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Mini Project: Ionic liquids


Comparison of selected 'onium' cations

Optimisation of [N(CH3)4]+



The optimisation file can be found here and this is the Dspace-URL. 

Item               Value     Threshold  Converged?
Maximum Force            0.000074     0.000450     YES
RMS     Force            0.000017     0.000300     YES
Maximum Displacement     0.001369     0.001800     YES
RMS     Displacement     0.000363     0.001200     YES
Predicted change in Energy=-5.564733D-08
Optimization completed.
-- Stationary point found.






Frequency analysis of [N(CH3)4]+

The frequency file can be found here and this is the Dspace-URL. 

Low frequencies ---  -13.0244   -0.0008   -0.0004    0.0007    6.1739   11.9602
 Low frequencies ---  179.8943  278.8652  285.7089
Vibrational frequencies
Number frequency intensity Number frequency intensity Number frequency intensity
1 179 0 16 1076 0 31 1530 54
2 279 0 17 1182 0 32 1531 54
3 286 0 18 1183 0 33 1533 53
4 293 0 19 1306 1 34 3087 1
5 358 0 20 1306 1 35 3087 1
6 360 0 21 1307 1 36 3088 1
7 453 0 22 1452 5 37 3096 0
8 454 0 23 1454 5 38 3188 0
9 455 0 24 1454 5 39 3188 0
10 736 0 25 1486 0 40 3188 0
11 939 22 26 1486 0 41 3189 0
12 939 22 27 1501 0 42 3190 0
13 940 22 28 1502 0 43 3194 1
14 1075 0 29 1511 0 44 3195 1
15 1075 0 30 1530 0 45 3195 1

All the vibrational frequencies are positive and thus a minimum has been obtained.

NBO analysis of [N(CH3)4]+

The NBO analysis file can be found here and this is the Dspace-URL.

Charge Distribution of [N(CH3)4]+ Specific NBO charges for N, C and H

Bright red colour indicates negative charge,
green colour positive charge.

NBO charge of N atom = -0.295
NBO charge of each C atom = -0.483
NBO charge of each H atom = 0.269

Charge range: -0.500 to 0.500


The N atom donates its lone pair to form one of the N-C bonds and thus decreasing its negative charge. It is electron deficient. This is compensated a bit by the strong inductive effect that is due to a good orbital overlap and the great electronegativity of nitrogen. Ergo it is still negatively charged but not as much as the nitrogen atom in for example trimethylamine would be.
BD ( 1) C   1 - N  17
( 33.65%)   0.5801* C   1 s( 20.76%)p 3.81( 79.07%)d 0.01(  0.16%)
( 66.35%)   0.8146* N  17 s( 25.00%)p 3.00( 74.97%)d 0.00(  0.03%)

All carbon atoms are negatively charged to balance some of the overall positive charge of this molecule. They do this by withdrawing electron density from the surrounding hydrogen atoms. 

BD ( 1) C   1 - H   2
( 63.47%)   0.7967* C   1 s( 26.42%)p 2.78( 73.53%)d 0.00(  0.05%)
( 36.53%)   0.6044* H   2 s( 99.95%)p 0.00(  0.05%)

Consequently, the hydrogen atoms are positively charged because they do not have much electron density in the first place. In addition, due to the good C-H orbital overlap the slightly more electronegative carbon pulls off their electron density.
Interesting to look at is the total of all NBO charges in this molecule. This should prove the overall 1+ charge: (4 x -0.483) + 0.295 + (12 x 0.269) = 1.053

Placing the positive charge on the central nitrogen thus represents its electron deficiency due to its lone pair donation to form a bond but not the actual charge of the atom. That is, as discussed above, still negative. The actual positive charge is held by the hydrogen atoms. However, for drawing purposes it is very hard to show a total of one positive charge allocated on 12 different H-atoms. Therefore it would be correct and easy to draw the cation like shown on the picture on the right.


