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Dr. Andreas Götz: Research

jump to: Research Sponsors - Workshops - GPU accelerated MD - QM/MM
CAICE - Cytochrome c oxidase - Many-body potentials - GAL17 force field
Subsystem DFT - OEP and TDDFT - Density Fitting (PhD) - Work camp
Molecular simulation methods and software for high-performance computing platforms based on quantum mechanics, classical molecular mechanics, statistical mechanics, machine learning and data science. Application areas include biochemistry, biophysics, atmospheric chemistry, catalysis, and materials science.

Building the Computational Tools for Scientific Discovieries
  • High performance computing (HPC) and large scale, data intensive scientific computing with focus on (bio)chemistry and nanotechnology.
  • Highly parallel algorithms and software implementations for predictive computational science through quantum mechanical (QM) and classical atomistic numerical simulations on well established and emerging HPC platforms including graphics processing units (GPUs).
  • Implementations into (mainly) the ADF software package for density functional theory (DFT) and the AMBER software package for classical MM and mixed QM/MM molecular dynamics (MD) simulations, both used by a large number of academic and industrial researchers world wide.
  • Education and training of the next generation of scientists in software engineering and numerical simulation methods, quantum chemistry, molecular dynamics, and data science.
Research Sponsors
U.S. Department of Energy National Institutes of Health National Science Foundation
U.S. Department of Energy Office of Science NIH National Institute of General Medical Sciences National Science Foundation
Intel Nvidia NSF Supercomputer access
Intel Parallel Computing Center at SDSC NVIDIA CUDA Teaching Centers NSF XSEDE Extreme Science and Engineering Discovery Environmnet

Cover of the Journal of Computational Chemistry featuring my QM/MM software

My research on QM/MM simulation software featured on the cover page of the Jan 2014 edition of the Journal of Computational Chemistry.

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Workshops and Symposia

Computational Chemistry Across Catalysis, ACS National Meeting San Diego (March 2016)

In March 2016 I organized a 4-day symposium at the spring 2016 ACS national meeting that brought together researchers that share a common interest in the computational modeling of catalytic processes. Presentations spanned all domains of catalysis including homogeneous and heterogeneous catalysis, biocatalysis, photocatalysis, and electrocatalysis. A wide range of modeling methods were discussed, including ab initio electronic structure theory, kinetics simulations (mean field, KMC), molecular dynamics, non-adiabatic dynamics and free energy perturbations. Co-organizers of the symposium were my collaborators Dion Vlachos from University of Delaware and Carine Michel and Philippe Sautet from the ENS Lyon in France.

GPU Computing Symposium and Workshop at SDSC (November 2013)

This two day GPU computing event was organized by myself and Ross Walker (co-directors of the CUDA Teaching Center at SDSC) with help from Jon Saposhnik (NVIDIA). The symposium covered trends, tools and research discoveris using GPU accelerated computing in areas ranging from pharmaceutical research to geophysics (see the program). The workshop featured lectures on GPU programming using both CUDA and OpenAcc as well as hands-on exercises.

AMBER workshop at ECNU in Shanghai (August 2011)

I am organizer and instructor of an AMBER workshop at East China Normal University (ECNU) in Shanghai. This five day workshop (22-26 August, 2011) aims to introduce researchers in the field of (bio)molecular simulations to the broad collection of computational tools implemented in the AMBER and AmberTools software packages for molecular dynamics simulations.

ADF workshop at SDSC (March 2011)

Together with Dr. Matt Kundrat from SCM I have organized and tutored an ADF workshop that was held on Thursday, 24 March 2011 at the San Diego Supercomputer Center. The workshop was geared both at begineers and expert users of ADF wishing to learn about the new features of the ADF2010.02 release.

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GPU Accelerated Molecular Dynamics for Biomolecular Simulations
Work done at SDSC since June 2009

This work is partially supported by NSF award ACI-1835144.

Graphical processing units (GPUs) offer a tremendous amount of computing power in a compact package (see graphics to the right). Both the peak floating point operations per second and the memory bandwidth of NVIDIA GPUs compare favorably to Intel CPUs. However, this comes at the cost of reduced flexibility and increased programming complexity as compared to CPUs.

