Practical 1: Structure and electronic properties of organic molecules. B/ Structure, electronic and vibrational properties of the water molecule
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1 D1CH MMCO Molecular Modelling applied to organic chemistry Practical 1: tructure and electronic properties of organic molecules B/ tructure, electronic and vibrational properties of the water molecule Optimize the geometry of the water molecule at the AM1 and PM6 levels and check: - the correct convergence of the calculation (gradient and frequencies) - the heat of formation - the relevant structural parameters - the vibrational frequencies - the molecular orbitals and their symmetry - the ionization potential - the atomic charges - the orientation and magnitude of the dipole moment Compare the theoretical results to experiments when available, and comment. Results Property AM1 PM6 Exp error wrt exp AM1 error wrt exp PM6 O- H bond (Å) 0,961 0,949 0,957-0,004 0,008 H- O- H angle (deg) 103,51 107,56 104,5 0,99-3,06 dipole (D) 1,861 2,068 1,85-0,011-0,218 charge O - 0,383-0,619 / / / charge H 0,191 0,309 / / / req, ym (cm- 1) req, Asym (cm- 1) req, Bending (cm- 1) IP (ev) 12,464 11,906 12,62 0,156 0,714 Heat of formation (kcal/mol) - 59,24-54,31-57,8 1,44-3,49 Conclusions AM1 compares better to experiments than PM6 regarding the electronic and strciural properties of the water molecules. As a genral remark, the computed properties always depend on the theoretical level of approximation. C/ Impact of the semi- empirical parameterization on the molecular geometry: Example of the - Acetyl Proline Amide Reference ab initio RH/6-31G(d,p) calculations have provided the following structural features for the - Acetyl Proline Amide (igure 1): 1
2 H 3 C O O H H! igure 1: - Acetyl Proline Amide. - A H- bond of 2.09 Å length exists between one of the H atoms of the amide group and the oxygen of the ether - The five membered proline ring is in the envelope form, with atoms C- - C- C approximately in one plane and the β carbon atom out of this plane (- C- C- Cb = 29 ) - The amide group is planar Optimize the geometry of the molecule using the MDO, AM1, PM3 and PM6 parameterizations, and compare with the reference results. Results MDO o H bond - C- C- C b = - 1 on- planar amide group AM1 H bond = 2.14 Å - C- C- C b = 1 Planar amide group PM3 H bond = 2.59 Å - C- C- C b = 0 on- planar amide group PM6 H bond = 2.01 Å - C- C- C b = 11 Planar amide group Conclusions Due to an overestimation of the repulsion between nuclei at large distances, the MDO parameterization does not predict the existence of H- bonds. Moreover, the proline ring is found planar and the amide group is pyramidal. AM1 predicts the hydrogen bond with the correct geometry and a planar amide group. However, it does not correct the wrong geometry of the proline ring. With PM3, the H- bond is much too long and both the proline ring and amide group geometries are poorly described. PM6 gives the better results with respect to the reference ab initio calculations, despite the torsional angle of the proline ring is underestimated (11 vs. 29 at the RH/6-31G(d) level). 2
3 D/ tructure and electronic properties of π- conjugated molecules Optimize the geometry of the increasingly large linear polyenes CnH2n+2 (n=2, 4, 6, 8, 10, 20) at the PM6 level and check: - the Bond Length Alternation (BLA) along the central part of the molecule - the shape of the HOMO and LUMO - the evolution of the HOMO and LUMO energies with n - the evolution of the HOMO- LUMO gap with n Plot the BLA and the HOMO- LUMO gap with respect to n, and comment !"# =!"!"!!!"!!!"! Results Bond Length Alternation n d 2-3 d 1-2 = d 3-4 BLA 4 1,469 1,335 0, ,344 1,465 0, ,461 1,345 0, ,346 1,461 0, ,46 1,346 0,114!"#'%$!"#'$!"#$%&'$!"#&%$!"#&$!"##%$!"##$!$ %$ #!$ #%$ &!$ &%$ ()*+,$-.,/0)$%,'$ Energies of the frontier orbitals and HOMO- LUMO gap n HOMO LUMO GAP 2-10, , , , , , , , , , , , , , , , , ,
