- Email: [email protected]
Study of the electronic structure of molecules. Barriers to internal rotation in polynucleotide chains
Volume 20, number I
1 May 1973
CHEMICAL PHYSICS LEfTERS
STUDY OF THE ELECTRONIC STRUCTURE OF MOLECULES. BARRIERS TO INTERNAL ROTATION IN POLY!WCLEOTDE CHAINS E. CLEMENT1 and H. POPKIE IBM Research Laboratory,
San Jose, California 95193. USA
Received 19 February 1973 Revised manuscript received 19 March 1973
The barrier to internal rotation for the 0” angle (using Olson and Flory’s notation) in the ngar-phosphate-mgar complex, CloH IgOaP, has been obtained from ab initio computations. The barrier height at 0” = 60” is 4.5 kcalimole, a: 0” = 180” is 3.3 k&/mole and at 9” = 310” is 7.5 kcal/mole. The corresponding minima at 0 = O”, 120’ and 240” have depths of 1.3 kcal/mole, 3.3 kcal/mole and 3.1 kcaljmole, respectively. The aim of this work is to start testing the validity range of empirical or highly approximate techniques airned at the configurational analysis in polymeric materials.
As known, the barriers to internal rotation can be computed with 10% to 20% accuracy for small molecules in the Hartree-Fock approximation [ 1, 21. In addition, the numerous studies on the ethane barrier indicate the near-independency of the computed barrier height
from
the choice
of the basis set (see for
example refs. [3,4] ). In studies of the spatial configuration of polymeric chains, one often needs an expression for the potential energy requiring expljcit inclusion of the barrier heights [5]. Since, however, such data might not be available for complex molecules, traditionally one often must attempt to infer the barrier height from smaller (but related) molecules. Recently, we have advocated the direct computation of the barrier heights for the complex molecule under consideration [I], since this task is now feasible due to recent progress in ab initio computational techniques for large molecules [6, ‘71. In this work we report the barrier to internal rotation, computed for one rotational angle in the sugarphosphate-sugar complex, as represented in fig. 1.
For the rotational angles we use the designation of Olson and Flory [8--IO]. The fragment of the polynucleotide chain that we have considered has the chemical formula C.,oH,gO,P. The 158 electrons are
described with 373 primitive gaussian functions* contracted into 118 functions. The computations were performed for constant values ofthe angles U’ = $’ = jl” = 9’ = 0’ and w” = 45’ (again using OIson and Flory’s notation). In the five illustrations of fig. I, the first is the chemical structure with Olson and Flory’s notation [8-lo], theremaining four are computer generated projections of the C,oH,gOsP compIex for 9” = 0”, 20”, 240” and 300”. The resulting total energies for different values of @”(given in parentheses) are -1324.5341 au (0”) -1324.5331 -1324.5351
au (30”), -1324.5320 au(90”),-1324.5383
au (60”), au(120”),
-1324.5354 au(150”), -1324.5332 au(lPO’), -1324.5360 au (2 lo”), - 1324.53’78 au (240”), -1324.5326 au (270”), -1324.5272 au (300’): and - 1324.5302 au (330”). Thus, we have three barriers (see fig. 2) as expected, end the corresponding heights are given in fig. 2 as 3.95 kc.al/moIe, 3.26 kcai/mole znd 7.29 k&mole. *The carbons and the oxygena are represented by seven 1s gaussian, three 2p,r, three 2pv an-d three 2pi; the hydrogens are represented by three Is gausnans; the phosphorous is represented by ten Is gaussians, six 2p,, six 2py and SLX2p, gaussia.ns.
-.
_.
