Macrocycle Conformational Sampling by DFT-

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1 Supporting Information Macrocycle Conformational Sampling by DFT- D3/COSMO-RS Methodology. Ondrej Gutten, Daniel Bím, Jan Řezáč, Lubomír Rulíšek* The Institute of Organic Chemistry and Biochemistry of the Czech Academy of Sciences, Gilead Sciences Research Center & IOCB, Flemingovo náměstí 2, Praha 6, Czech Republic * 1

2 Individual components of G DFT/COSMO-RS : detailed analysis (Section S3.1) Importance of individual components of the free energy. From the computational perspective, the total free energy is composed of three components, discussed individually below. Knowledge of relative importance of these components allows for designing a protocol with cost and accuracy tailored to available resources and specific requirements. Figure S3 (below) presents the range of values of the components for two of the systems in the test set. The three components, in order of importance, are the gas-phase energy, E gp, the solvation energy, G solv, and the sum of zero-point vibrational energy, entropic, and thermal contributions, µ. The energy spans for these components are loosely related to the size of the system. The total free energy, G DFT/COSMO-RS, which is a sum of the three contributions, exhibits ranges that are significantly smaller, because the individual components are strongly correlated, as discussed below (Figure 4, main text). Gas-Phase Energies: Performance of DFT Functionals. The same conclusion is obtained from the pairwise average absolute differences for several popular DFT functionals (vide supra). The data are reported in the Table SI_test.data. It can be seen that the MAE for any two of the D3-corrected functionals is within 5 kj.mol -1. The same holds true for any pair from the D3-uncorrected set whereas the mutual comparison (D3-corrected vs. D3- uncorrected) yields much larger errors (> 10 kj.mol -1 ). With respect to our calibration work 1 and similar test sets reported by Grimme and coworkers, 2 the D3-corrected functionals should provide considerably more accurate values. Therefore, our choice of functional is driven by computational cost towards pure GGA functionals and BLYP-D3 is used in the remaining part of this work. The BP86-D3 is also a reasonable alternative, since the COMSO-RS protocol has been parametrized for this functional and we have demonstrated in our previous work concerning thermodynamics of metal ion complexation 3,4 that G BP86-D3/COSMO-RS values were 2

3 in the best agreement with experimental stability constants despite the poor performance of BP86 in the in vacuo component of the overall free energy change. The apparent contradiction had been attributed to cancellation of errors between gas-phase thermodynamics and the COSMO-RS solvation energies. Solvation Energies. Previous studies carried out in our group identified COSMO-RS as one of the most robust implicit solvation methods and therefore, it was used as the solvation method of choice in this study. Importantly, we have observed that it is critical to use the so-called FINE parametrizations and the $cosmo_isorad keyword in the COSMO input which prevents rare numerical failures of the protocol for conformers with very small ring cavity. As can be seen in Table SI_test.data, the computed COSMO-RS solvation energies of the conformers of the single compound spanned a seemingly wide range of energies (~100 kj.mol -1 ). Somewhat surprisingly, size of a system is not a decisive factor. A careful inspection of several extreme cases revealed that differences originate, inter alia, in large differences in dipole moments between such conformations, which appear as a result of an alignment of local dipoles corresponding to polar groups in the given conformer. As discussed below, such changes are largely compensated by an opposing change in gas-phase electronic energies. Low-lying vibrational modes and the treatment of imaginary frequencies. In our test set of 120 structures, there are 22 such cases (DZ gas-phase frequency analysis, Table SI_test.data). Upon re-optimizing all structures with finer DFT grid and weighting of the derivatives in calculations of the analytical second derivatives (denoted FINE below), only one system with imaginary frequency remained. In systems with no imaginary frequencies in REGULAR setup (non-problematic cases), the thermal contributions differ almost negligibly from their FINE counterparts (MAE of ~1.3 kj.mol -1 ). Thus, in well converged systems the increased numerical accuracy does not provide 3

4 an attractive tradeoff since it comes at the expense of approximately one order of magnitude greater computational price (REGULAR vs. FINE setup). For the 21 structures with vanishing imaginary frequencies we observe only negligible structural changes after re-optimization and re-calculation in FINE setup. Moreover, the vibrational spectrum is almost identical, the only change being the imaginary frequency turning into a real low-lying frequency (0-200 cm -1 ). A quick and dirty trick that circumvents the need for costly re-optimization is to simply flip an imaginary frequency into its positive value. This approximate solution is also implemented in the Grimme s program thermo which has been employed throughout for the gas-phase thermodynamics. 5 In this small subset of 21 structures, MAE increased to 2.3 kj.mol -1 (again, using FINE setup as reference). 4

5 Table S1: Number of low-energy conformers similar to a crystal structure, as found by a composite protocol and by standalone protocols (the remaining numerical columns). The number of similar structures is judged by energy (<20kJ/mol above global minimum), geometry (<1.0 Å RMSD) or both. True positives represent number of structures found by both the composite protocol and the standalone protocol. False positives represents number of structures found by standalone protocol that are not found to be similar by the composite protocol. False negatives represent number of structures found by the composite protocol but not found by the standalone protocol. Even using just the geometry or just the energy criterium, the number of true positivies is significantly lower for standalone protocols than for the composite protocol. Energy & geometry Geometry only Energy only System Composite True False False True False True False protocol positives positives negatives positives negatives positives negatives CAMVES CHPSAR COHVAW defllmod GS POXTRD SANGLI YIVNOG CAMVES CHPSAR COHVAW extllmod GS

