3.1. Heterocyclic Planar Molecules including Nucleic Acid Bases
The theoretical scheme described in
Section 2 was employed to calculate the HOMO and LUMO eigenenergies for a variety of heterocyclic planar organic molecules. We make the convenient simplifying assumption that the HOMO absolute value expresses the ionization energy, and the HOMO–LUMO gap expresses the excitation energy (in most cases the first
-
transition). Below, the ionization energies are of
molecular orbital character and the excitation energies are
-
transitions, unless otherwise stated. We studied the following groups of molecules: adenine and isomers; guanine and isomers; purine and isomers; thymine, cytosine, uracil, and isomers; pyrimidine and isomers; and other planar heterocyclic molecules.
Table 4 summarizes our LCAO results using all valence orbitals, along with relevant experimental values.
and
are calculations of the vertical ionization energies at the Ionization Potential Equation of Motion Coupled Cluster with Singles and Doubles (IP-EOMCCSD)/aug-cc-pVDZ level of theory and vertical excitation energies at the Completely Renormalised Equation of Motion Coupled Cluster with Singles, Doubles, and non-iterative Triples (CR-EOMCCSD(T))/aug-cc-pVDZ level of theory, respectively, ref. [
29].
Table 4 also includes transition oscillator strengths
f that we calculated in a simplistic approximation, considering point contribution of the corresponding orbitals; i.e., the transition dipole moment
was approximated as
where |
L〉 (|
H〉) is the LUMO (HOMO) state. The oscillator strength is [
30]
Regarding the ionization energy, the LCAO obtained results are in very good agreement with both the experimental data and the CC results, although there are some deviations. The Root Mean Square Percentage Error (RMSPE), with respect to the experimental values, is
. Differences in tautomer ionization energies are as expected negligible, that is
eV for purine tautomers and
eV for indazole tautomers. As for the excitation energies of the
-
transition, the RMSPE, with respect to the experimental values, is
. Both purine and indazole tautomers have a negligible
eV difference in their excitation energies. Based on the presented data and reported comments about individual bases, we note that the LCAO method used in this work, though not exact, is capable of producing results in a good agreement with experimental data, when choosing the suitable set of parameters. This outcome has motivated the use of the same method for all other systems of interest, whose computational results are presented in the remainder of this article. Vertical ionization energies of nucleic acid bases in the gas phase with different electronic structure methods are, generally, in agreement with our results, cf. Reference [
51] and references therein.
3.2. B-DNA Base Pairs
In this subsection, we present our results for the B-DNA base pairs. In
Table 5, we show the HOMO, LUMO, and HOMO–LUMO gap energies of the two B-DNA base pairs (Adenine (A)-Thymine (T) and Guanine (G)-Cytosine (C)), according to the procedure described in
Section 2.3 using LCAO with all valence orbitals, along with the corresponding energies found in Ref. [
52] using only 2p
orbitals. At this point, we should state that the bases making up the base pairs are slightly deformed in comparison to their structure when isolated (cf.
Section 3.1), so the corresponding HOMO and LUMO energies for these two cases may differ. Thus,
Table 5 also contains the HOMO, LUMO, and HOMO–LUMO gap energies of the distorted bases. The HOMO (LUMO) energies are of
(
) molecular orbital character and the HOMO–LUMO gap energies are
-
transitions, unless otherwise stated.
The energy values for the bases are slightly different from those in
Table 4, as expected. In addition, based on
Table 5, one can assume that the HOMO energy of a particular base pair is very close to the largest of the HOMO energies of the two bases of the base pair, while the LUMO energy of the base pair is closer to the lowest of the two LUMO energies.
In
Figure 6 and
Figure 7 we represent the occupation probabilities of holes and electrons on each atomic orbital of bases and base pairs, calculating the squared coefficients
(cf. Equations (
1) and (
12)) of the corresponding states (HOMO for holes, LUMO for electrons). We observe that our calculated HOMO state for the base pair A-T (G-C) is localized almost totally in Adenine (Guanine), while the corresponding LUMO wave function is localized in Thymine (Cytosine), in accordance to results from ab initio techniques of References [
53,
54], which locate the HOMO of a base pair in purine and the LUMO in pyrimidine. This is due to the higher HOMO energy of Adenine (Guanine) and lower LUMO energy of Thymine (Cytosine) and the large values of these differences compared to the transfer integrals (see
Table 6). We calculate the first transition character of A, T, A-T, and G to be
-
, while C and G-C have
-
transition character.
