Computational Study of the Alkylation Reaction of the Nitrogen Mustard Mechlorethamine Using NBO Model and the QTAIM Theory

Substances known as nitrogen mustards turn into aziridinium ion through the intramolecular cyclization SN1. This ion reacts with the DNA preferably at the N7 position of the guanine, and because of this, it is an important antineoplastic agent. Based on this, the objective of this study is to quantify the interaction between the nitrogen mustard mechlorethamine and the guanine, using the NBO analysis and the QTAIM theory. The results of the NBO analysis showed that when the triangular cycle C4-N1-C5 is formed, there is some resonance among these atoms. This analysis also showed that the electronic transition at the sigma antibondingorbital σ* N1-C4 presents higher perturbation energy of second order, indicating that this bond is broken at the nucleophilic attack of the N7 nitrogen of guanine. The analysis that refers to the electron density obtained by the QTAIM theory indicates that the guanine proximity enables an electron density polarization of the BCPs aziridinium ion of mechlorethamine making that the frontal part of the ion becomes electron deficient. Finally, the relative results to the Laplacian of the electron density obtained by the QTAIM theory showed that the guanine approximation increases the “hole” factor at the C4, proving that the nucleophilic attack based on the “lump-hole” concept causes the region of that atom is the site of alkylation reaction.


Introduction
Antitumor alkylating agents are classified as Celular-Cycle non specific [1] and form crosslinked bonds with DNA.These crosslinked bonds cause DNA lesions requiring complex repair mechanisms, including replication inhibition.Because of it, in 1942, mechlorethamine was successfully used to induce transient tumor remission in a patient with lymphoma, this event marked the beginning of the modern era cancer chemotherapy [1].Among the alkylating agents, the mechlorethamine was the first anti-cancer drug effectively used for clinic purpose, and today it is the most common one used against tumor cells [2].
The alkylating agents efficiency, like the mechlorethamine, was studied previously using molecular model [3,4] and also by rational planning [5,6] that highlighted the correlation between the intramolecular distance of the electrophilic centers of these agents and the nucleophilic nitrogen of nucleotide [1].As the traditional QSAR techniques are laborious and require a long investigation time and high cost [7], the computational analysis of the alkylating agents is becoming more attractive.
The mustard nitrogen compounds are among the most popular agents studied [2,[8][9][10][11] by the theoretical computational chemistry.These compounds form the aziridinium ion, being this ion highly reactive through the intramolecular cyclization SN 1 .The ion reacts with the DNA, preferably at the guanine N 7 position [1], however experiments have been noticing alkylation at the positions N 1 , N 3 , N 6 e O 6 .[1,2].The physical fundamental understanding of this alkyalting family reaction can be interesting for the development on new drugs.With this objective, one of the ways to theoretically quantify the interaction intensity between the nitrogen mustards and the guanine, besides the analysis of the highest occupied molecular orbital (HOMO) [12], lowest unoccupied molecular orbital (LUMO) [13] and its difference [14][15][16], it is through the NBO model [17].A distinguishing feature of localized NBO functions is the simultaneous requirement of orthonormality and maximum occupancy, leading to compact expressions for atomic and bond properties [18].This way, ab initio wavefunctions transformed to NBO form are found to be in good agreement with the Lewis concept and with the classic bond form with hybridization and polarization from Pauling-Slater-Coulson [18][19][20][21].
Another way to quantify the nitrogen mustards interaction with the guanines is using the QTAIM theory (Quantum Theory: Atoms in Molecules) [22] from Bader.At this theory, the Laplacian of the electron density 2   is shown at the local form of the virial theorem giving the mechanics of an atom inside of a molecule [23].This way, the Laplacian can identify the reactivity sites of the molecule [23,24].
So, the objective of the present study is to quantify the interactions of the mechlorethamine molecule with the guanine using the Natural Bond Orbital (NBO) Analysis from Donor-Acceptor Viewpoint, the electron density, and the Laplacian of the electron density obtained by the QTAIM theory.