Examples of moleculare orbitals of [N(CH3)4]+
MO no 6 MO no. 10 MO no. 12
Strong, bonding AO interactions
Weak through-space interactions (bonding)
MO is very delocalised
No nodes 		Strong, bonding AO interactions
Strong through-space interactions (bonding & antibonding)
MO is partly delocalised
4 nodes at atoms 		Strong, bonding AO interactions
Strong & weak through-space interactions (antibonding & bonding respectively)
MO is not very delocalised
3 nodes at atoms
MO no 16 MO no 21
Strong, antibonding AO interactions
Strong through-space interactions (antibonding & bonding)
MO is not very delocalised
4 nodes at atoms 		Weakly bonding AO interactions
Strong through-space interactions (antibonding)
MO is partly delocalised
3 nodes at atoms






Optimisation of [P(CH3)4]+



The optimisation file can be found here and this is the Dspace-URL. 

Item               Value     Threshold  Converged?
 Maximum Force            0.000148     0.000450     YES
 RMS     Force            0.000033     0.000300     YES
 Maximum Displacement     0.000899     0.001800     YES
 RMS     Displacement     0.000305     0.001200     YES
 Predicted change in Energy=-1.785060D-07
 Optimization completed.
    -- Stationary point found.





Frequency analysis of [P(CH3)4]+



The frequency file can be found here and this is the Dspace-URL. 

Low frequencies ---  -16.5110   -0.0012    0.0019    0.0028    4.9692   16.2247
 Low frequencies ---  153.3828  183.0512  191.0039

NBO analysis of [P(CH3)4]+

The NBO analysis file can be found here and this is the Dspace-URL.

Charge Distribution of [P(CH3)4]+ Specific NBO charges for P, C and H

Bright red colour indicates negative charge,
green colour positive charge.


NBO charge of P atom = 1.667
NBO charge of each C atom = -1.060
NBO charge of each H atom = 0.298

Charge range: -0.500 to 0.500


The positive charge on phosphorus can be explained by several factors. It donates its lone pair to form one of the P-C bonds and thus decreases its negative charge. So it is electron deficient. In contrast to [N(CH3)4]+ however, phosphorus has more diffuse orbitals than nitrogen does so that the orbital overlap between carbon and phosphorus is worse. In addition phosphorus is also less electronegative than carbon. Therefore phosphorus is not able to effectively compensate its electron deficiency. It stays positively charges. 
BD ( 1) C   1 - P  17
( 59.56%)   0.7718* C   1 s( 25.24%)p 2.96( 74.68%)d 0.00(  0.08%)
( 40.44%)   0.6359* P  17 s( 24.99%)p 2.97( 74.16%)d 0.03(  0.85%)

To balance some of the overall positive charge of this molecule all carbon atoms are negatively charged. They do this by withdrawing electron density from the surrounding hydrogen atoms. 

BD ( 1) C   1 - H   2
( 64.78%)   0.8049* C   1 s( 24.88%)p 3.02( 75.07%)d 0.00(  0.04%)
( 35.22%)   0.5934* H   2 s( 99.95%)p 0.00(  0.05%)

The hydrogen atoms are positively charged because they do not have much electron density in the first place. In addition, due to the good C-H orbital overlap the slightly more electronegative carbon pulls off electron density. This is why carbon is actually the most negatively charged.

Interesting to look at is the total of all NBO charges in this molecule. This should prove the overall 1+ charge:
(4 x -1.060) + 1.667 + (12 x 0.298) = 1.003






Optimisation of [S(CH3)3]+



The optimisation file can be found here and this is the Dspace-URL. 

Item               Value     Threshold  Converged?
 Maximum Force            0.000040     0.000450     YES
 RMS     Force            0.000009     0.000300     YES
 Maximum Displacement     0.000519     0.001800     YES
 RMS     Displacement     0.000142     0.001200     YES
 Predicted change in Energy=-1.109390D-08
 Optimization completed.
    -- Stationary point found.





Frequency analysis of [S(CH3)3]+

The frequency file can be found here and this is the Dspace-URL. 

Low frequencies --- -12.9857 -8.1326 -0.0022 0.0025 0.0030 22.9251
 Low frequencies --- 158.4653 194.1206 198.5766


NBO analysis of [S(CH3)3]+

The NBO analysis file can be found here and this is the Dspace-URL.

Charge Distribution of [S(CH3)3]+ Specific NBO charges for S, C and H

Bright red colour indicates negative charge,
green colour positive charge.


