The Simulation of NMR Data of Flexible Molecules-Sagittamide A as Example for MD Simulations with Orientational Constraints

The Simulation of NMR Data of Flexible Molecules Sagittamide A as Example for MD Simulations with Orientational Constraints Ulrich Sternberg, Pavleta Tzvetkova and Claudia Muhle-Goll 1 Formulae of MDOC Methods 1.1 The recursion Formula for the Time Average with an Exponential Decaying Memory Function The time average of all components the dipolar tensor D is calculated using the following exponentially decaying memory function:


1
Formulae of MDOC Methods

The recursion Formula for the Time Average with an Exponential Decaying Memory Function
The time average of all components the dipolar tensor D is calculated using the following exponentially decaying memory function: The values on the main diagonal of the matrix in eq. (2) are 1. To obtain the final < D > kΔt values (<>t indicates the time average) the elements of the column on the left side have to be divided by the norm: The vector of the norm values can be obtained by replacing the column vector on the right side of equation (2) with a vector containing only 1 as elements. From (2) we can write down the following recursion for d and N: Electronic Supplementary Material (ESI) for Physical Chemistry Chemical Physics. This journal is © the Owner Societies 2020 In this version the norm N i has to be stored together with d k . Depending on resources and the speed of memory access it may be favorable to run the recursion directly using < D > kΔt : The sum within the parenthesis is calculated before the recursion of the norm is executed. The exponential factor has to be calculated only once at the beginning of the recursion.

Coordinate Derivative of the Altona Equation
For the force field the derivative of the Altona equation 5 is needed. The Altona correction term has the form: The derivative to cos(φ) gives: (7)       5 6 6 2 cos cos cos If the coupling atoms are denoted with A and B the cos(φ) is calculated from a scalar product of the unit vectors that are perpendicular to A-C-C and C-C-B. Finally we have only to perform the derivative of cos(φ) with respect to the coordinates of the atoms A-C-C-B. In the case of the Altona equation A and B are H atoms and in the case of the correction term of Palermo et al. 6 atom A is a hydrogen and atom B a carbon atom.

3.
Sagittamide A In the work on Sagittamide A only one bond 1 H-13 C dipolar couplings are taken into account as orientational constraints. Therefore we assigned a dipolar tensor to every H-C-bond under investigation. The value of D = 23.13665 kHz was calculated for the nuclear distance of 1.093 Å. All calculated 1 H-13 C dipolar couplings are scaled down by an order parameter of the alignment medium of S am = 0.004. The experimental RDC values are obtained from Schuetz et al. 4 The off diagonal elements of the calculated mean DD tensors are smaller than 0.025 Hz. RMS deviation: 0.25 Hz Quality criterion n/χ 2 3.94 The experimental 3 J coupling values are obtained from Schuetz et al. 4 The 3 J HH couplings are calculated using the method of Haasnoot et al. 5 and the 3 J CH couplings according to Palermo et al. 6 . The time mean value was calculated using the equations (5) and (6). The error was estimated as the sum of the experimental error and the RMS deviation of the prediction 5, 6 . Root mean square deviation: 1.60 Hz χ 2 7.69 Quality criterion n/χ 2 1.70

Full statistics of the torsion angles C7 to C10
The analysis is performed using Mathematica. The following matrix contains the population of the combination of torsion states. The torsion angles are counted within two regions: values between -120 and 120° are regarded as gauche and the values between +/-120 and +/-180 are counted as trans.