Computationaldetails
The tridimensional molecule structures were built using the software GaussView 3.0 [25].The structures of the mechlorethamine molecule were drawn in several steps of thealkylation reaction with the guanine.These structures were built in four states: isolated mechlorethamine, isolated aziridinium ion of mechlorethamine, aziridinium ion in the presence of guanine and the transition state of the aziridinium ion.All these structures were optimized to the lower energy state with the program Gaussian03 [26] at the level B3LYP with the basis set 6-31G (d, p).All the post calculations were made with the same wavefunction, B3LYP/6-31G (d, p).The transition state of the aziridinium ion was obtained with the QST3 algorithm.With the optimized geometry, using the same software [26], the Natural Bond Orbitals (NBO) were obtained and also the electronic transitions determined by this theory.The electronic transitions chosen for the discussion were the ones with the second order perturbation energy E 2 ≥ 5 kcal•mol −1 .All these calculations were made in a machine SGI Altix 1350/Altix 450 with 174 CPU's Intel Itanium2, 866GB of RAM memory, technology NUMAFlexGeração 4, interconnection Infiniband and storage system SGI TP9300 with 43 TB.This system is installed at CENAPAD-SP [27].
Using personal computers, continuing from the optimized geometries obtained, the critical points position (3,−1) and (3,−3) of the gradient of the electron density, were determined.Later, the electron density of these critical points were calculated and also the Laplacian of these densities, using the QTAIM theory.These quantities were calculated using the software AIM2000 [28].This software was also used to generate the relief maps of Laplacian of the electron density.

Construction of the Mechlorethamine Molecule in Different States of the Alkylation Reaction
The different steps of the mechlorethamine molecule alkylation with the guanine have been widely discussed at the previous art [1,2,[8][9][10][11]29,30]. It is know that this molecule reacts with aintramolecular cyclization SN 1 releasing a chloride ion, forming the aziridinium ion.Right after the aziridinium ion gets close to the guanine, it goes to a transition state and lately suffers a nucleophilic attack from the N 7 of these nitrogenous base.This way, the molecules used in this study, according to the reaction steps, were built using the software Gaussview03 and they were optimized to the lowest energy state using the program Gaussian03.The molecules were built in the following order: State (1)-isolated mechlorethamine molecule State (2)-isolated aziridinium ion of mechlorethamine molecule State (3)-molecular cluster formed by the aziridinium ion of mechlorethamine + guanine State (4)-mechlorethamine molecule at the transition state + guanine (obtained with the algorithm QST3 from Gaussian03) These geometries obtained for the four states of the reaction, shown at Figure 1, were used at the NBO analysis and also to obtain the electron density of the QTAIM theory.

NBO Analysis of the Intermolecular Interaction between Donor and Acceptor at the Four Reactions States
Thedata obtained with the NBO analysis represent the electronic transition within only one reaction state.The NBO analysis of the mechlorethamine molecule (state 1) did not show any electronic transition that satisfies the minimum stabilization energy condition E 2 ≥ 5 kcal•mol −1 .However, Table 1 shows that when the mechlorethamine becomes the aziridinium ion, forming the triangle C 4 -N 1 -C 5 (state 2), there is a kind of resonance between the electrons of the sigma bond N 1 -C 4 and N 1 -C 5 .However, a slight asymmetry can be noticed at

LP
It is interesting to notice that at this reaction step, where there is the transition state, the intermolecular transition N19 N1-C4 presents a second order energy of E 2 = 63.59 kcal•mol −1 .This value corresponds to an increase of 80.35% in the E 2 energy of this transition when compared to the value obtained at the previous state (3).This result demonstrates that there is a transition state (4) of the aziridinium ion of mechlorethamine that favors the nucleophilic attack of the guanine N 7 at the ion C 4 .