I am involved in an effort to port the all-atom classical MD engine PMEMD of the AMBER biomolecular simulation package to GPUs [1-3]. The AMBER implementation uses CUDA which is a relatively simple extension of the standard C programming language that allows one to code in an inherently parallel fashion and perform all necessary operations to access and manipulate data on a GPU device.

Peak floating point operations per second (Flop/s; left) and memory bandwidth (right) for Intel CPUs and NVIDIA GPUs. (Taken from our publication [1] on GPU accelerated MD) The data is from 2012 but the performance differential looks similar as of 2018.

Peak Flop/s for Intel CPUs and NVIDIA GPUs

Peak memory bandwidth for Intel CPUs and NVIDIA GPUs

Throughput timings (ns/day) for AMBER GB simulations (2fs time step) with the MPI parallel CPU code and the CUDA GPU code (data from 2012).

GPU performance

We have developed a new precision model in which the contributions to the forces are calculated in single precision floating point arithmetics but accumulated in accumulated in 64-bit fixed-point integers (SPFP). The numerical noise due to rounding errors in a pure single precision implementation is sufficiently so large that it leads to accumulation of errors that can result in unphysical trajectories for long timescale simulations. The numerical results of the mixed-precision SPFP model are comparable to a full double precision model and the reference double precision CPU implementation but at significantly reduced computational cost.

The AMBER GPU implementatin provides performance for MD simulations on a single desktop machine that is on par with, and in some cases exceeds, that of traditional supercomputers (see table on the left). Routine microsecond MD simulations are now possible for systems with several hundred thousands of atoms under periodic boundary conditions. With GPUs becoming ubiquitous in workstations and also as accelerators in HPC platforms, the impact of this implementation on the field of molecular dynamics is broad and transformative.

[1] A. W. Götz, M. J. Williamson, D. Xu, D. Poole, S. Le Grand, R. C. Walker, J. Chem. Theory Comput. 8, 1542 (2012). DOI: 10.1021/ct200909j

[2] S. Le Grand, A. W. Götz, R. C. Walker, Comput. Phys. Commun. 184, 374-380 (2013). DOI: 10.1016/j.cpc.2012.09.022

[3] R. Salomon-Ferrer, A. W. Götz, D. Poole, S. Le Grand, R. C. Walker, J. Chem. Theory Comput. 9, 3878-3888 (2013). DOI: 10.1021/ct400314y

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QM/MM for Biomolecular Simulations
Work done at SDSC since June 2009

This work is partially supported by NSF award ACI-1835144 and NSF award CHE-1416571.

QM/MM approaches in AMBER

Hybrid quantum mechanical and molecular mechanical (QM/MM) approaches are used extensively to study local electronic events in large molecular systems with a diverse area of applications ranging from enzymatic catalysis to properties of materials systems. We are continuously developing new QM/MM approaches. Among others we are working on a GPU accelerated software library for QM and QM/MM simulations.

We have developed an implementation that couples the MD software AMBER to electronic structure software packages including ADF, GAMESS-US, Gaussian, Orca, NWChem and TeraChem [1,2]. With this interface, ab initio wave function theory and DFT methods become available for QM/MM MD simulations with AMBER.

This represents a set of widely used programs, both commercial and freely available, each with its own strengths for different electronic structure methods and computing platforms ranging from desktop workstations to supercomputers. In the case of TeraChem this also includes accelerator hardware in form of graphics processing units (GPUs). Data exchange between AMBER and the external QM software is currently implemented by means of files and system calls or the message passing interface (MPI) standard.

This interface was used for example to study the absorption spectrum of the photoactive yellow protein (PYP) (see picture on right). It was shown that a large QM region (hundreds of atoms) is required to achieve a converged spectrum [2].

[1] A. W. Götz, M. A. Clark, R. C. Walker, J. Comput. Chem. 35, 95-108 (2014). DOI: 10.1002/jcc.23444

[2] C. M. Isborn , A. W. Götz , M. A. Clark , R. C. Walker, T. J. Martínez, J. Chem. Theory Comput. 8, 5092-5106 (2012). DOI: 10.1021/ct3006826

The picture shows a snapshot of PYP (photoactive yellow protein). The chromophore (highlighted) and its environment are treated quantum mechanically. See publication [2].