NBO charge of S atom = 0.917
NBO charge of each C atom = -0.845
NBO charge of each H atom = 0.297

Charge range: -0.500 to 0.500


The positive charge on sulfur can be explained by several factors. It donates one of its lone pair into the S-C bonds and thus decreases its negative charge. In contrast to [N(CH3)4]+ however, sulfur has more diffuse orbitals than nitrogen so that the orbital overlap between carbon and sulfur is worse. In addition sulfur is almost as electronegative as carbon. Therefore sulfur is not able to effectively compensate its electron deficiency. It stays positively charged. 
BD ( 1) C   1 - S  13
( 48.67%)   0.6976* C   1 s( 19.70%)p 4.07( 80.16%)d 0.01(  0.14%)
( 51.33%)   0.7165* S  13 s( 16.95%)p 4.86( 82.42%)d 0.04(  0.63%)

To balance some of the overall positive charge of this molecule all carbon atoms are negatively charged. They do this by withdrawing electron density from the surrounding hydrogen atoms. 

BD ( 1) C   1 - H   2
( 64.82%)   0.8051* C   1 s( 26.50%)p 2.77( 73.45%)d 0.00(  0.05%)
( 35.18%)   0.5931* H   2 s( 99.95%)p 0.00(  0.05%)

The hydrogen atoms are positively charged because they do not have much electron density in the first place. In addition, due to the good C-H orbital overlap the slightly more electronegative carbon pulls off electron density.
Interesting to look at is the total of all NBO charges in this molecule. This should prove the overall 1+ charge: (3 x -0.845) + 0.917 + (9 x 0.297) = 1.055






Comparison of [N(CH3)4]+,[P(CH3)4]+ and [S(CH3)3]+

Electronegativities[1]
Element N S C P H
Electronegativity 3.0 2.5 2.5 2.1 2.2
Bond distances (in Å) and angles
[N(CH3)4]+ [P(CH3)4]+ [S(CH3)3]+ Interpretation
C-X 1.51 (lit. 1.451[2]) 1.81 (lit. 1.841[3]) 1.82 (lit. 1.83[4]) The bond length order of N-C < P-C < S-C can be rationalised by the fact that nitrogen is the smallest and most electronegative atom. Sulfur and phosphorus are both in the second period and their bond to C is of almost equal length. Even though sulfur has a greater electronegativity S-C is slightly longer. This can be reasoned by the electron-electron repulsion from sulphur's lone pair or considering the orbital overlap. Nitrogen and carbon are in the same period and so their orbitals overlap very well while those of phosphorus and sulfur are more diffuse. The worse the overlap the longer is the bond.
All computed bond lengths are close to the literature value.

The angles are except for minor differences very similar. Just the C-S-C angle is quite different from the other two, which is due to its lone pair. Sulphur is in group 6 rather than 5 like the others and thus three methyl groups are already sufficient to form the cation. One lone pair is left for the S atom while the one in nitrogen and phophorus is used for the fourth methyl group. A lone pair of electrons blocks more space than electrons bonding to a methyl group, squeezing the three methyls on sulphur a bit more. Ergo the angle is smaller.

C-H 1.09 1.09 1.09
C-X-C 109.5° 109.5° 102.7°
H-C-X 108.9° 109.9° 110.6°
H-C-H 110.1° 109.0° 109.4°
Orbital Contribution of an C-X bond
Molecule Orbital contribution Interpretation
[N(CH3)4]+ 
BD ( 1) C   1 - N  17
( 33.65%)   0.5801* C   1 s( 20.76%)p 3.81( 79.07%)d 0.01(  0.16%)
( 66.35%)   0.8146* N  17 s( 25.00%)p 3.00( 74.97%)d 0.00(  0.03%)
 The data obtained gives information about the orbital contributions of both atoms to their bond.
Following on from the interpretation above it can be noticed that sulfur has a higher p-orbital contribution to the a S-C bond than nitrogen or phosphorus do. Since all three p-orbitals are aligned 90° to each other this also accounts for the fact that the C-S-C angles in [S(CH3)3]+ are smaller — closer to 90° — than those of the other two compounds.

While nitrogen contributes about two third to the C-N bond, S-C is of almost equal contribution with sulphur's being slightly higher than carbons. Phosphorus, however, contributes quite some electron density less to the P-C bond than does carbon. This can be mainly explained by the electronegativity order: N > S > C > P . Nitrogen is much more electronegative than carbon and thus the electron density of the N-C bond is situated closer to N than to C. This inductive effect is almost balanced in the S-C bond and shifts towards carbon when swapping from S to P.