 
It is thought that this fact happens due to the proximity of the C 4 to N 7 at the transition state (4), because the distance between these two atoms at the state (4) is 2.11 Å, while at state (3) this same distance is 3.34 Å (Figure 2).

Application of the QTAIM Theory to Obtain the Electron Density and the Laplacian of the Electron Density of Molecules at the Four Reaction Sites
The QTAIM theory (Quantum Theory: Atoms in Molecules) was used to calculate the electron density and the Laplacian of the electron density for the critical points (3,−1) and (3,−3) and for all the structures at each alkylation reaction state of the mechlorethamine with the guanine (Figure 3).It can be noticed by Table 3, that in all changes of state, the critical points of electron density variation (State 3)     (3,−3), which means the atomic nuclei, this variation is very low.The exception is the critical points that correspond to the carbon atoms 4 and 5, when the system passes from state 1 to state 2. The positive signal of Δρ indicates that these atoms had an electron density increase when the triangular cycle C 4 -N 1 -C 5 was formed, probably because of the N 1 higher electronic sharing with these atoms.The variation of electron density of the Hatoms usually have an order of magnitude around de ~10 −3 u.a. because of its high polarization capacity, not being important to the analysis of the alkylation reaction mechanism.
hydrogen with the carbonyl oxygen (H  .Even more noticeable are the Δρ data that corresponds to the change from state 2 to state 3.
All the negative values of Δρ that correspond to the BCPs of the aziridinium ion are related to the critical points that are placed in a frontal position to the guanine molecule approach.The positive values of the ion BCPs correspond to the critical points that are in the opposite direction to the nitrogenous base.
According to these results, it is believed that the guanine approach causes an electron density polarization of the aziridinium BCPs, making the frontal part of the more susceptible to the nucleophilic attack, while the critical points at the opposite direction present a gain in electron density.When the Δρ from states (3) and ( 4) are compared, the triangular bond σ N 1 -C 4 is broken, probably shifting the electron density of the region between these two atoms to the critical points N 1 -C 5 and C 4 -C 5 , since these two BCPs had an expressive gain in the electron density of 0.5754 and 0.5445 u.a.respectively.The sum of these two Δρ values being 1.1200 u.a. is very close to the N 1 -C 4 BCP Δρ value of −1.0036 u.a., a good indication that this electron density is distributed between the triangular cycle atom at the transition state.
It is interesting to note that the Δρ values between states 1 and 2 of the BCPs (Bond Critical Point) are much higher than the values at of the critical points (3,−3).It also can be noticed that the sum of the Δρ values for the critical points (3,−1) with the negative signal results in −1.0772 u.a., a close value to the determined value of ρ for the bond critical point N 1 -C 4 of 1.0124 u.a.This result maybe can suggest that there is an electron delocalization of these BCPs at the formation process of the bond σ N 1 -C 4 when the triangular cycle C 4 -N 1 -C 5 is formed.
Figure 4 shows that when the aziridinium ion of mechlorethamine is close to the guanine molecule, there is the formation of hydrogen bonds (3,−1): three bonds of In the Table 4 that refers to the Laplacian of the electron density, it is noticed that at the aziridinium ion of mechlorethamine (state 2), there is a low asymmetry between the Δ 2 ρ values of the carbon 4 and 5 (3.3838 and  3.3836 u.a.respectively), besides there is also an asymmetry to the BCPs N 1 -C 4 and N 1 -C 5 (−0.5191 and −0.5172 u.a.).Can also be observed in the Table 4 that the state (3), with the presence of the guanine, an increase on the Laplacian difference is seen between the BCPs N 1 -C 4 and N 1 -C 5 for states (2) and ( 3 .This demonstrates that the guanine approach increases the hole factor at the C 4 (Figure 5), and that the nucleophilic attack, based on the lump-hole concept, makes the region of this atom to become the reaction site for this alkylation.The results of the when the triangular cycle C 4 -N 1 -C 5 is formed at the cyclization process, there is a kind of electronic resonance among these atoms.It was also noticed a certain asymmetry between the second order perturbation energy of the C 4 and C 5 of the triangular cycle, indicating that the C 4 is more susceptible to a nucleophilic attack.Finally, the NBO analysis showed that the nucleophilic attack occurs through an electronic transition between the guanine N 7 lone pair and the C 4 of the triangular cycle of the aziridinium ion of mechlorethamine transition state, state found by the algorithm QST3.
The data obtained with th TAIM) theory showed that when there is a change in the state of the mechlorethamine molecule, the main variation in electron density is at the critical points (3,−1) and not at (3,−3).It was also noticed that the approach of the guanine molecule possibly generates a polarization of the BCPs electron density of the aziridinium ion of mechlorethamine, making that the frontal part of the molecule (related to the guanine position) becomes more deficient in electrons, being more susceptible to a nucleophilic attack.
The values o nsity showed that the region around the C 4 of the C 4 -N 1 -C 5 triangular cycle is the reaction site of the alkylation reaction of the aziridinium ion of mechlorethamine, due to the presence of a greater hole than the C 5 .