Volume 20, number 1
CHEMICAL PHYSICS LETTERS
1 May 1973
It is nored
I
’ -\
@-C
._I’0
c=H
that Olsonand Flory 193 had to infer a rotational barrier height from n-butane and n-propylfluoride, i.e., in the range from 2.7 kcal/mole to 3.5 k&l/mole; their final choice for the three peaks was 3 .O kcaI/mole. Since we believe that our computed values are within 20% (or thereabouts) of the exact values, we conclude that there is no possibility of full internal rotation around @“. (At room temperature, the Boltzmann distribution will essentially eliminate any conformation with an energy higher than two to three kcal/mole above the lowest energy configuration.) This conclusion is expected, however we conclude in addition that our values are not in agreement with those selected by Olson and F!ory on the basis of steric hindrance considerations [8]. In addition there is the above noted disagreement on the value of the barrier height for 9” = 310”. We should, however, stress that because of the mutual interaction of first and second order between rotations (see refs. [g--IO]) it is difscult to assess how much Olson and Flory’s conclusions about the spatial configuration of polynucleotide chains might have to be questioned as a consequence of their choice of the values for the rotational barriers. Recently, Pullman et al. [ 111 have reported a conformational analyses study of the backbone structure of di- and poly-nucleotides. Subsequently Saran et al. [12] have reported a detailed analysis especially for the 9” rotation [ 121. The conclusions of these authors are in disagreement with those by Olson and Flory [&IO] . On the basis oi experimental data the work of Pullman and coworkers [I 1, 121 seems to be the correct one. However the number of simplification and empirical approximations contained in the theoretical formulation and by Pullman and coworkers is considerable*. We have previously pointed out our reservations concerning the approach of Flory and coworkers [l] _Thus, we feel that at this stage it is of importance to analyze the limits of validity of various proposals aimed at conformational studies+. For this reason we have started this ab initio computation.
O-P-
* Pullman and
coworkers b~avc been using a technique called b PClLO (perturbative configuration interaction using localizad orbit&). 7 The exxt input geometry used in the computations of the conformational energy, is clearly a basic factor to allow comparison between different computations. Our input geometry used in this work for 0” = 0’ is reported in table 1.
Fig. 1. Sugar-phosphate-sugar complex. The illustration on the top gives the chemical formula, the identification code .for the constituent atoms and the rotational angles. The other four illustrations are computer generated projections fo~~‘=~“~~‘~~“~0,~“~45°andfor~“=O”, 120”, 240” and 3000, respecitiely.
2.
:-: .; -, :.
.’ ._ ; :
-I .’ ,‘,
-,
‘.
Volume 20, number 1
CHEbiICAL
PHYSICS LETTERS
-1324.5280
-1324.5300
-1324.5320
- 1324.5340
-1324.5360
-1324.5380
I
-1324.54001
’ O0
’
60”
’
’
1 20°
’
Barriers
Fig. 2. Barrier to internal
rotation
cartesian coordinates
Atom
X-coordinate
Y-coordinate
Z-coordinate
Cl
-3.1820369 -3.6041767 -2.7045201 -3.6996521 -6.2578476 -3.7865991 -7.0941828 -1.3387176 -4.4289410
-1.3330856 0.9791042 -0.0000000 -2.7282760 -3.1274045 -3.4383009 -5.7111531 -1.2840899 -1.3879385 1.0598965 2.7242471
-4.2036990 -2.5745890 -0.0000000 -0.0000000 1.2028339 -2.6600582 1.1499466 -5.1632793 -5.8660230 -2.77c4153 -3.3125122
1.1660839 -3.7415684 -2.5087542 -1.7636877 -5.4547587 0.0000000 1.8283478 4.6687303
1.6249293 1.1177320 3.1654147 0.5062052 -0.1297928 0.00~0000 1.8283478 0.8793666
C3 c4 c5 01 05 HI H2
03
-5.6720335 -2.7491425 -3.2711401 -2.2696264 -5.9636754 -7.66349 19 -8.4080915 0.0000000
P 08
1.5672720 1.1499697
H3 H4 H5 H6 H? HB H9
180”
’
I
’
240”
of Rotation
--
I
I
,
300”
360”
420’
At~out 9”
ford” in CloH 190sP. The open dots represent
Sugar-phosphate-sugar
c2
’
computed
values in OK ab initio Calculation.