Solvated protein with highlighted
                                                   QM region

The picture shows the scheme used for adaptive QM/MM simulations. Solvent can move via a transition region between the active region (QM) and the environment (MM).

Adaptive QM/MM approach

Adaptive QM/MM approaches

I have implemented a parallelized adaptive QM/MM approach into the AMBER MD software package [1]. It is based on a method developed by Rosa Bulo [2].

Adaptive QM/MM enables the QM treatment of an active region of a solvated molecular system including the solvent molecules in its vicinity (see left). The environment is handled with MM to reach high computational efficiency. During a simulation, solvent molecules can move via a transition region between the active and environment regions.

I was awarded a TRO (Triton Research Opportunity) grant by SDSC to collaborate with Francesco Paesani and use my implementation to study processes of relevance for atmospheric chemistry. Together with Kyoyeon Park we have shown the potential of adaptive QM/MM for MD simulations of aqueous systems [3].

Adaptive QM/MM can be applied to lots of exciting problems, for example solvent effects on absorption spectra, binding free energies of ions or drug-like molecules to proteins or enzymes.

[1] A. W. Götz, K. Park, R. E. Bulo, F. Paesani, R. C. Walker, publication in preparation (2015).

[2] R. E. Bulo, B. Ensing, J. Sikkema, L. Visscher, J. Chem. Theory Comput. 5, 2212-2221 (2009).

[3] K. Park, A. W. Götz, R. C. Walker, F. Paesani,
J. Chem. Theory Comput. 8, 2868-2877 (2012). DOI: 10.1021/ct300331f

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CAICE (Center for Aerosol Impacts on Chemistry of the Environment) - Atmospheric Chemistry
Work done at SDSC since 2017

This work is supported by NSF award CHE-1801971.

The Goetz group is part of the NSF Center for Aerosol Impacts on Chemistry of the Environment (CAICE), a multi-institution, interdisciplinary research center with headquarters at UC San Diego. The goal of CAICE is to understand fundamental processes regarding the chemistry of aerosol particles and their impact on the environment.

We develop highly accurate many-body potentials based on correlated electronic structure reference data and machine learning techniques for atmospherically relevant molecules and their interactions with aqueous aerosol particles containing ions and surfactants. We use these potentials for computer simulations of gas scattering and reactive uptake of atmospheric gases to sea spray mimics.

Molecular dynamics simulations with rare events sampling methods give access to structural, thermodynamic, and spectroscopic properties from small model clusters to condensed phase systems with explicit liquid-gas interfaces. We also employ QM/MM methods to study chemical reaction dynamics.

The figure to the right shows an early application with a simple Amber GAFF force field for the important pollutant dinitrogenpentoxide (N2O5) and the TIP4P water potential. We have determined the free energy change when N2O5 transfers from liquid water to the gas phase. We are currently developing a highly accurate potential that will allow a quantitative prediction of the solubility, a quantity that is hard to obtain experimentally.

[1] B. Hirshberg, E. Rossich molina, A. W. Götz, A. Hammerich, G. Nathanson, T. H. Bertram, M. A. Johnson, R. B. Gerber, Phys. Chem. Chem. Phys. 20, 17961-17976 (2018). DOI: 10.1039/c8cp03022g

The figure shows the potential of mean force for N2O5 crossing the liquid water / vapor interface. The solvation free energy determines the solubility of N2O5 in water. Amber GAFF / TIP4P data. See publication [1].

Potential of mean
	      force for n2o5 entering water

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Cytochrome c oxidase - electronic structure, reactions, molecular dynamics
Work done at SDSC since 2012

This work is supported by NIH award R01 GM100934.

Cytochrome c oxidases (CcOs) are redox driven proton pumps in the membranes of mitochondria and many aerobic bacteria. CcOs are the terminal oxidases (Complex IV) of the electron transport chain and drive ATP synthesis by producing the required electrochemical potential gradient across the membrane, in conjunction with Complexes I and III.

We employ density functional theory (DFT) calculations and classical and QM/MM molecular dynamics simulations to provide a detailed mechanistic understanding of the catalytic reaction pathways and mechanisms of proton pumping in CcO.

We work closely with the group of Prof. Louis Noodleman at Scripps Research. Based on DFT calculations we have developed a detailed reaction mechanism for the oxygen reduction to water in the dinucler reaction center (DNC) of CcO. [1] This is a chemically difficult but biologically important reaction.

