sign. In table 4 are listed all the values of PVED effect on mercury atoms for the different structures considered.
It seems reasonable to think that the PVED of atoms in these structures might depend on the position of the main inertia axis of the molecule. In fact, for the cinnabar analogue having one mercury atom, the value is high for the mercury (being close to the center of mass of the molecule). For the case with two atoms, the inertia axis runs parallel to the segment connecting the two Hg centers but is shifted towards the SH ends. In this case, the effect is lower since the axis is not close to the atomic centers. In the last case, with 3 mercury atoms, the inertia axis is parallel to the Hg atoms closer to SH ends, but it is shifted toward the central mercury atom. The sign of PVED might change with respect to the distance, as already mentioned by Lazzeretti (Faglioni and Lazzeretti 2001).