Table 1 (au) for w’ = $’ = II/” = 9’ = 0” = 0’ and W” ~45” X-coordinate
Atom
0.9035627 0.4996166 4.4138439 6.42296 19 6.3921931
O6 HII 0; c; Hb
6.2323475 9.0293’179
HiS G
11.4398127 11.8310137 11.2567648 9.3866580 13.4076758 13.2202342 10.9192948 LO.2878699 13.6514977 10.9310963 9.2971542 15.0046223
Ci C; C; 0’1 0; Hi H; H; Hi l-G Hk HIO
Y-coordinate
Z-coordinate
1.2860058
45699709
5.57687&I 1.1073298 2.4000966 1.9304793 4.4699533 1.5763633 3.8018409 5.0820521 2.8940366 2.1144045 1.2551539 3.0747213 5.1344990 6.4645365 6.0658038 3.4564914 -0.4175351, 1.7683552
2.3565108 1.1075298 2.4000966 4.4248188 2.4144913 1.5763633 -1.4440046 1.0831379 2.8940373 -1.1014092 2-9395396 -2.2329391 -2.952043 1 0.9!.47719 1.2811539 4.868571’7 2.09955 16 3.710843 1
3
Vqltirne 20. number 1 .’
CHEMICAL PtiYSICS LETTERS
Further data and computations are in progress. ., k table i, the carteskin coordinates (in au) for the stigir-phosphate-sugar complex are given. .-’ Refer&es [l} c. Clementi, in: The physics of electronic and atomic collisions, eds. T.R. Covers and F.J. de Heer (NorthHolland, Amsterdam, 1972). [2] L.C. t*L!en, Ann. Rev. Phys. Chem. 20 (1969) 31.5. [I] E. Clementi and H. Popkie, Study of the Electronic Structure of Molecules XVII, J. Chem. Phys., to be published.
1 M3Y 1973
[4] J.P. Lowe, Science 179 (i9731.527. [5] P-J. Flory, Statistical mechanics of chain molecules (Interscience, New York, 1969). [6] E. Clementi, Proc. Natl. Acad. Sci. 69 (1972) 2942. (71 E. Clementi, J. Mehl and H. Popkic, Study of the Electronic Structure of Molecules XX, to be submitted for publication. [8] W.K. Olson and P.I. Flory, Biopolymers 11 (1972) 1. [9] W.K. Olson and P.J. Flory, Biopolymers 11 (1972) 25. [IO] W.K. Olson and P.J. Flory, Biopoiymers 11 (1972) 57. [l I] B. Pullman, D. Perahia and A. Saran, Biochim. Biophys. Acta 269 (1972) 1. [ 121 A. Saran, B. Pullman and D. Perahia, Biochim. Biophys Acta 287 (1972) 211, and references therein.
1 May 1973
CHEMICAL PHYSICS LEfTERS
STUDY OF THE ELECTRONIC STRUCTURE OF MOLECULES. BARRIERS TO INTERNAL ROTATION IN POLY!WCLEOTDE CHAINS E. CLEMENT1 and H. POPKIE IBM Research Laboratory,
San Jose, California 95193. USA
Received 19 February 1973 Revised manuscript received 19 March 1973
The barrier to internal rotation for the 0” angle (using Olson and Flory’s notation) in the ngar-phosphate-mgar complex, CloH IgOaP, has been obtained from ab initio computations. The barrier height at 0” = 60” is 4.5 kcalimole, a: 0” = 180” is 3.3 k&/mole and at 9” = 310” is 7.5 kcal/mole. The corresponding minima at 0 = O”, 120’ and 240” have depths of 1.3 kcal/mole, 3.3 kcal/mole and 3.1 kcaljmole, respectively. The aim of this work is to start testing the validity range of empirical or highly approximate techniques airned at the configurational analysis in polymeric materials.
As known, the barriers to internal rotation can be computed with 10% to 20% accuracy for small molecules in the Hartree-Fock approximation [ 1, 21. In addition, the numerous studies on the ethane barrier indicate the near-independency of the computed barrier height
from
the choice
of the basis set (see for
example refs. [3,4] ). In studies of the spatial configuration of polymeric chains, one often needs an expression for the potential energy requiring expljcit inclusion of the barrier heights [5]. Since, however, such data might not be available for complex molecules, traditionally one often must attempt to infer the barrier height from smaller (but related) molecules. Recently, we have advocated the direct computation of the barrier heights for the complex molecule under consideration [I], since this task is now feasible due to recent progress in ab initio computational techniques for large molecules [6, ‘71. In this work we report the barrier to internal rotation, computed for one rotational angle in the sugarphosphate-sugar complex, as represented in fig. 1.