[P(CH3)4]+ 
BD ( 1) C   1 - P  17
( 59.56%)   0.7718* C   1 s( 25.24%)p 2.96( 74.68%)d 0.00(  0.08%)
( 40.44%)   0.6359* P  17 s( 24.99%)p 2.97( 74.16%)d 0.03(  0.85%)
[S(CH3)3]+ 
BD ( 1) C 1 - S 13
( 48.67%) 0.6976* C 1 s( 19.70%)p 4.07( 80.16%)d 0.01( 0.14%)
( 51.33%) 0.7165* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)







Influence of functional groups

Optimisation of [N(CH3)3(CH2OH)]+



The optimisation file can be found here. 

Item               Value     Threshold  Converged?
Maximum Force            0.000004     0.000015     YES
RMS     Force            0.000001     0.000010     YES
Maximum Displacement     0.000036     0.000060     YES
RMS     Displacement     0.000009     0.000040     YES
Predicted change in Energy=-1.020218D-10
Optimization completed.
-- Stationary point found.






Frequency analysis of [N(CH3)3(CH2OH)]+

The frequency file can be found here. 




Low frequencies --- -14.4774 -5.6007 0.0010 0.0011 0.0014 10.3045
Low frequencies --- 128.6428 210.7614 255.3099

NBO analysis of [N(CH3)3(CH2OH)]+

The NBO analysis file can be found here.

Charge Distribution of [N(CH3)3(CH2OH)]+

Bright red colour indicates negative charge,
bright green colour positive charge.

Charge range: -0.500 to 0.500


NBO charges
N atom O atom C atoms H atoms
16 -0.322 17 -0.725 1 -0.492 2 0.265
5 -0.494 3 0.274
9 0.089 4 0.269
12 -0.491 6 0.271
7 0.262
8 0.272
10 0.249
11 0.237
13 0.265
14 0.266
15 0.282


Here the charges are not all the the same for every atom of the same element. This is due to the reduced symmetry compared to the first three examples.

The negative charge on nitrogen is obviously due to its great electronegativity, which is nicely shown by the contribution nitrogen does to the N-C(5) bond i.e. the percentage of the electron density of the bond that is situated on nitrogen. This will be almost the same figures for C(1) and C(12). 

BD ( 1) C   5 - N  16
( 34.06%)   0.5836* C   5 s( 20.81%)p 3.80( 79.03%)d 0.01(  0.16%)
( 65.94%)   0.8120* N  16 s( 25.47%)p 2.93( 74.50%)d 0.00(  0.03%)

However, the N atom donates its lone pair to form one of the N-C bonds and thus decreasing its negative charge. Nitrogen's contribution is slightly higher in its bond to C(9) because carbon 9 already looses so much electron density to the neighboring oxygen thus it is easier for nitrogen to withdraw more electron density relative to the amount it sucks off the other bonded carbons. 

BD ( 1) C 9 - N 16
( 32.72%) 0.5720* C 9 s( 20.27%)p 3.92( 79.55%)d 0.01( 0.18%)
( 67.28%) 0.8203* N 16 s( 23.47%)p 3.26( 76.50%)d 0.00( 0.03%)

The oxygen atom is the most negatively charged since it has the greatest electronegative of all elements in this molecule and can suck off electron density from its neighboring atoms very effectively due to a good orbital overlap. Both carbon and hydrogen are in the same period as oxygen. Therefore O has a greater bond contribution to the O-C bond than carbon. 

BD ( 1) C   9 - O  17
( 33.90%)   0.5822* C   9 s( 23.72%)p 3.21( 76.04%)d 0.01(  0.24%)
( 66.10%)   0.8130* O  17 s( 32.28%)p 2.10( 67.64%)d 0.00(  0.08%)

Consequently, the electron suction from both oxygen and nitrogen results in carbon atom 9 to have the most positive charge relative to the other C atoms.
The hydrogen atoms are positively charged because they do not have much electron density in the first place. In addition, due to the good C-H orbital overlap the slightly more electronegative carbon pulls off their electron density. This is why carbon is actually the most negatively charged. Hydrogen atom 18, however is the most positively charged compared to the others attached to carbons. This is because it is bonded to oxygen and thus looses more electron density than the others as described above. 