We obtain the charge transfer parameters between two successive base pairs by calculating the corresponding overlap integrals from Equation (
26). We denote by XY two successive base pairs, X-X
and Y-Y
. The bases X and Y are located at the same strand in the direction
-
, while X
and Y
, respectively, are their complementary bases on the other strand. In the most common B-DNA conformation, X-X
and Y-Y
are approximately separated by 3.4 Å and twisted by 36
.
Table 6 summarizes our LCAO results using all valence orbitals for the transfer parameters, for all possible combinations of successive base pairs and close-to-ideal geometrical conformations. The Table also contains comparisons with other methods.
In
Figure 8, we illustrate the absolute values of transfer parameters for all possible combinations of successive base pairs for holes and for electrons. The figure contains the transfer parameters obtained from our LCAO calculations using all valence orbitals, along with the corresponding parameters found in Ref. [
55] (where various estimations from bibliography had been taken into account). Furthermore, those from Ref. [
29], where only 2p
orbitals had been used, and finally, electron transfer parameters from Ref. [
52], where only 2p
orbitals had been used. Peluso et al. [
56], based on electrochemical and time-dependent spectroscopic measurements, find for GG a transfer integral ≈ 0.1 eV, which is very close to our results, while, for AA, they report a value ≈ 0.3 eV, which seems large compared to the parametrization reported here taking into account all valence orbitals as well as to the parametrization in Reference [
55], which takes into account, for holes, the works [
52,
57,
58,
59,
60,
61].
In
Figure 9, we depict the maximum transfer percentage of Equation (
28) obtained by our LCAO calculations using all valence orbitals, compared to the values using parameters from Reference [
55] for holes (an estimation from various articles from bibliography). Furthermore, from Reference [
29] for electrons and holes as well as from Reference [
52] for electrons (where only 2p
orbitals had been used). For ideal B-DNA geometries and for dimers made of identical monomers, the maximum transfer percentage is 1, while in the case of different monomers,
p is smaller than 1, both for holes and for electrons. Both for
t and
p, we observe that the current LCAO using all valence orbitals is closer to the results from Reference [
55] for holes (where various estimations from bibliography of different origin had been taken into account). For electrons, as far as we know this current LCAO calculation is the only one beyond simple Hückel models, using only 2p
orbitals.
3.3. Effects of Structural Variability
In this subsection, we analyze the effects of structural variability on the electronic structure and charge transfer properties of B-DNA using the fragments derived from MD, as detailed in
Section 2.4. In
Figure 10, we present the absolute values of the parameters
(difference between the HOMO eigenenergies of the two base pairs of each studied dimer) and
t (transfer integral between the two base pairs’ HOMOs of each studied dimer), as well as the maximum transfer percentages
p as calculated via Equation (
28). The values of
and
p can also be found in Reference [
16] in comparison with results obtained by Density Functional Theory (DFT) techniques.
From Equation (
28) it is expected that ideal dimers (made up of ideal monomers) should have a maximum transfer percentage equal to 1. However, by observing
Figure 10, one can notice that not all AA and GG dimers have
. Specifically, dimers with a
p considerably different from unit (and a
different than zero) are: A11A12_cl2, A12A13_cl1, A121A13_cl2, A13A14_cl2, G15G16_cl1, and G16G17_cl1. This is expected because the studied monomers are not ideal, which means their consisting bases have relative translations and rotations (
Figure 1) as depicted in
Figure 2. More specifically, a small
p value is related to a large
value, in accordance with Equation (
28). Thus, it is expected that the structural parameters (shear, stretch, stagger, buckle, propeller twist, opening) have a reasonable effect on the HOMO (and LUMO) base-pair energy values and consequently on the values of
and
p. As for the contribution of transfer integrals
t to the above discussion, it is documented in Reference [
16].