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Theoretical conformational analysis by the positive core potential energy method
Volume 48, number 1
CHEMICAL PHYSICS LE-M.ERS
15 Sky 1977
THEORETICAL CONFORMATIONAL ANALYSIS BY THE POSHIVE CORE POTENTIAL ENERGY METHOD A.F. MARCHINGTON and W.G. RICHARDS Physica Chemistry Laboratoty.
Oxfcrd OXI 3QZ. UK
Received 21 February 1977 A simple combination of quantum mechanical and classical methods appears to lead to a new method for theoretical conformational analysis. 1. Introduction Theoretical calculations of the conformational energy of flexible molecules have largely been either .
quantum mechanical or have involved empirical potential energy functions. The former method is only reliable if expensive ab initio methods are employed, which restricts attention to small model systems, while the second type of cdculation is unsatisfactory because so many disposable parameters are required in the atom-atom potential functions. We present here a new approach which is a synthesis of quantum mechanical and classical ideas and appears to be capable of treating large molecular systems with an accuracy superior to earlier methods yet uses very little computer time and no totally arbitrary parameters or empirical fitting of data.
describing the method we chose to avoid integration difficulties by successively moving the ceztre of the coordinate system from atom to atom, bu’. our current programme uses a single molecular crbital calculation and a matrix transformation, dztaik of which will be given elsewhere. The result of this calculation is an accurate value For the number of electrons within the sphere centred on each atom. Subtraction of this number from the atomic number OF the atom at the centre of the sphere yields a positive number which is the effective positive charge at the centre of the appropriate sphere or an estimate of the shielded nuclear charge. Fig. 1 shows such results For the ethane case.
2. Method and results By way of illustration we can consider a calculation of the barrier to internal rotation in etbane. The starting point of the new method is a single ab initio molecular orbital cakulation on ethane with the atomic coordinates derived from the known structure of the molecule. We have used the Gaussian 70 programme with an ST0 3G basis set [l]. From the molecular wavefunction we have derived the charge distribution
in the precise way defined by Dean and
Richards 121. The square of the total wavefunction is integrated over a sphere of covalent radius centred on each of the atoms in the molecule. In the paper
Fig. 1. Net positive charges within spheres of covalent radii
centred on the atomic nuclei in ethane. The spheres are of standard covalent radii and the numbers indicated Gthin the spheres are the atomic number of the nucleus minus the nurnber of electrons calculated to be within the sphere.
Volume 48. number 1
From fig. 1 it is qualitatively obvious that if we alIow free rotation about the single carbon-carbon bond then the most stable conformation will be the staggered form since the small positive charges will repel each other. Less obvious, but striking, is the difference in energies between the staggered and eclipsed forms computed on a simple coulombic basis by summing all positive-positive core electrostatic energies. The barrier to internal rotation calculated in this way is 16.5 kJ mol-t compared with the experimental value of 11.5 kJ mol-l [3]. The value calculated by the positive core potential energy method is not sensitive to the initial starting conformation, used for the molecular orbital calculation, So that it is not necessary to know the most stable conformation before starting the problem, nor in principle must the molecular geometry come from experiment, siice theoretical computations are reliable for bond lengths and angles. This simple technique has been used to study a number of other model systems with the results shown in table 1. For the range of nuclei involved the results are generally superior to either quantum mechanical or empirical methods. It would be possible to achieve even closer agreement with experiment if the covalent radii used for each atom were taken as adjustable parameters. We have chosen not to do this and have taken in each case published Pauling radii so that our calculations do not involve any arbitrary parameterization. Alternatively the introduction of a dielectric constant as a parameter can improve agreement. The advantage of this method is that molecules are treated quantum mechanically to achieve the electron distribution, and delocalization effects are incorporate& Thereseernsnorea~onwhy thisapproachshould not work for any type of rotation barrier with very
150
15 May 1977
CHEMICAL PHYSICS LElTERS Table 1
Comparison of some observed barriers with those calculated usinp:the PCPE method Molecule
CH3-CH3 CH3-CH2F CH3 -OH CH3 -NH2 a) Ref. [3].
Observed barrier
Calculated
(kJ m01-~)
(kJ mol-I)
11.48a) 13.91 b) 4.45 c) 8.27 d)
16.51 18.28 6.36 11.28
b) Ref. [4].
c) Ref. [S].
d) Ref. [6].
little restriction as to the size of the molecule if the initial computations are performed on suitable overlapping fragments. The close agreement with experiment indicates perhaps that it is indeed the repulsion between the shielded positive charges of nuclei which dominates the question of molecular conformation_
Acknowledgement Computing facilities from the SRC.
were supported
by a grant
References [l] W.J. Hehre, RF. Stewart and J.k Pople, J. Chem. Phys. 51 (1959) 2657. [2] S.M. Dean and W.G. Richards, Nature 256 (1975) 473. [3] S. Weiss and G.F. Leroi, J. Chem. Phys. 48 (1968) 962. [4] P.H. Verdier and F.E. Wilson, J. Chem. Phys. 29 (1958) 340 [S] E.V. Ivash and D.M. Denninsson, J. Chem. Phys. 21 (1953) 1804. [61 T. Nishikawa. T. Itoh and KmShimoda. J_ Chem Phys 23
(1953) 1735.