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Another relevant electronic transition is the intermolecular transition of E 2 = 35.26kcal•mol −1 indicating that a nucleophilic attack of the N 19 (the guanine N 7 mentioned at the references [1,2,9]) possibly contributes to the  N 1 -C 4 bond break.The algorithm QST3 that determined the geometry of theaziridinium ion of mechlorethamine transition state (state 4) shows that before the alkylation, there is a break at the triangular cycle C 4 -N 1 -C 5 .This new geometry is obtained with the bond break of σ N 1 -C 4 , what was already predicted by the NBO analysis of

Figure 2 .
Figure 2. Distance between the N 19 (guanine N 7 ) and themechlorethamine C 4 at the state (3) and (4) of the alkylation reaction.

Figure 3 .
Figure 3. Structures of the 4 reaction states with the critical points obtained by the QTAIM theory.The red critical points are the Bond Critical Points (BCP), and the yellow critical points are the Ring Critical Points (RCP).

Figure 4 .
Figure 4. Structure at state (3) showing the mechlorethamine approach to the guanine.The picture shows that the BCPs u.a..It is also observed at state (3), a reduction in the Laplacian of the electron density of C 4 with respect to the state (2), and when states (3) and (4) are compared, this reduction is even greater (

Figure 5 .
Figure 5. Relief maps of the Laplacian of the electron density of the states 2 (up) and 3 (down).It is noticed a greater hole at carbon 4 at the structure on right, emphasizing that the guanine presence increases the electrophilic carater of stabilization energy of the electronic transition at the acceptor antibonding orbitals σ* of the carbons of the triangular cycle C 4 -N 1 -C 5 .The data indicate that the electronic transition at the antibonding orbital σ* N 1 -C 4 stabilizes the system more, making that this carbon (C 4 ) be more susceptible to a nucleophilic attack.Looking at the data regarding state 3, at Table1, an increase of around 20% can be noticed at the stabilization energy E 2 of the acceptor antibonding σ* of the traingular cycle carbons C 4 -N 1 -C 5 .It is also observed the appearance of two new intramolecular transitions of the aziridinium ion in which the electronic donor is the bond orbital σ N 1 -C 4 , another indication that this bond is the most probable to be cleaved with the guanine nucleophilic attack.The electronic transitions obtained for the guanine are the typical resonance transitions of the aromatic rings and of the carbonyl formed by the atoms C 24 and O 26 .The most important transitions that occur at the guanine were with 72.65 kcal•mol −1 and with 64.29 kcal•mol −1 . the

Table 1
and by the new intramolecular transition with 10.75 kcal•mol −1 from

Table 2 .
Among the guanine intra-molecular transitions at this reaction state, two Lone Pair transitions of the C 21 , e can be highlighted, with stabilization energies of 244.46 and 97.92 kcal•mol −1 respectively.