For the rotational angles we use the designation of Olson and Flory [8--IO]. The fragment of the polynucleotide chain that we have considered has the chemical formula C.,oH,gO,P. The 158 electrons are
described with 373 primitive gaussian functions* contracted into 118 functions. The computations were performed for constant values ofthe angles U’ = $’ = jl” = 9’ = 0’ and w” = 45’ (again using OIson and Flory’s notation). In the five illustrations of fig. I, the first is the chemical structure with Olson and Flory’s notation [8-lo], theremaining four are computer generated projections of the C,oH,gOsP compIex for 9” = 0”, 20”, 240” and 300”. The resulting total energies for different values of @”(given in parentheses) are -1324.5341 au (0”) -1324.5331 -1324.5351
au (30”), -1324.5320 au(90”),-1324.5383
au (60”), au(120”),
-1324.5354 au(150”), -1324.5332 au(lPO’), -1324.5360 au (2 lo”), - 1324.53’78 au (240”), -1324.5326 au (270”), -1324.5272 au (300’): and - 1324.5302 au (330”). Thus, we have three barriers (see fig. 2) as expected, end the corresponding heights are given in fig. 2 as 3.95 kc.al/moIe, 3.26 kcai/mole znd 7.29 k&mole. *The carbons and the oxygena are represented by seven 1s gaussian, three 2p,r, three 2pv an-d three 2pi; the hydrogens are represented by three Is gausnans; the phosphorous is represented by ten Is gaussians, six 2p,, six 2py and SLX2p, gaussia.ns.
-.
_.
Volume 20, number 1
CHEMICAL PHYSICS LETTERS
1 May 1973
It is nored
I
’ -\
@-C
._I’0
c=H
that Olsonand Flory 193 had to infer a rotational barrier height from n-butane and n-propylfluoride, i.e., in the range from 2.7 kcal/mole to 3.5 k&l/mole; their final choice for the three peaks was 3 .O kcaI/mole. Since we believe that our computed values are within 20% (or thereabouts) of the exact values, we conclude that there is no possibility of full internal rotation around @“. (At room temperature, the Boltzmann distribution will essentially eliminate any conformation with an energy higher than two to three kcal/mole above the lowest energy configuration.) This conclusion is expected, however we conclude in addition that our values are not in agreement with those selected by Olson and F!ory on the basis of steric hindrance considerations [8]. In addition there is the above noted disagreement on the value of the barrier height for 9” = 310”. We should, however, stress that because of the mutual interaction of first and second order between rotations (see refs. [g--IO]) it is difscult to assess how much Olson and Flory’s conclusions about the spatial configuration of polynucleotide chains might have to be questioned as a consequence of their choice of the values for the rotational barriers. Recently, Pullman et al. [ 111 have reported a conformational analyses study of the backbone structure of di- and poly-nucleotides. Subsequently Saran et al. [12] have reported a detailed analysis especially for the 9” rotation [ 121. The conclusions of these authors are in disagreement with those by Olson and Flory [&IO] . On the basis oi experimental data the work of Pullman and coworkers [I 1, 121 seems to be the correct one. However the number of simplification and empirical approximations contained in the theoretical formulation and by Pullman and coworkers is considerable*. We have previously pointed out our reservations concerning the approach of Flory and coworkers [l] _Thus, we feel that at this stage it is of importance to analyze the limits of validity of various proposals aimed at conformational studies+. For this reason we have started this ab initio computation.
O-P-
* Pullman and
coworkers b~avc been using a technique called b PClLO (perturbative configuration interaction using localizad orbit&). 7 The exxt input geometry used in the computations of the conformational energy, is clearly a basic factor to allow comparison between different computations. Our input geometry used in this work for 0” = 0’ is reported in table 1.
Fig. 1. Sugar-phosphate-sugar complex. The illustration on the top gives the chemical formula, the identification code .for the constituent atoms and the rotational angles. The other four illustrations are computer generated projections fo~~‘=~“~~‘~~“~0,~“~45°andfor~“=O”, 120”, 240” and 3000, respecitiely.
2.
:-: .; -, :.
.’ ._ ; :
-I .’ ,‘,
-,
‘.
