Analytical Gradients for Subsystem Density Functional Theory within the Slater-Function-Based Amsterdam Density Functional Program Danny Schl € uns, [a] Mirko Franchini, [b,c] Andreas W. G€ otz, [d] Johannes Neugebauer,* [a] Christoph R. Jacob,* [e] and Lucas Visscher* [b] We present a new implementation of analytical gradients for subsystem density-functional theory (sDFT) and frozen-density embedding (FDE) into the Amsterdam Density Functional pro- gram (ADF). The underlying theory and necessary expressions for the implementation are derived and discussed in detail for various FDE and sDFT setups. The parallel implementation is numerically verified and geometry optimizations with different functional combinations (LDA/TF and PW91/PW91K) are con- ducted and compared to reference data. Our results confirm that sDFT-LDA/TF yields good equilibrium distances for the systems studied here (mean absolute deviation: 0.09 A ˚ ) com- pared to reference wave-function theory results. However, sDFT-PW91/PW91k quite consistently yields smaller equilibrium distances (mean absolute deviation: 0.23 A ˚ ). The flexibility of our new implementation is demonstrated for an HCN-trimer test system, for which several different setups are applied. V C 2016 Wiley Periodicals, Inc. DOI: 10.1002/jcc.24670 Introduction The desire to understand the properties and function of increasingly complex chemical systems by means of first- principles theoretical approaches has triggered the develop- ment of fragment-based quantum-chemical methods (for recent reviews, see Refs. 1,2). Two particular examples from this class are subsystem density functional theory (sDFT) [3–5] and the related frozen-density embedding (FDE) [6] (see also the reviews in Refs. 7,8). Contrary to classical force field or QM/MM approaches, sDFT treats all components of a system on a fully quantum mechanical basis. Thus, changes in the electronic structure can be modeled from first principles while keeping the computational cost low, since sDFT only requires to solve subsystem (rather than more expensive supersystem) problems. Of course, sDFT can also be combined with stan- dard linear scaling techniques. By construction, sDFT allows for the interpretation of results for complex systems based on the constituting subsystems, which is often desired, e.g., for treat- ing energy- [9] or electron-transfer processes. [10,11] Even a first principles treatment of proteins was recently established on the basis of sDFT. [12–15] Analytical sDFT gradients enable the efficient optimization of geometries of super-molecular complexes as shown in the work by Wesolowski et al., [16,17] which addressed CO adsorbed in a ZSM-5 zeolite model as well as several bimolecular com- plexes from test sets developed by Zhao and Truhlar. [18–20] These investigations also demonstrate that similar to conven- tional Kohn-Sham DFT (KS-DFT), both interaction energies and optimized structures strongly depend on the choice of the density-functional approximations. Also for molecular dynamics simulations, analytical gradients are needed for efficient force calculations as shown in Refs. 21,22. So far, FDE or sDFT gradients are available in a locally modi- fied version of the molecular code DeMon, [16] and the periodic codes CP2K, [21,23] and Quantum Espresso. [24] In this contribu- tion, we introduce the implementation of subsystem-DFT gra- dients into the highly parallelized molecular Slater-basis code ADF. [25,26] Previous features of this implementation have been presented in another Software News article. [27] The focus of our implementation, which is concentrated on molecular prop- erties, is to provide a flexible setup for arbitrary molecular sub- systems that can be treated with different approximations in a user-friendly way. Some of the aspects presented here have been touched on in previous work. [16,28] However, no details [a] D. Schl € uns, J. Neugebauer Theoretische Organische Chemie, Organisch-Chemisches Institut and Center for Multiscale Theory and Computation, Westf € alische Wilhelms- Universit € at M€ unster, Corrensstraße 40, M€ unster, 48149, Germany E-mail: j.neugebauer@uni-muenster.de [b] M. Franchini, L. Visscher Amsterdam Center for Multiscale Modeling, Vrije Universiteit Amsterdam, De Boelelaan 1083, HV Amsterdam 1081, The Netherlands E-mail: l.visscher@vu.nl [c] M. Franchini Scientific Computing & Modelling NV, Vrije Universiteit, Theoretical Chemistry, De Boelelaan 1083, HV Amsterdam 1081, The Netherlands [d] A. W. G€ otz San Diego Supercomputer Center, University of California San Diego, 9500 Gilman Drive, La Jolla, California 92093-0505, USA [e] C. R. Jacob Institute of Physical and Theoretical Chemistry, TU Braunschweig, Hans- Sommer-Straße 10, Braunschweig 38106, Germany E-mail: c.jacob@tu-braunschweig.de Contract grant sponsor: Deutsche Forschungsgemeinschaft (DFG) through SFB 858; Contract grant sponsor: European Cooperation in Science and Technology (COST) through COST Action CM1002 “CODECS” V C 2016 Wiley Periodicals, Inc. Journal of Computational Chemistry 2016, DOI: 10.1002/jcc.24670 1 SOFTWARE NEWS AND UPDATES WWW.C-CHEM.ORG