4 !"#$%&'()*)"+$),(-)./( #$ %$ )$ "%$ ")$ #%$ #)$ %$!#$!($!'$!&$!"%$ *+,+$ -.,+$!"#$ 01&$*(')*+%1(-*/( hape of the frontier orbitals (example for n=6) tructure HOMO (top view) LUMO (top view) HOMOs have nodes on the single bonds. LUMOs have nodes on the double bonds. Conclusions When several atomic π- orbitals are combined along a sequence of adjacent atoms in sp 2 - hybridisation, a so- called π- conjugated system is formed in which the electrons are delocalised over the atoms of the molecule. The molecular energy levels are affected by π- conjugation: the larger the extent of conjugation, the smaller the energy gap between the frontier orbitals. The reduction of the gap with Increasing n is induced by a reduction of the BLA. This structural parameter is thus an indicator of the extent of the electron conjugation along the molecule. E/ tructure and electronic properties of push- pull molecules 1/ Optimize the geometry of the acrolein molecule (ig. 2) at the PM6 level (specify the keywords VECTOR and DEITY in the field ADDITIOAL KEYWORD ) and check: - the relevant structural parameters - the molecular orbitals - the atomic charges - the orientation and magnitude of the dipole moment igure 2: - M effect of the carbonyl group in the acrolein molecule. 4
5 a/ Write the ground state wavefunction of the acrolein molecule by using a 2- state model implying the neutral form and the zwitterionic form Z schematized ig. 2. b/ Calculate the π charge on the oxygen atom and evaluate the weights of the neutral and zwitterionic forms in the electronic ground state. c/ Extract from the density matrix the π bond index between adjacent atoms, and confirm the contribution of the zwitterionic form in the ground state wavefunction. d/ Deduce from the shapes of the frontier π- MOs whether an optical excitation would increase or decrease the weight of the zwitterionic form. 2/ Repeat the procedure for the ether molecule shown igure 2. Results (acrolein molecule) a/ 2- state model igure 3: +M effect of the methoxy group in an ether molecule. Using the simple model implying the forms > and Z>: = Z = the electronic ground state of the molecule can be expressed as: g = 1!"!" #"! $" # %" ( ) + " Z ( 0! "!1) with ρ the amount of charge transfer in the ground state (electron conjugation)! "!" # $!" b/ Populations and charges π LCAO coeff pz LCAO coeff pz population pi charge pi (C1) - 0,1506-0,6631 0,925 0,075 (O) - 0,769 0,3219 1,390-0,390 The +M effect in the molecule in induced by the delocalisation of the π lone pair of the oxygen atom. Therefore, ρ can be evaluated as the π charge of the oxygen : ρ = The ground state wavefunction is thus : g> = > + 0,6245 Z> c/ π bond index between adjacent atoms 5
6 Atoms Bond index C1- C2 C2- C C3- C4 C4- O The non- zero values of the BI (2-3) and (4- O), and the values smaller than 1 for the BI (1-2) and (3-4), confirm the contribution of the zwitterionic form in the ground- state wavefunction. d/ rontier orbitals HOMO- 1 LUMO / Photochromic systems 1/ Cis- trans isomerization of the Disperse Red 1 (DR1) molecule O 2 O nm h!, " HO HO igure 4: Cis- trans isomerization of DR1 a/ Optimize the cis and trans forms of DR1 at the PM6 level, and check for the two conformers: - the heat of formation - the HOMO- LUMO gap b/ The maximum absorption band of both forms is characterized by a HOMO- to- LUMO electronic transition. What can be expected regarding the displacement of the maximum absorption band along the trans- cis commutation? 6
7 2/ Answer the same questions for the commutation in the diarylethene system: C C 365 nm >600 nm C C igure 5: Photochromic equilibrium in a diarylethene derivative 7
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