Ab Initio Study of the Structure and Stability of DNA Base Pairs in the Presence of Bound Waters and Metal Cations

The study of the DNA structure and dynamics is performed by the use of many 
experimental and computational techniques, e.g. high-resolution X-ray 
crystallography, NMR spectroscopy and molecular dynamics simulations.  In the last 
decade, the rapid development of computer hardware and software led also to a 
broad application of ab initio quantum chemistry methods to the study of the 
structure and stability of the nucleic acids base pairs
2
. 
 
This Thesis presents the ab initio study of the effects of bound waters and ions on 
the structure and stability of both canonical and non-canonical base pairs. In 
particular the three topics under investigation are: 
 
¾ Interaction of Ia and IIa group cations with the cytosine-guanine base pair. 
 
¾ Stabilization of the non-complementary G.A base pairs and of the G.GC triplex 
by Zn(II) ions. 
 
¾ Hydration of canonical base pairs. 
 
 The Thesis is organized as follows:  
 
Chapter 1: briefly summarize the problems arising in the study of weakly 
interacting systems, like hydrogen bonded base pairs, by means of ab initio 
methods. The Self Consistent Field for Molecular Interaction (SCF-MI) method 
used for all the calculations is presented. 
 
Chapters 2-4: present in detail the discussion of the three topics previously listed. 
All the chapters are structured in the same way: 
General introduction on the systems under study. 
Survey of previous ab initio calculations. 
Explanation of the aims of the present work. 
Description of the employed method and of the problem specific strategy. 
Detailed presentation of the results of the ab initio calculations. 
    2
 
Comparative analysis of the results and relevant conclusions.    
 
 
 
    3
 
References 
 
(1) Privé, G. G.; Yanagi, K.; Dickerson, R. E. J. Mol. Biol. 1991, 217, 177-199. 
(2) Hobza, P.; Sponer, J. Chemical Reviews 1999, 99, 3247-3276. 
    4
 
CHAPTER 1 
 
A Glimpse to the Computational Approach  
 
 
In spite of the heavy costs of the calculations, the study of van der Waals and 
hydrogen bonded molecules is one of the fields of chemistry where quantum 
chemical methods have increased our understanding both in a quantitative and 
qualitative way. In fact, while experimental techniques can provide information on 
average equilibrium geometries and corresponding binding energies of the molecular 
complexes and clusters, quantum chemical ab initio methods can cover the entire 
potential surface, providing valuable information for a deeper understanding of these 
systems. 
The interaction energy involved in weakly interacting systems is a very small 
fraction of the total energy. As a consequence, a great challenge is set to the accuracy 
of the quantum mechanical methods employed for its theoretical determination. For 
this reason, methods based on perturbation theories, computing the interaction 
directly rather than as a difference between the energies of the complex and that of 
the separated systems, are frequently applied. On the other hand, variational 
procedures have the possibility to rely on the power of the variational theorem. The 
implicit advantages of the variational approach are: 
 
¾ the wide range of applicability. 
¾ it yields a wavefunction usable to derive various system properties.  
¾ many-body interactions and charge transfer effects are explicitly taken into 
account.  
 
Among the drawbacks of the variational approach, the appearance of the Basis Set 
Superposition Error (BSSE), which can be of the same order of magnitude of the 
interaction energy itself, represents a major inconvenience. 
    5
 
  
1.1 The Basis Set Superposition Error 
 
The BSSE is due to the use of all the basis functions located on the molecular 
centers of each monomer to compute the molecular orbitals of the complex 
considered as a single system, the so called supermolecule. In this way, when the 
molecules approach one another, the basis functions centered on the approaching 
partners become better suited to describe the wavefunction of the whole 
supermolecular complex in the region where the interaction becomes stronger. This 
involves a de facto use of an artificially too flexible functional space at shorter 
intersystem distances causing a bias which is the origin of the BSSE. This error has a 
strong effect; in particular it upsets the predicted binding energy and the anisotropy 
of the forces, quantities which are important in determining the geometry of clusters 
in both finite systems and in the liquids.  
There have been many attempts to formulate a procedure to correct for BSSE and 
both a posteriori and a priori schemes are available. The counterpoise approach 
(CP)
1
, based on the use of the ghost orbitals, is the most common a posteriori 
procedure. The expression of the counterpoise corrected binding energy (E
int
) for a 
generic AB dimer is: 
 
[ ] [ ] [ ]
BA#BBA#ABAABCP
int
EEEE χχχχχχ ⊕−⊕−⊕=
 
 
where χ
A
 and χ
B
 are the basis sets for the two monomers, and the # means the 
energy of the monomers are computed at the geometry of the dimer. However, to 
obtain a correct description of the supermolecule with respect to the isolated 
monomers these fragments cannot be frozen to the cluster geometry. The CP-
corrected interaction energy could be rewritten including also terms concerning the 
relaxation energy of the monomers: 
 