CHEMICAL PHYSICS LE-M.ERS
15 Sky 1977
THEORETICAL CONFORMATIONAL ANALYSIS BY THE POSHIVE CORE POTENTIAL ENERGY METHOD A.F. MARCHINGTON and W.G. RICHARDS Physica Chemistry Laboratoty.
Oxfcrd OXI 3QZ. UK
Received 21 February 1977 A simple combination of quantum mechanical and classical methods appears to lead to a new method for theoretical conformational analysis. 1. Introduction Theoretical calculations of the conformational energy of flexible molecules have largely been either .
quantum mechanical or have involved empirical potential energy functions. The former method is only reliable if expensive ab initio methods are employed, which restricts attention to small model systems, while the second type of cdculation is unsatisfactory because so many disposable parameters are required in the atom-atom potential functions. We present here a new approach which is a synthesis of quantum mechanical and classical ideas and appears to be capable of treating large molecular systems with an accuracy superior to earlier methods yet uses very little computer time and no totally arbitrary parameters or empirical fitting of data.
describing the method we chose to avoid integration difficulties by successively moving the ceztre of the coordinate system from atom to atom, bu’. our current programme uses a single molecular crbital calculation and a matrix transformation, dztaik of which will be given elsewhere. The result of this calculation is an accurate value For the number of electrons within the sphere centred on each atom. Subtraction of this number from the atomic number OF the atom at the centre of the sphere yields a positive number which is the effective positive charge at the centre of the appropriate sphere or an estimate of the shielded nuclear charge. Fig. 1 shows such results For the ethane case.
2. Method and results By way of illustration we can consider a calculation of the barrier to internal rotation in etbane. The starting point of the new method is a single ab initio molecular orbital cakulation on ethane with the atomic coordinates derived from the known structure of the molecule. We have used the Gaussian 70 programme with an ST0 3G basis set [l]. From the molecular wavefunction we have derived the charge distribution
in the precise way defined by Dean and
Richards 121. The square of the total wavefunction is integrated over a sphere of covalent radius centred on each of the atoms in the molecule. In the paper
Fig. 1. Net positive charges within spheres of covalent radii
centred on the atomic nuclei in ethane. The spheres are of standard covalent radii and the numbers indicated Gthin the spheres are the atomic number of the nucleus minus the nurnber of electrons calculated to be within the sphere.
Volume 48. number 1
From fig. 1 it is qualitatively obvious that if we alIow free rotation about the single carbon-carbon bond then the most stable conformation will be the staggered form since the small positive charges will repel each other. Less obvious, but striking, is the difference in energies between the staggered and eclipsed forms computed on a simple coulombic basis by summing all positive-positive core electrostatic energies. The barrier to internal rotation calculated in this way is 16.5 kJ mol-t compared with the experimental value of 11.5 kJ mol-l [3]. The value calculated by the positive core potential energy method is not sensitive to the initial starting conformation, used for the molecular orbital calculation, So that it is not necessary to know the most stable conformation before starting the problem, nor in principle must the molecular geometry come from experiment, siice theoretical computations are reliable for bond lengths and angles. This simple technique has been used to study a number of other model systems with the results shown in table 1. For the range of nuclei involved the results are generally superior to either quantum mechanical or empirical methods. It would be possible to achieve even closer agreement with experiment if the covalent radii used for each atom were taken as adjustable parameters. We have chosen not to do this and have taken in each case published Pauling radii so that our calculations do not involve any arbitrary parameterization. Alternatively the introduction of a dielectric constant as a parameter can improve agreement. The advantage of this method is that molecules are treated quantum mechanically to achieve the electron distribution, and delocalization effects are incorporate& Thereseernsnorea~onwhy thisapproachshould not work for any type of rotation barrier with very
150
15 May 1977
CHEMICAL PHYSICS LElTERS Table 1
Comparison of some observed barriers with those calculated usinp:the PCPE method Molecule
CH3-CH3 CH3-CH2F CH3 -OH CH3 -NH2 a) Ref. [3].
Observed barrier
Calculated
(kJ m01-~)
(kJ mol-I)
11.48a) 13.91 b) 4.45 c) 8.27 d)
16.51 18.28 6.36 11.28
b) Ref. [4].
c) Ref. [S].
d) Ref. [6].
little restriction as to the size of the molecule if the initial computations are performed on suitable overlapping fragments. The close agreement with experiment indicates perhaps that it is indeed the repulsion between the shielded positive charges of nuclei which dominates the question of molecular conformation_
Acknowledgement Computing facilities from the SRC.
were supported
by a grant
References [l] W.J. Hehre, RF. Stewart and J.k Pople, J. Chem. Phys. 51 (1959) 2657. [2] S.M. Dean and W.G. Richards, Nature 256 (1975) 473. [3] S. Weiss and G.F. Leroi, J. Chem. Phys. 48 (1968) 962. [4] P.H. Verdier and F.E. Wilson, J. Chem. Phys. 29 (1958) 340 [S] E.V. Ivash and D.M. Denninsson, J. Chem. Phys. 21 (1953) 1804. [61 T. Nishikawa. T. Itoh and KmShimoda. J_ Chem Phys 23
(1953) 1735.