Assignment 06
Soma& Jiasen
Discussion:
In this assignment, we optimize ethanol at B3LYP level with basis set 6-311+G(2d,p), exploring the charge distribution and the dipole moment of the optimized structure, showed in Figure 1, and based on the optimized structure, we further determine the H-NMR spectrum for ethanol, showed in Figure 2. We also optimized ozone at the same theoretical level and basis set, and performed a stability test, to explored which one between the restrictedwave function or the unrestricted wave function describe the ozone better.
Figure 1. (left) shows the direction of the dipole moment of the optimized structure of the ethanol. From the Mulliken charge distribution, shows in Figure 1. (center)we observe that oxygen atom has the most negative charge and the hydrogen atom which is attached with this oxygen. So most of the dipole moment comes from the OH group. The mythle group has also smaller contribution in the dipole moment. Most of the moment is directed in the Y-direction and there is a very small component in the X-direction. There is no moment in Z-direction.
Figure 1. (center) shows atoms color-coded according to their Mulliken charge. Oxygen atom of the hydroxyl group has the most negative charge with a value of -0.438. Then carbon atom of the mythle group has negative charge of -0.0335. All the hydrogen atom has positive charge with hydroxyl hydrogen has most positive charge of 0.262. Other hydrogen atom has very less significant positive charge.
Figure 1. (right) shows the electrostatic potential (ESP) mapped on electron density (ED) surface. The used color range was from -4.769E-2 to -4.769E-2. As it expected from the Mulliken charge distribution, that the oxygen atom will have most negative electrostatic potential and the hydrogen atom will have most positive electrostatic potential we observe that fact. From the color contribution we observe most of the part of the surface is green which represent neutral. We observe a little bit of positive ESP close to CH2group.
The ethanol H-NMR is showed in Figure 2. Which is determined according to the Gaussian calculated magnetic shielding tensor and spin-spin coupling constants calculated with GIAO method at the same level and basis set as the optimization. The reference substance is tetramethylsilane (TMS) with the same level, and the N+1 rule is used to split the average chemical shift based on the nuclear spin-spin coupling, and an experimental magnetic magnitude of 90 MHz is to determine the displacement between the splits. Noted that one of the hydrogen atom in the CH3 group differs in terms of chemical environment comparing with the other two, thus shows as a separate chemical shift in the original Gaussian determined H-NMR spectrum. We believe that this is because of the existence of the terminal hydroxyl group,which block the configuration conversion, namely, the rotation of the CH3group, due to the principle of minimal energy. To simplify the H-NMR determination, here in this work, we recalculate the average chemical shift in a weighted way, where the weight is taken as the intensity of the corresponding signal.
In the ethanol H-NMR spectrum, we observe totally three signals. one quadruple-splitted signal of at around 3.864 ppm, and one triply-splitted signal at around 1.138 ppm, the average spin-spin coupling constant for both these to group is determined to be 0.071 Hz. They can be assigned to CH2 of ethanol and CH3 respectively. That means that the CH3 hydrogens are more electron shielded compared to the CH2 hydrogens. Compare to the experimental ethanol H-NMR
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Assignment 06
Soma& Jiasen
[i], The calculated CH2 signal is slightly higher than the corresponding experimental signal, whereas the calculated CH3 signal is a little lower than the experimental value.Another signal at around 0.020 ppm in the calculated H-NMR spectrum differs significantly again the experimental signal, which is at 2.61, further work need to be done to assign this signal.
Restricted wave function means that the α and β electrons are required to be paired, whereas unrestricted wave function means that the α and β electrons are allowed to be in different molecular orbitals, which means the molecule will be biradical, this phenomenon is also called spin contamination[ii]. Figure 3.shows the optimized structure of ozone with restricted wave function and unrestricted wave function with the same basis set and theoretical level, respectively. By comparison, the calculation with unrestricted wave function gives lower total energy, which means the unrestricted wave function gives more stable structure, hence being better to describe ozone. The calculation with unrestricted wave function also shows lower dipole moment, as well as Mulliken charges for both centered oxygen and terminal oxygen. This is expected since in Scheme 1. we see that the unrestricted resonance forms have more positive as well as negative charges on atoms, which, averagely, contribute to higher positive charge for centered oxygen atom, and lower negative changes for terminal oxygen atoms.
Figure 4. shows the spin density of ozone calculated with unrestricted wave function. Combine with the ozone resonance forms in Scheme 1, we observe that for two unpaired α and β electrons, they can be on either of the two terminal oxygen atoms, which results in the spin density of opposite signs, in this case, different colors, localized on the two terminal oxygen atoms; also the unpaired two α and β electrons can be on the centered oxygen, which gives the spin density of opposite signs on both sides of the centered oxygen atom, hence the total spin density goes to be zero.
Figure 1. Optimized structure of ethanol with B3LYP/6-311+G(2d,p) showed with dipole moment (left), color-coded according to Mulliken charges (center), and with electrostaticpotential (ESP) mapped on electron density (ED) surface (right). Dipole moment is 1.6744 Debye and total energy is -155.098453 Hartree, the Mulliken charges of CH3, CH2, O, H(O) are 0.030763,0.155649, -0.438043, and 0.261850 respectively. The color range used on the right picture is -0.438 to +0.438, and the density value of electron density surface is 0.004. The ESP value was -4.769E-2 to -4.769E-2, the red region is most negative ESP which is on the oxygen atom and the blue region is the most positive ESP which is on hydrogen atom.
Figure 2. Ethanol H-NMR calculated with 6-311+G(2d,p) at B3LYP level, average chemical shift CH3 hydrogens and CH2 hydrogens are 1.138 ppm and 3.864 ppm respectively, the chemical shift of the another signal, of which the source we are not sure is 0.020 ppm, coupling constants for both the CH3 hydrogens and CH2 hydrogens is 0.071 Hz
Figure 3. Ozone with electric dipole moment (top left) and ozone color-coded according to Mulliken charges (top right) based on restricted wave function, optimized with RB3LYP/6-311+G(2d,p), the total energy and the dipole moment are -255.490176 Hartree and 0.6817 Debye, and the Mulliken charges are 0.254327on centered oxygen, -0.127163 for terminal oxygens; Ozone with electric dipole moment (bottom left) and ozone color-coded according to Mulliken charges (bottom right) based on unrestricted wave functions, the total energy and the dipole moment are -225.491780 Hartree and 0.5974 Debye, and the Mulliken charges are 0.223067 for centered oxygen, and -0.111534 for terminal oxygens.
Figure 4. Ozone spin density surface determined with unrestricted wave function with B3LYP/6-311+G(2d,p), the Mulliken spin populations of the centered oxygen is 0.000000, that of the terminal oxygens are 0.441834 and -0.441834, and the spin density is 0.00
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Assignment 06
Soma& Jiasen
Resonance forms for Restricted Wave Function / Resonance forms for Unrestricted Wave FunctionScheme 1. Ozone resonance forms for restricted wave function (left) and unrestricted wave function (right)
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Assignment 06
Soma& Jiasen
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([i])SDBS Web: (National Institute of Advanced Industrial Science and Technology, date of access)
([ii]) Ambili S. Menon and Leo Radom* J. Phys. Chem. A 2008, 112, 13225–13230