*N*-methylacetamide

^{1,a)}, Stephan P. A. Sauer

^{1}and Jacob Kongsted

^{2}

### Abstract

We present a benchmark study of a combined multipole shielding polarizability/reaction field (MSP/RF) approach to the calculation of both specific and bulk solvation effects on nuclear magnetic shielding constants of solvated molecules. The MSP/RF scheme is defined by an expansion of the shielding constants of the solvated molecule in terms of electric field and field gradient property derivatives derived from single molecule *ab initio* calculations. The solventelectric field and electric field gradient are calculated based on data derived from molecular dynamics simulations, thereby accounting for solute–solvent dynamical effects. The MSP/RF method is benchmarked against polarizable quantum mechanics/molecular mechanics (QM/MM) calculations. The best agreement between the MSP/RF and QM/MM approaches is found by truncating the electric field expansion in the MSP/RF approach at the linear electric field level which is due to the cancelation of errors. In addition, we investigate the sensitivity of the results due to the choice of one-electron basis set in the *ab initio* calculations of the property derivatives and find that these derivatives are affected by the basis set in a way similar to the shielding constants themselves.

The authors thank the Danish Center for Scientific Computing (DCSC) for the computational resources and the Danish Natural Science Research Council/The Danish Councils for Independent Research for financial support. S.P.A.S. thanks the Carlsberg Foundation, and J.K. thanks the Lundbeck Foundation for financial support.

I. INTRODUCTION

II. THEORY

III. COMPUTATIONAL DETAILS

A. Derivatives

B. Molecular geometry of NMA

C. MD simulations

D. MSP/RF and QM/MM calculations

IV. RESULTS

A. Accuracy of the numerical derivatives

B. Basis set effects

C. Effect of the electronic structure method

D. Solvent effects

E. Discussion

V. SUMMARY

### Key Topics

- Solvents
- 65.0
- Electric fields
- 56.0
- Polarizability
- 19.0
- Magnetic shielding
- 16.0
- Tensor methods
- 11.0

## Figures

Molecular structure of *N*-methylacetamide (NMA).

Molecular structure of *N*-methylacetamide (NMA).

(a) The basis set convergence of the nuclear magnetic shielding of nitrogen. (b) The basis set convergence of the nuclear magnetic shielding of hydrogen.

(a) The basis set convergence of the nuclear magnetic shielding of nitrogen. (b) The basis set convergence of the nuclear magnetic shielding of hydrogen.

(a) The basis set convergence of the first derivative, , of the nuclear magnetic shielding of nitrogen with respect to the electric field in the *z*-direction. (b) The basis set convergence of the first derivative, , of the nuclear magnetic shielding of hydrogen with respect to the electric field in the *z*-direction.

(a) The basis set convergence of the first derivative, , of the nuclear magnetic shielding of nitrogen with respect to the electric field in the *z*-direction. (b) The basis set convergence of the first derivative, , of the nuclear magnetic shielding of hydrogen with respect to the electric field in the *z*-direction.

(a) The basis set convergence of the second derivative, , of the nuclear magnetic shielding of nitrogen with respect to the electric field in the *xx*-direction. (b) The basis set convergence of the second derivative, , of the nuclear magnetic shielding of hydrogen with respect to the electric field in the *xx*-direction. Both Turbomole-TZVP, 6-311++G** and aug-pcS-2, give −450 .

(a) The basis set convergence of the second derivative, , of the nuclear magnetic shielding of nitrogen with respect to the electric field in the *xx*-direction. (b) The basis set convergence of the second derivative, , of the nuclear magnetic shielding of hydrogen with respect to the electric field in the *xx*-direction. Both Turbomole-TZVP, 6-311++G** and aug-pcS-2, give −450 .

(a) The basis set convergence of the first derivative, , of the nuclear magnetic shielding of nitrogen with respect to the electric field gradient in the *xx*-direction. (b) The basis set convergence of the first derivative, , of the nuclear magnetic shielding of hydrogen with respect to the electric field gradient in the *xx*-direction.

(a) The basis set convergence of the first derivative, , of the nuclear magnetic shielding of nitrogen with respect to the electric field gradient in the *xx*-direction. (b) The basis set convergence of the first derivative, , of the nuclear magnetic shielding of hydrogen with respect to the electric field gradient in the *xx*-direction.

The field from the surrounding solvent at the positions of the different nuclei of NMA. The nitrogen is nucleus number 4, while the amide-hydrogen is nucleus number 6.

The field from the surrounding solvent at the positions of the different nuclei of NMA. The nitrogen is nucleus number 4, while the amide-hydrogen is nucleus number 6.

## Tables

The nuclear magnetic shielding and the electric field and gradient derivatives of the shielding of the amide N and H atoms of the NMA molecule for different one-electron basis sets calculated using the geometry of the isolated NMA molecule. The nuclear magnetic shielding constant is given in ppm, the first derivatives is given as ppm/a.u., and the second derivative as . The relative deviations in % are with respect to the aug-pcS-3 results.

The nuclear magnetic shielding and the electric field and gradient derivatives of the shielding of the amide N and H atoms of the NMA molecule for different one-electron basis sets calculated using the geometry of the isolated NMA molecule. The nuclear magnetic shielding constant is given in ppm, the first derivatives is given as ppm/a.u., and the second derivative as . The relative deviations in % are with respect to the aug-pcS-3 results.

The nonvanishing components of the derivatives of the nuclear magnetic shielding with respect to the electric field and gradient of the amide N and H atoms of the isolated NMA molecule calculated using the aug-pcS-1 basis set. The first derivatives are given as ppm/a.u. and the second derivative as .

The nonvanishing components of the derivatives of the nuclear magnetic shielding with respect to the electric field and gradient of the amide N and H atoms of the isolated NMA molecule calculated using the aug-pcS-1 basis set. The first derivatives are given as ppm/a.u. and the second derivative as .

Solvent effects obtained using either the MSP/RF or QM/MM approaches for different one-electron basis sets. LF: linear field, QF: quadratic field, and LFG: linear field gradient. Diff. is the difference in the solvent shift of the nuclear magnetic shielding constant between the MSP/RF and QM/MM methods. All nuclear magnetic shieldings are given in ppm.

Solvent effects obtained using either the MSP/RF or QM/MM approaches for different one-electron basis sets. LF: linear field, QF: quadratic field, and LFG: linear field gradient. Diff. is the difference in the solvent shift of the nuclear magnetic shielding constant between the MSP/RF and QM/MM methods. All nuclear magnetic shieldings are given in ppm.

Solvent effects calculated by using the averaged field from all MD-configurations and across all nuclei. “Averaged field” specifies the calculation where the field is directly included in the molecular Hamiltonian, while “expansion approach” refers to the MSP/RF approach. All calculations have been carried out at the level of B3LYP/aug-pcS-3.

Solvent effects calculated by using the averaged field from all MD-configurations and across all nuclei. “Averaged field” specifies the calculation where the field is directly included in the molecular Hamiltonian, while “expansion approach” refers to the MSP/RF approach. All calculations have been carried out at the level of B3LYP/aug-pcS-3.

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