    6
 
[ ] [ ] [ ]
B
rel
A
rel
BA#BBA#ABAABCP
int
EEEEEE ++⊕−⊕−⊕= χχχχχχ
 
 
where the two new contributions are defined as 
 
[ ] [ ]
AAA#AA
rel
EEE χχ −=
  
[ ] [ ]
BBB#BB
rel
EEE χχ −=
 
 
corresponding to the energy loss due to the deformation of the monomers in the 
geometry of the dimer. 
Nevertheless, the CP method does not allow a sufficiently precise correction of 
the BSSE. The addition of the partner’s functions or ghost orbitals to counter balance 
the BSSE does not provide a definite solution to the problem
2
. Moreover, the 
introduction of the secondary superposition error, a spurious electrostatic 
contribution due to the modification of the multipole moments and polarizabilities of 
the monomers, is a seemingly unavoidable and incorrigible complication. This is 
particularly important in the case of anisotropic potentials for charged species, where 
these errors can contribute to alter the shape of the PES and the resulting physical 
picture
3
.  
 
 
1.2 The Self Consistent Field for Molecular 
Interactions  approach 
 
Among the attempts to overcome the BSSE, the SCF-MI was proposed as an ab 
initio variational method avoiding its onset in an a priori fashion. The very essence of 
the method consists in the partitioning of the full basis set into subsets centered on 
each fragment and in expanding the molecular orbitals of the different fragments 
only in their own sets. In this way the appearance of the BSSE is avoided. Because of 
this partitioning, the orbitals of the different fragments do overlap; this overlap being 
a proper reflection of the physics of the problem. The obvious computational penalty 
    7
 
introduced by the overlap of the orbitals is well alleviated by the SCF-MI strategy. A 
definite advantage of the a priori SCF-MI method is that it is always correct, 
contrarily to the CP procedure which is exact only in the case of Full CI 
wavefunctions
4
. In addition, geometry relaxation effects are naturally taken into 
account, without computational penalty. Another important characteristic of the 
approach is that the schemes for first and second derivative evaluation at the Hartree 
Fock level are successfully applicable to the SCF-MI wavefunction: the intrinsic 
features of the method are consistent with those required by the standard procedures 
for computing gradients and Hessians. This makes possible to explore the shape of 
intermolecular potential energy surfaces as well as to determine vibrational 
frequencies and related properties within a BSSE free procedure. The algorithm was 
implemented
5
 into the GAMESS-US suite of programs
6
. 
 
 
1.2.1 Outline of the SCF-MI for K interacting fragments 
This section reports an introduction to the most relevant elements of the SCF-MI 
approach; a more detailed account can be found elsewhere
5,7
. The validity of the 
method extends from the long range to the region of the minimum and of short 
distances. 
According to the SCF-MI strategy, a supersystem of K closed shell interacting 
fragments containing 2N electrons (N=N
1
+N
2
+....N
K
) is described by the one 
determinant wave function 
 
( ) ( ) ( ) ()[ ]N21N221
KK
N,KN,K1,11,1
)N2.....1( ϕϕϕϕ=Ψ −KA
 (1) 
 
where A is the total antisymmetrizer operator. The key of the method is the 
partitioning of the total basis set 
 
( )
K21
χχχχ K=
     (2) 
    8
 
 where M=M
1
+......+M
K
 is the basis set size, so as the MOs of different fragments are 
expanded in different subsets centered on each fragment. In this way, the N
k
 doubly 
occupied molecular orbitals of the fragment k, 
),,(
k
N,k2,k1,kk
ϕϕϕ= Kϕ
 are 
expanded in the proper set 
( )
k
M,k2,k1,kk
,, χχχ= Kχ
 
 
kkk
Tχ ⋅=ϕ
     (3) 
 
where T
k
 is an M
k
×N
k
 matrix and M
k
 is the number of basis orbitals centered on the 
fragment k. The orbitals of different fragments are free to overlap; the non 
orthogonality problem is solved without involving any particularly severe 
computational difficulty. The total (MxN) matrix of the partitioned molecular orbital 
coefficients T, 
 
( )
K21
ϕϕϕϕ K=
 
Tχ ⋅=ϕ
   (4) 
 
is assumed in a block diagonal form where the diagonal blocks are the T
1
.....T
K
 
matrices while the other blocks are null matrices (see Fig. 1.1 for the case of three 
interacting fragments). 
 
 
Fig. 1. 1: Atomic and molecular orbitals in the case of K=3 fragments.  
    9