Using molecular dynamics simulations, we have identified water exit pathways from the water pool above the DNC to the P-side of the membrane, which could also act as proton transfer pathways. [2] We are currently investigating plausible proton transport mechanisms.

[1] L. Noodleman, W. Han Du, J. Fee, A. W. Götz, R. C. Walker Inorg. Chem. 53, 6458-6472 (2014). DOI: 10.1021/ic500363h

[2] L. Yang, A. A. Skjevik, W.-G. Han Du, L. Noodleman, R. C. Walker, A. W. Götz, BBA, Bioenergetics. 1857, 1594-1606 (2016). DOI: 10.1016/j.bbabio.2016.06.005

The figure shows the two water exit pathways (red dots) leading from the reaction center of ba3-type CcO to the P-side of the membrane that we identified using molecular dynamics simulations. See publication [2].

Cytochrome c
	      oxidase embedded in membrane with water exit pathways

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Many-body potentials and machine learning
Work done at SDSC since 2017

This work is supported by NSF award ACI-1642336.

Computer simulations are a powerful tool for the modeling of molecules and materials but are still limited by a tradeoff between the accuracy of the molecular models and the associated computational cost. The many-body expansion of the total energy can be effectively employed in combination with machine learning techniques to develop highly accurate models that are useful for practical applications.

Long-range and higher-order terms are represented by classical dispersion, permanent electrostatics, and induction. Machine learning techniques are then used to encode the highly complex quantum mechanical many-body interactions that arise when molecules interact at short range. A successful example of this approach is the MB-pol water model and its extension to atomic ions in water, see for example [1,2].

[1] S. K. Reddy, S. C. Straight, P. Bajaj, C. H. Pham, M. Riera, D. R. Moberg, M. A. Morales, C. Knight, A. W. Götz, F. Paesani J. Chem. Phys. 145, 194594 (2016). DOI: 10.1063/1.4967719

[2] M. Riera, N. Mardirossian, P. Bajaj, A. W. Götz, F. Paesani J. Chem. Phys. 147, 161715 (2017). DOI: 10.1063/1.4993213

Data centric
	      workflow tools for the automated generation of many-body
	      potentials

Behler-Parinello type neural network architecture
	      for water 3-body interactions

We are developing an open-source software infrastructure for the automated generation of many-body potentials for generic molecules. The central building block is a database that stores all relevant properties and molecular configurations that are required to train machine learning models of 1-body monomer distortions and 2-body and 3-body interaction potentials. We exploit distributed and volunteer computing for massively parallel electronic structure calculations.

We recently have shown that different machine learning techniques can be used to represent the short-range interactions of the many-body expansion. [3] We currently work with permutationally invariant polynomials (PIPs) and Behler-Parinello type neural networks (BPNN), see Figure on the left. We work closely with Professors Francesco Paesani from the Chemistry Department and Sean Gao from Computer Science to improve these machine learning algorithms.

These alternative machine learning models are both highly accurate, which means that researchers can choose the algorithms that best map to the available hardware. Modern many-core processors, for instance, are well-suited to evaluate the complex expressions of the PIPs, while massively parallel graphics processing units (GPUs) perform exceptionally well for neural networks.

We also work on efficient implementations of these machine learning based many-body potentials. We employ C++ with OpenMP for many-core CPUs and C++ with CUDA and Nvidia's deep learning library for massively parallel GPUs.

[3] T. T. Nguyen, E. Székely, G. Imbalzano, J. Behler, G. Csányi, M. Ceriotti, A. W. Götz, F. Paesani, J. Chem. Phys. 148, 241725 (2018). DOI: 10.1063/1.5024577

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GAL17: a force field for water over platinum; and multiscale simulations of catalysis
Work done at SDSC since 2014

This work is supported by NSF award CHE-1416571.

We develop models and software to better understand at a molecular level how catalysts function to ultimately improve processes for the production of fuels and raw materials for the chemical industry from renewable biomass. Detailed computer simulations can play a key role in understanding how these catalysts function at a molecular level and guide the development of improved catalysts for industrially viable processes in biorefineries.

