Investigating the Spectroscopy of the Gas Phase Guanine–Cytosine Pair: Keto versus Enol Configurations

We report on a vibrational study of the guanine–cytosine dimer tautomers using state-of-the-art quasiclassical trajectory and semiclassical vibrational spectroscopy. The latter includes possible quantum mechanical effects. Through an accurate comparison to the experimental spectra, we are able to shine a light on the hydrogen bond network of one of the main subunits of DNA and put the experimental assignment on a solid footing. Our calculations corroborate the experimental conclusion that the global minimum Watson-and-Crick structure is not detected in the spectra, and there is no evidence of tunnel-effect-based double proton hopping. Our accurate assignment of the spectral features may also serve as a basis for the development of precise force fields to study the guanine–cytosine dimer.


K7E-1
Figure S1: Quasi-Classical Trajectory (QCT) spectra and frequencies for the N 7 H (orange) and N 9 H (blue) out-of-plane bending of k7e-1 and k9k-1 respectively; the limit of the experimental range is shown as dashed black line.

Semiclassical Approaches
As stated in the letter, the Time-Averaged Semiclassical Initial Value Representation (TA-SCIVR) power spectrum I(E) is able to include quantum effects from multiple classical trajectories.The TA-SCIVR power spectrum is evaluated as Usually, the time-dependent wavefunction |g t is espressed using Heller's coherent states.
Coherent states have the following Gaussian representation in the configuration space: 4-8 where Γ is the coherent state width matrix, usually expressed as the diagonal matrix of the harmonic frequencies of vibration.
TA SCIVR uses a time-averaging filter to improve the phase space integration, but still requires thousands of trajectories to compute a single power spectrum.This limits the application of the method to systems that already have a computationally affordable potential energy surface (PES).However, when the system grows in dimensionality, obtaining a reliable PES becomes more and more difficult, and running the trajectory on-the-fly is the most viable option.This means that at each step of the dynamics, the potential energy and forces are evaluated ab initio, using an electronic structure software.This greatly reduces the number of trajectories that could be computed at a reasonable computational cost, making the Multiple Coherent Semiclassical Initial Value Representation (MC SCIVR) necessary for ab initio potentials.
The reference state usually employed in a MC-SCIVR calculation is of the type 9,10 |Ψ = Nv j 1,j |p eq,j , q eq,j + 2,j |−p eq,j , q eq,j an approximate projected potential Ṽ (q M ) = V (q M ; q eq Nv−M ) + λ where Ṽ is the projected potential on the M -dimensional subspace, V (q M ; q eq Nv−M ) is the potential of the system with all but the M modes fixed at equilibrium position, and λ is an artificial external field of the type λ = V (q M ; q Nv−M ) − V (q M ; q eq Nv−M ) + V (q eq M ; q Nv−M ) The vibrational space is divided into subspaces according to either the Hessian or the Jacobian criteria.The former method groups the normal modes according to the off-diagonal terms of the Hessian matrices, 18,19 while the latter selects the subspaces based on the determinant of the subspace Jacobian matrix closer to unity. 20This last criterion has been successfully implemented with a machine learning algorithm. 21

Table S4 :
Comparison between the QCT frequencies (QCT, in cm −1 ) of the normal modes above 3300 cm −1 for the four tautomers, and the harmonic frequencies at theory level dftd/b3lyp def2-TZVP (Harm., in cm −1 ); the QCT frequencies where obtained from a single 25 000 au trajectory at theory level dft-d/b3lyp def2-TZVP.Double harmonic intensities (Int., in km mol −1 ) are included