LP (   2) O  17                /144. BD*(   1) C   9 - N  16           18.99    0.51    0.088

Interesting is also the fact that oxygen donates one of its lone pair into the C(9)-N(16) antibonding orbital weakening this bond and providing partial delocalisation.






Optimisation of [N(CH3)3(CH2CN)]+



The optimisation file can be found here and this is the Dspace-URL. 


Item               Value     Threshold  Converged?
 Maximum Force            0.000023     0.000450     YES
 RMS     Force            0.000005     0.000300     YES
 Maximum Displacement     0.000661     0.001800     YES
 RMS     Displacement     0.000148     0.001200     YES
 Predicted change in Energy=-7.074140D-09
 Optimization completed.
    -- Stationary point found.





Frequency analysis of [N(CH3)3(CH2CN)]+

The frequency file can be found here and this is the Dspace-URL. 


Low frequencies ---  -12.0745   -0.0009   -0.0006    0.0002    5.4144   13.3080
Low frequencies ---   91.4571  153.9675  210.0185

NBO analysis of [N(CH3)3(CH2CN)]+

The NBO analysis file can be found here and this is the Dspace-URL.

Charge Distribution of [N(CH3)3(CH2CN)]+

Bright red colour indicates negative charge,
bright green colour positive charge.

Charge range: -0.500 to 0.500



NBO charges
N atoms C atoms H atoms
16 -0.289 1 -0.358 2 0.309
18 -0.186 4 -0.489 3 0.309
8 -0.485 5 0.270
12 -0.489 6 0.274
17 0.209 7 0.282
9 0.271
10 0.277
11 0.271
13 0.282
14 0.282
15 0.269





Here the charges are not all the the same for every atom of the same element. This is due to the reduced symmetry compared to the first three examples.

The negative charge on nitrogen 16 is obviously due to its great electronegative. Ergo more electron density of for example the N(16)-C(4) bond is on nitrogen. These figures will be very similar in the C(8)-N(16) and C(12)-N(16) bonds. 

BD ( 1) C   4 - N  16
( 33.12%)   0.5755* C   4 s( 20.23%)p 3.93( 79.60%)d 0.01(  0.17%)
( 66.88%)   0.8178* N  16 s( 25.36%)p 2.94( 74.61%)d 0.00(  0.03%)

However, it donates its lone pair to form one of the N-C bonds and thus decreasing its negative charge. It becomes electron deficient. Nitrogen atom 18 is negatively charged since it withdraws electron density from carbon 17. 

BD ( 1) C  17 - N  18
( 42.68%)   0.6533* C  17 s( 47.95%)p 1.09( 52.03%)d 0.00(  0.02%)
( 57.32%)   0.7571* N  18 s( 45.15%)p 1.21( 54.49%)d 0.01(  0.36%)

It can be noticed that the contribution of N(18) to the N(18)-C(17) bond is less than that of N(16)-C(4), which is due N(18) lacking electron deficiency. Also nitrogen atom 18 can suck off electron density only from its neighboring carbon atom 17 while N(16) has 4 surrounding carbon atoms. Therefore nitrogen atom 16 is more negatively charged than 18.
Carbon 1 is more positively charged than the other C atoms attached to N(16) because of the electron withdrawing effect of the nitrile group bonded to it. In addition it has one hydrogen atom less attached to it to gain electron density of.
C(17) is even positively charged, which is caused by several factors. First of all N(18) sucks off electron density as seen by the bond contributions below. 