In a collaboration with Philippe Sautet (UCLA), Paul Fleurat-Lessard (Université de Bourgogne) and Carine Michel and Stephan Steinmann (ENS Lyon) we have developed a new force field for water over platinum that is more accurate than any existing model. We implemented the force field in the Amber software.

GAL17 can be combined with different water models and reparameterized for metals other than platinum. We are currently extending GAL17 to chemical compounds with alcohol groups at metal surfaces in aqueous solution. This will allow efficient sampling of the structure of water and biomass processing reactants/products at the metal/liquid interface and determination of solvation free energies along catalytic reaction pathways.

[1] S. Steinmann, R. Ferreira de Morais, A. W. Götz, P. Fleurat-Lessard, M. Iannuzzi, P. Sautet, C. Michel, J. Chem. Theory Comput. 14, 3238-3251 (2018). DOI: 10.1021/acs.jctc.7b01177

Water molecules over a Pt(111) surface, simulated with the new GAL17 force field and TIP3P water. See publication [1].

Water over
	      Pt(111) surface

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Subsystem Density Functional Theory
Postdoc in Amsterdam with Dr. L. Visscher (November 2006 - April 2009)

I have been and still continue to work on the extension of the frozen density embedding (FDE) method in density functional theory (DFT). The main research topics are analytical gradients for FDE and nuclear spin-spin coupling constants in the framework of FDE. The research work is done with Dr. L. Visscher at the chair of theoretical chemistry at the Vrije Universiteit Amsterdam which is headed by Prof. Dr. E.-J. Baerends.

DFT is undoubtedly the most popular computational method for the investigation of the electronic structure of molecules. It allows to obtain accurate information on molecular properties at a moderate computational cost. Studies of molecules of interest for classic organic or inorganic chemistry are routine by now. It is the time to find new approaches to be able to study also more complex systems in fields of increasing importance such as life sciences and nanotechnology.

The extension of FDE to a general subsystem DFT has a tremendous potential as an accurate (in principle exact) multi-scale modelling method. Such methods allow to focus the computational effort on those parts of the system which is of importance for the property of interest, while still taking into account the interaction with the remaining parts of the system. Proper implementations will allow to tackle the investigation of properties of chemical systems of unprecedented size and complexity. The implementation is done in the Amsterdam Density Functional (ADF) program package.

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Optimized Effective Potential Method and Time-dependent Density Functional Theory
Postdoc in Erlangen with Prof. Dr. A. Görling (October 2005 - October 2006)

Conventional density functional theory (DFT) methods like those based on the local density approximation (LDA) or generalized gradient approximations (GGAs) employ approximate functionals for the exchange-correlation (XC) energy that are integrals of functions of the electron density and its gradient. GGA methods are widely and successfully employed routine methods to investigate electronic ground states and their properties in chemistry and solid state physics. Despite their success, these conventional DFT methods are not accurate enough for many questions of interest.

In recent years, a new generation of DFT methods emerged that uses functionals that not only depend on the elctron density and its gradients but also on Kohn-Sham orbitals. These DFT methods require the solution of the optimized effective potential (OEP) equations which are plagued by numerical stability problems if localized basis sets are employed. Together with Dr. A. Heßelmann I have developed a numerically stable approach which can be used for ground state calculations with orbital-dependent functionals [1,2]. Our method has been implemented and tested for exact-exchange (EXX) DFT which employs the exact exchange functional instead of approximations to it.

Time-dependent density functional theory (TD-DFT) is a very efficient and in many cases encouragingly accurate method to describe electronically excited states of molecules. A fundamental problem which has not yet been solved concerns excited states with charge-transfer (CT) character. Such excited states, which are of importance for a great deal of applications, cannot be described by GGA XC functionals. A very promising avenue to solve this problem is the extension of the EXX approach to excited states [3]. Although the theory has been worked out already in 1998, no practical implementation for molecules exists so far.

EXX and localized Hartree-Fock exchange potentials for pyridine along the carbon nitrogen ring [2].

EXX potential for pyridine

Based on our numerically stable OEP approach I have worked out algorithms and implemented these into the TD-DFT module of the quantum chemical program package TURBOMOLE. Research along these lines is further pursued in Prof. Dr. A. Görling's group.

[1] A. Heßelmann, A. W. Götz, F. Della Salla, A. Görling, J. Chem. Phys. 127, 054102 (2007).

