Multiple hydrogen-bonded dimers: are only the frontier atoms relevant?

Non-frontier atom exchanges in hydrogen-bonded aromatic dimers can induce significant interaction energy changes (up to 6.5 kcal mol−1). Our quantum-chemical analyses reveal that the relative hydrogen-bond strengths of N-edited guanine–cytosine base pair isosteres, which cannot be explained from the frontier atoms, follow from the charge accumulation in the monomers.


Method S2. Hydrogen-bond and interaction energy analyses
In this work, the hydrogen-bond interactions of the various isosteres of the guanine-cytosine (GC) base pair were studied.The hydrogen-bond energy (∆E) of the GC base pair (isostere) is formulated by Equation S1.
In this equation, E(GC), E(G), and E(C) correspond to the electronic energies E of the hydrogenbonded GC base pair isostere, and of the two separate nucleobases, each in their equilibrium geometry.Although all optimized G and C isosteres are not planar (i.e., C1 symmetric), the minimum energy structures of all GC base pair isosteres are Cs symmetric, that is, planar (see Supporting Data S5).
To understand the different components that determine the relative stabilities of the hydrogen-bonded base pairs, ∆E was partitioned according to the activation strain model (ASM) [S11] of reactivity and bonding into a strain and interaction energy component (Equation S2).

∆E = ∆Estrain + ∆Eint (S2)
In this decomposition, the strain energy (∆Estrain) is the energy required to deform the nucleobase monomers from their equilibrium geometry to the geometry they acquire in the hydrogen-bonded pair.
The interaction energy (∆Eint) accounts for the stabilizing interaction between the two prepared (i.e., deformed) bases.
∆Eint can be further decomposed based on Kohn-Sham molecular orbital theory using a quantitative energy decomposition analysis (EDA). [S12] In the EDA, the total interaction energy (∆Eint) is decomposed into components of electrostatic interaction (∆Velstat), Pauli repulsion (∆EPauli), orbital interaction (∆Eoi), and dispersion (∆Edisp) (see Equation S3).∆Eint = ∆Velstat + ∆EPauli + ∆Eoi + ∆Edisp (S3) [S11] (a) P. Here, ∆Velstat comprises the (usually attractive) classical electrostatic interactions between the unperturbed charge distributions of the prepared (i.e., deformed) interacting monomers.∆EPauli accounts for the destabilizing interactions resulting from overlapping closed-shell orbitals and accounts for any steric repulsion.The ∆Eoi term comprises i) charge transfer between the interacting monomers (i.e., donor-acceptor interactions between occupied and unoccupied orbitals on the interacting monomer, including HOMO-LUMO interactions) which occurs for hydrogen-bonded dimers in the s-electronic system, and ii) mutual polarization of the monomers (i.e., empty-occupied orbital mixing on one monomer due to the presence of the other monomer) which occurs for hydrogenbonded dimers in the p-electronic system.Due to the planar (Cs) symmetry of the hydrogen-bonded pairs, the total orbital interaction term (∆Eoi) can be decomposed into these contributions stemming from the s-charge transfer (∆E oi s ) and p-polarization (∆E oi p ) orbital interactions (Equation S4).Lastly, the ∆Edisp term includes a dispersion energy correction because of the use of Grimme's D3 dispersion correction in the computations (see Method S1 for the full computational details).
Besides in the equilibrium geometries of the GC base pair (isosteres) (see Data S1), the interaction energies ∆Eint were also analyzed as a function of the middle hydrogen-bond distance rN(H)•••N of the GC base pairs (see Fig. 2 in the main text and Data S2).In this approach, the hydrogen-bond distances were varied over a certain hydrogen-bond distance interval while keeping the monomers frozen in the geometry that they acquire in the optimized GC base pair (isostere).The advantage of this approach is that we can compare the base pairs at similar hydrogen-bond distances while preserving the other geometrical characteristics.This allows us to differentiate between interaction terms that are intrinsically more stabilizing, from the interaction terms that are simply enhanced by the shortened hydrogen-bond distances.In other words, comparing the base pairs at similar hydrogen-bond distances allows us to identify which interaction energy term (∆Velstat, ∆EPauli, ∆Eoi, or a combination thereof) causes the relative hydrogen-bond strengths.This approach, in which the monomer geometries approach each other as frozen fragments, has been demonstrated before to yield identical results compared to the approach in which the geometries of the hydrogen-bonded monomers are allowed to relax (i.e., optimize) at each step of a consistent hydrogen-bond distance. [S13]   [S13] S. C. C. van der Lubbe, F. Zaccaria, X.Sun and C. Fonseca Guerra, J. Am. Chem. Soc., 2019, 141, 4878.

Method S3. Voronoi deformation density (VDD) charges
The Voronoi Deformation Density (VDD) charge analysis allows for the quantification of the flow of electronic charge as a direct consequence of chemical-bond formation. [S14] VDD atomic charges (Q) are computed by the spatial integration of the deformation density over the Voronoi cell of atom A, which is the space defined by the bond midplanes on and perpendicular to all bond axes between this atom A and its neighboring atoms (see Equation S5).
Herein, the deformation density ] is the density change going from a superposition of the original atomic densities at the positions of the molecule to the actual density of that molecule.This atomic or so-called promolecular density is defined as the sum of the (spherically averaged) ground-state atomic densities ∑ ρ i (r) i .This is the fictitious state in which the charge density has not been affected by chemical bonding and in which all atoms have zero charge.Q in Equation S5then represents the amount of charge that, due to chemical bonding, flows to a position closer to nucleus A (Q < 0) or to a position further away from nucleus A (Q > 0).
The third possible guanine isostere (G3) yields an average effect on the hydrogen-bond strength compared to G1 and G2 because it has a molecular charge accumulation which is in between that of G1 and G2 (molecular dipole moments: 8.8 (G2), 6.9 (G3), 5.0 (G1) Debye).

Figure S4 .
Figure S4.Isosurfaces (at 0.03 au) and corresponding energies e (in eV) of the empty (sLUMO) and filled (sHOMO) orbitals involved in the H-bonding of the C and C1 bases in the base pair with G1.Computed at ZORA-BLYP-D3(BJ)/TZ2P.

Table S1 .
Decomposition of the equilibrium hydrogen-bond energy ∆E (in kcal mol -1 ) of the planar GC hydrogen-bonded base pair (isosteres) of FigureS1.[a]

The orbital interaction can be decomposed into components of the s-and p-orbital interactions due to the Cs symmetry of the base pairs: ∆E oi = ∆E oi s
Complete EDA results as a function of the hydrogen-bond distance