BD ( 1) C  17 - N  18
( 42.68%)   0.6533* C  17 s( 47.95%)p 1.09( 52.03%)d 0.00(  0.02%)
( 57.32%)   0.7571* N  18 s( 45.15%)p 1.21( 54.49%)d 0.01(  0.36%)
BD ( 2) C  17 - N  18
( 47.13%)   0.6865* C  17 s(  0.00%)p 1.00( 99.95%)d 0.00(  0.05%)
( 52.87%)   0.7271* N  18 s(  0.00%)p 1.00( 99.59%)d 0.00(  0.41%)
BD ( 3) C  17 - N  18
( 49.36%)   0.7026* C  17 s(  0.09%)p99.99( 99.87%)d 0.45(  0.04%)
( 50.64%)   0.7116* N  18 s(  0.03%)p99.99( 99.57%)d15.47(  0.40%)

Furthermore, The hydrogen atoms are positively charged because they do not have much electron density in the first place. In addition, due to the good C-H orbital overlap the slightly more electronegative carbon pulls off their electron density. This is why carbon is actually the most negatively charged.
Probably unexpected is that the lone pair of N(18) is donated into the C(1)-C(17) antibonding obitals through C(17) weakening their bond and proving partial delocalisation. This happens even though N(18) has already formed a triple bond to C(17). 

27. LP (   1) N  18                /122. RY*(   1) C  17                   16.69    1.20    0.127
27. LP (   1) N  18                /145. BD*(   1) C   1 - C  17           12.71    0.94    0.098



Comparison of [N(CH3)4]+,[N(CH3(CH2OH)3]+ and [N(CH3)3(CH2CN)]+

Comparison of HOMO-LUMO energies
[N(CH3)4]+ [N(CH3)3(CH2OH)]+ [N(CH3)3(CH2CN)]+
LUMO
-0.13305 a.u. -0.12462 a.u. -0.18182 a.u.
HOMO
-0.57929 a.u. -0.48765 a.u. -0.50048 a.u.
HOMO-LUMO -0.44624 -0.36303 -0.31866

The stability order of the HOMOs (starting with the most stable) is the following: [N(CH3)4]+ > [N(CH3)3(CH2CN)]+ > [N(CH3)3(CH2OH)]+.
This is because the one from [N(CH3)4]+ is weakly bonding as already shown above. It has π-bonding interactions and nodes are only at atoms through p-orbitals. [N(CH3)3(CH2CN)]+ is almost non-bonding except for two π-antibonding interactions of which the biggest would be the nitrile group interacting with the CH2 carbon out-of-phase. However, the nitrile functional group itself has a large electron density interacting in-phase, probably making the overall molecule very slightly bonding. The mostly antibonding interactions in [N(CH3)3(CH2OH)]+ continue throughout the molecule. The only in-phase overlap worth mentioning is that of oxygen's lone pair with the H s-orbitals and C p-orbital of CH2.

The stability order of the LUMOs (starting with the most stable) is the following: [N(CH3)3(CH2CN)]+ > [N(CH3)4]+ > [N(CH3)3(CH2OH)]+.
This is because the one of [N(CH3)3(CH2CN)]+ has a nice interaction of the nitrile carbon with the CH2 carbon in a π-bonding manner and overlaps also with p-orbitals of all other carbons. The large difference to the HOMO, however, is obvious since many other antibonding interactions such as the out-of-phase central nitrogen are present. [N(CH3)4]+ and [N(CH3)3(CH2OH)]+ are lower in energy than [N(CH3)3(CH2CN)]+ because of the to the strong through-space antibonding interactions and the internuclear node between the central nitrogen atom and the surrounding methyl carbons.[N(CH3)3(CH2OH)]+ however, is the most destabilised one since it has stronger antibonding interactions, which are due to the in-phase overlap of the oxygen, CH2 and nitrogen orbitals with all other orbitals around.

The nitrile functional group makes the acceptance of electron density more profitable while an alcohol functional group results in more destabilisation relative to [N(CH3)4]+. Conversely, the alcohol group makes donation of electron density easier. However, this is rather hypothetical considering that these compounds are cations already.
The HOMO-LUMO gap gives information about the conjugation of each ion. The smaller the gap, the greater the degree of conjugation. Also the smaller the gap the easier electrons can be promoted to excited states.

  1. ↑ Atkin's Physical Chemistry, 4th edition
  2. ↑ J.E. Wollrab and V.W. Laurie, J. Chem. Phys., 1969, 51, 1583 DOI:10.1063/1.1672214
  3. ↑ D.R. Lide and D.E. Mann, J. Chem. Phys., 2004, 29, 914 DOI:10.1063/1.1744611
  4. ↑ D.E. Zuccaro and J.D. McCullough, Zeitschirft für Kristallog., 2010, 112, 401 DOI:10.1524/zkri.1959.112.1-6.401
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