[2] A. Görling, A. Ipatov, A. W. Götz, A. Heßelmann, Z. Phys. Chem. 224, 325-342 (2010).

[3] A. Görling, Int. J. Quant. Chem. 69, 265-277 (1998).

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Density Fitting Approaches for Efficient Density Functional Calculations
PhD thesis, Erlangen, Germany (November 2001 - August 2005)

My PhD thesis in Theoretical Chemistry was accomplished at the University of Erlangen under the supervision of Prof. Dr. B. A. Heß (University of Bonn, deceased) and later under the supervision of Prof. Dr. A. Görling. I have been working on the LEDO-DFT [1] formalism and its implementation into the quantum chemical program package TURBOMOLE. LEDO-DFT speeds up density functional theory (DFT) calculations and thus enables simulations of larger molecules.

LEDO is an acronym for limited expansion of diatomic overlap densities and is a novel density fitting approach to speed up molecular DFT calculations. Conventional density fitting methods (also called RI methods) as generally employed in DFT expand the complete electron density into a fit basis which is distributed over the whole system (molecule). As a result one- to three-center two-electron repulsion integrals (ERIs) have to be evaluated and the computational expense is O(N3) with respect to the size N of the system under investigation as compared to O(N4) for conventional DFT.

In the LEDO-DFT formalism each individual diatomic overlap density is expanded into a fit basis which is restricted to the atoms of that overlap density. Thus, two-center matrix elements of the Coulomb- and Exchange-Correlation contribution to the Kohn-Sham matrix can be expressed in terms of the one-center elements using the LEDO expansion coefficients. Consequently only one- and two-center ERIs have to be evaluated and the computational expense of the Kohn-Sham matrix formation in a LEDO-DFT calculation is reduced to O(N2).

CPU time for the SCF of linear alkanes on a single core 2.0 GHz Intel Xeon processor.

LEDO-DFT scaling behavior

During my PhD I have implemented the calculation of analytical gradients [2] within the LEDO-DFT formalism [1]. Furthermore, I have worked out criteria for the optimization of auxiliary basis sets for the LEDO expansion and optimized auxiliary orbitals which allow for LEDO-DFT calculations with sufficient accuracy [3].

My PhD thesis can be downloaded in pdf format from the opus server of the University of Erlangen.

diploma thesis, Erlangen, Germany (April 2001 - October 2001)

My diploma thesis was accomplished during the time from April to October 2001 under the supervision of Prof. Dr. B. A. Heß (University of Bonn, deceased) at the University of Erlangen. It is entitled Implementierung eines vereinfachten Dichtefunktionalverfahrens (Implementation of a Simplified Density Functional Formalism) and deals with the implementation of the LEDO-DFT[1] formalism (see PhD thesis) in the SCF part of the DFT programs of the quantum chemical program package TURBOMOLE.

My diploma thesis (available only in German) can be download here: ps / pdf

[1] C. Kollmar, B. A. Hess, Molec. Phys. 100, 1945-1955 (2002).

[2] A. W. Götz, C. Kollmar, B. A. Hess, Molec. Phys. 103, 175-182 (2005).

[3] A. W. Götz, C. Kollmar, B. A. Hess, J. Comput. Chem. 26, 1242-1253 (2005).

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Renovating a Monastery in Northern Italy (back to top)
Work camp in Àcqui Terme, Italy (September 1995)

In September 1995, after finishing school and before university started, I participated in a workcamp organized by SCI (Service Civil International). It took place in a small village near Àcqui Terme which is close to the town of Asti in the Piemont region in northern Italy.

The philosohpy of the workcamps organized by SCI is to bring together the working and/or creative power of people from different countries in order to realize a project of social welfare. In general the participants have to pay the trip to the workcamp by themselves, but board and lodging at the working place are for free. In my case the project of the work camp was to renovate the run-down accomodations of a small protestant church for future use as a cost-free excursion center for schools or other institutions or people in need. We have been a dozen people from Great Britain, the Netherlands, Germany and Italy. It was hard work, but also a lot of fun.

The duration of the workcamp was two weeks, rather short. Nevertheless it was a unique and worthy experience. If you have time, I can just recommend to participate in a workcamp organized by SCI.

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last modification: 2018/10/23