Electrostatic DFT Map for the Complete Vibrational Amide Band of NMA

Abstract

An anharmonic vibrational Hamiltonian for the amide I, II, III, and A modes of N-methyl acetamide (NMA), recast in terms of the 19 components of an external electric field and its first and second derivative tensors (electrostatic DFT map), is calculated at the DFT(BPW91/6-31G(d,p)) level. Strong correlations are found between NMA geometry and the amide frequency fluctuations calculated using this Hamiltonian together with the fluctuating solvent electric field obtained from the MD simulations in TIP3 water. The amide I and A frequencies are strongly positively correlated with the CdO and N-H bond lengths. The CdO and C-N amide bond lengths are negatively correlated, suggesting the solvent-induced fluctuations of the contribution of zwitterionic resonance form. Sampling the global electric field in the entire region of the transition charge densities (TCDs) is required for accurate infrared line shape simulations. Collective electrostatic solvent coordinates which represent the fluctuations of the 10 lowest amide fundamental and overtone states are reported. Normal-mode analysis of an NMA-3H 2 O cluster shows that the 660 cm -1 to 1100 cm -1 oscillation found in the frequency autocorrelation functions of the amide modes may be ascribed to the two bending vibrations of intermolecular hydrogen bonds with the amide oxygen of NMA.

Vibrational−Exciton Couplings for the Amide I, II, III, and A Modes of Peptides

“…The amide A-A couplings have negative values along the antidiagonal line φ ) ψ similar to those of amide I-I couplings, where two N-H bonds are antiparallel. Amide A couplings are smaller than the coupling with the other three modes (<1 cm -1 ) since this vibration is localized on the N-H bond 30 and has a smaller transition dipole moment (Table 3). Contour plots of couplings between different amide modes in neighboring units (H II ) na,n+1b with respect to φ and ψ are shown in Figure 3.…”

“…The local Hamiltonian is where m and n label the amide bond site, and q mi , q mj , ... are the five LAMs (amide III, II, I, and A modes and one mode related to N-H bending and C-N stretch at site m 30 ). This Hamiltonian is expanded to sixth order in local amide modes.…”

“…15 The interaction functions for the dipole-dipole couplings form a 3 × 3 matrix 35 where R, ) x, y, z, and R mn is the distance between the two units. We took the origin at the middle point of the amide hydrogen and oxygen (same as that in the origin of the electrostatic potential expansion in EDM 30 ). The r R m is the product of the rotation matrix defining the local axis system of the m's unit and the unit vector in the direction from m to n, and c R is the product of the two rotation matrices for m and n.…”

“…The local effective vibrational Hamiltonian (eq 2) of NMA was diagonalized to yield 14 eigenstates (ground state, 4 amide fundamentals (III, II, I, and A), first overtones of amide III, II, and I, and the combination states of amide III, II, and I) in the presence of a different electric field and its derivatives C. The eigenfrequencies and transition dipole moments are reported as functions of C in ref 30. We employed these local amide states (LAS) as a basis set for the peptide Hamiltonian.…”

Optimization of Model Parameters for Describing the Amide I Spectrum of a Large Set of Proteins

“…A computationally inexpensive way of including solvent effects on the amide I frequencies is to parametrize ab initio calculations of N-methylacetamide (NMA) and water clusters. [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30] This method exploits the linear correlation found between the C=O bond length, stretching frequency and electrostatic potential at the atoms of NMA, 18,31,32 which provides a link between perturbation of molecular (and electronic) structure by the electric field of the solvent and the resulting shift of the vibrational frequency. Parametrized electrostatic calculations using the building block approach have been used in protein amide I sim-ulations of ubiquitin, 10,33 other proteins 34 as well as polypeptides in membrane environment.…”