6 POXTRD SANGLI YIVNOG CAMVES CHPSAR COHVAW PM6MD GS POXTRD SANGLI YIVNOG

7 Table S2: Number of unique low-energy conformers found simultaneously by two protocols (intersection). The second row of this table was used to construct Figure 8 corresponds to the size of the overlapping region of the full and dashed lines. 1 2 CAMVES CHPSAR COHVAW GS GS POXTRD SANGLI YIVNOG defllmod PM6MD defllmod extllmod PM6MD extllmod Table S3: Number of unique low-energy conformers found by one or more protocols (union). The first, third, and fifth row of this table was used to construct Figure 8 corresponds to the height of the full and dashed lines and their total height, respectively. 1 2 CAMVES CHPSAR COHVAW GS GS POXTRD SANGLI YIVNOG defllmod PM6MD extllmod defllmod PM6MD defllmod extllmod PM6MD extllmod all three

8 Table S4: Chapman estimate, E(N), of the total number of low-energy conformers based on hypergeometric distribution H(N,M,n,m). N is the total number of low-energy conformers, M is the number of low-energy conformers found by one of the protocols, n is the number of low-energy conformers found by the other protocol, and m is the number of low-energy conformers found by both of these protocols simultaneously. Chapman estimate is calculated as EE(NN) = (MM+1)(nn+1) 1. The (mm+1) second row of this table was used to construct Figure 8 corresponds to the coloured horizontal bar. 1 2 CAMVES CHPSAR COHVAW GS GS POXTRD SANGLI YIVNOG defllmod PM6MD defllmod extllmod PM6MD extllmod Table S5: Lower boundary of a 95%-confidence interval of the total number of low-energy conformers based on hypergeometric distribution H(N,M,n,m). N is the total number of low-energy conformers, M is the number of low-energy conformers found by one of the protocols, n is the number of low-energy conformers found by the other protocol, and m is the number of low-energy conformers found by both of these protocols simultaneously. For details on calculation of confidence intervals see Ref (VI). The second row of this table was used to construct Figure 8 corresponds to the lower end of the coloured bar. 1 2 CAMVES CHPSAR COHVAW GS GS POXTRD SANGLI YIVNOG defllmod PM6MD defllmod extllmod PM6MD extllmod

9 Table S6: Upper boundary of a 95%-confidence interval of the total number of low-energy conformers based on hypergeometric distribution H(N,M,n,m). N is the total number of low-energy conformers, M is the number of low-energy conformers found by one of the protocols, n is the number of low-energy conformers found by the other protocol, and m is the number of low-energy conformers found by both of these protocols simultaneously. For details on calculation of confidence intervals see Ref (VI). The second row of this table was used to construct Figure 8 corresponds to the upper end of the coloured bar. 1 2 CAMVES CHPSAR COHVAW GS GS POXTRD SANGLI YIVNOG defllmod PM6MD infinity 472 infinity 459 defllmod extllmod infinity 2722 PM6MD extllmod infinity infinity infinity infinity 9

10 Figure S1: A relationship between mutual RMSD of OPLS2005-optimized CAMVES conformers in the unpruned set (see Section 3.4 for details) and their final G DFT/COSMO-RS difference. The fraction of pairs with significant G DFT/COSMO-RS differences rises significantly above RMSD ~ 0.4 Å. 10

11 (a) (b) Figure S2: The number of total (a) and low-energy (b) unique conformers found in the unpruned MD/LLMOD sampling (see Section 3.4 for details) as a function of RMSD threshold used for pruning of conformers. An RMSD threshold of 0.4 Å was used for definitino of a unique conformer. The energy criterium of kj.mol -1 is used in all cases. The number of total unique conformers decreases approximately linearly as the threshold is loosened (a), however, a significant loss of the number of unique low-energy conformers only appears at thresholds above 0.6 Å. 11

12 Figure S3: Range of individual components ( X max X min, in kj.mol -1 ) of the overall free energy as defined in (1) equation in main text for two selected systems in the test set. The ranges of individual components sum up to total free energy, G DFT/COSMO-RS. The substantial decrease in the total range is due to correlation of individual components. 12

13 REFERENCES (1) Řezáč, J.; Bím, D.; Gutten, O.; Rulíšek, L.: Accuracy of Standard DFT Functionals and DLPNO-CCSD(T) Method in Conformational Sampling of Smaller Peptides and Medium- Sized Macrocycles: MP-CONF196 Data Set. Submitted. (2) Goerigk, L.; Kruse, H.; Grimme, S. Benchmarking density functional methods against the S66 and S66x8 datasets for non-covalent interactions. ChemPhysChem 2011, 12, (3) Gutten, O.; Beššeová, I.; Rulíšek, L.: Interaction of Metal Ions with Biomolecular Ligands: How Accurate Are Calculated Free Energies Associated with Metal Ion Complexation? J. Phys. Chem. A 2011, 115, (4) Gutten, O.; Rulíšek, L.: Predicting the Stability Constants of Metal-Ion Complexes from First Principles. Inorg. Chem. 2013, 52, (5) Grimme, S.: Supramolecular Binding Thermodynamics by Dispersion-Corrected Density Functional Theory. Chem. Eur. J. 2012, 18,

Intermolecular Forces in Density Functional Theory

Intermolecular Forces in Density Functional Theory Problems of DFT Peter Pulay at WATOC2005: There are 3 problems with DFT 1. Accuracy does not converge 2. Spin states of open shell systems often incorrect