Volume 20, number 1
CHEbiICAL
PHYSICS LETTERS
-1324.5280
-1324.5300
-1324.5320
- 1324.5340
-1324.5360
-1324.5380
I
-1324.54001
’ O0
’
60”
’
’
1 20°
’
Barriers
Fig. 2. Barrier to internal
rotation
cartesian coordinates
Atom
X-coordinate
Y-coordinate
Z-coordinate
Cl
-3.1820369 -3.6041767 -2.7045201 -3.6996521 -6.2578476 -3.7865991 -7.0941828 -1.3387176 -4.4289410
-1.3330856 0.9791042 -0.0000000 -2.7282760 -3.1274045 -3.4383009 -5.7111531 -1.2840899 -1.3879385 1.0598965 2.7242471
-4.2036990 -2.5745890 -0.0000000 -0.0000000 1.2028339 -2.6600582 1.1499466 -5.1632793 -5.8660230 -2.77c4153 -3.3125122
1.1660839 -3.7415684 -2.5087542 -1.7636877 -5.4547587 0.0000000 1.8283478 4.6687303
1.6249293 1.1177320 3.1654147 0.5062052 -0.1297928 0.00~0000 1.8283478 0.8793666
C3 c4 c5 01 05 HI H2
03
-5.6720335 -2.7491425 -3.2711401 -2.2696264 -5.9636754 -7.66349 19 -8.4080915 0.0000000
P 08
1.5672720 1.1499697
H3 H4 H5 H6 H? HB H9
180”
’
I
’
240”
of Rotation
--
I
I
,
300”
360”
420’
At~out 9”
ford” in CloH 190sP. The open dots represent
Sugar-phosphate-sugar
c2
’
computed
values in OK ab initio Calculation.
Table 1 (au) for w’ = $’ = II/” = 9’ = 0” = 0’ and W” ~45” X-coordinate
Atom
0.9035627 0.4996166 4.4138439 6.42296 19 6.3921931
O6 HII 0; c; Hb
6.2323475 9.0293’179
HiS G
11.4398127 11.8310137 11.2567648 9.3866580 13.4076758 13.2202342 10.9192948 LO.2878699 13.6514977 10.9310963 9.2971542 15.0046223
Ci C; C; 0’1 0; Hi H; H; Hi l-G Hk HIO
Y-coordinate
Z-coordinate
1.2860058
45699709
5.57687&I 1.1073298 2.4000966 1.9304793 4.4699533 1.5763633 3.8018409 5.0820521 2.8940366 2.1144045 1.2551539 3.0747213 5.1344990 6.4645365 6.0658038 3.4564914 -0.4175351, 1.7683552
2.3565108 1.1075298 2.4000966 4.4248188 2.4144913 1.5763633 -1.4440046 1.0831379 2.8940373 -1.1014092 2-9395396 -2.2329391 -2.952043 1 0.9!.47719 1.2811539 4.868571’7 2.09955 16 3.710843 1
3
Vqltirne 20. number 1 .’
CHEMICAL PtiYSICS LETTERS
Further data and computations are in progress. ., k table i, the carteskin coordinates (in au) for the stigir-phosphate-sugar complex are given. .-’ Refer&es [l} c. Clementi, in: The physics of electronic and atomic collisions, eds. T.R. Covers and F.J. de Heer (NorthHolland, Amsterdam, 1972). [2] L.C. t*L!en, Ann. Rev. Phys. Chem. 20 (1969) 31.5. [I] E. Clementi and H. Popkie, Study of the Electronic Structure of Molecules XVII, J. Chem. Phys., to be published.
1 M3Y 1973
[4] J.P. Lowe, Science 179 (i9731.527. [5] P-J. Flory, Statistical mechanics of chain molecules (Interscience, New York, 1969). [6] E. Clementi, Proc. Natl. Acad. Sci. 69 (1972) 2942. (71 E. Clementi, J. Mehl and H. Popkic, Study of the Electronic Structure of Molecules XX, to be submitted for publication. [8] W.K. Olson and P.I. Flory, Biopolymers 11 (1972) 1. [9] W.K. Olson and P.J. Flory, Biopolymers 11 (1972) 25. [IO] W.K. Olson and P.J. Flory, Biopoiymers 11 (1972) 57. [l I] B. Pullman, D. Perahia and A. Saran, Biochim. Biophys. Acta 269 (1972) 1. [ 121 A. Saran, B. Pullman and D. Perahia, Biochim. Biophys Acta 287 (1972) 211, and references therein.