Sauer Group

We study and have studied for example

1. NMR spectra of organic molecules [see e.g. 36, 38, 47, 50, 55, 56, 58, 59, 62, 69, 75, 100, 105, 108, 111, 113, 123, 126, 134, 135, 136, 138, 145, 147, 148, 154, 157, 171, 173, 175, 178, 183, 196, 205, 206]
2. NMR and ESR spectra of transition metal complexes [see e.g. 86, 107, 115, 121, 131, 132, 156, 169, 197, 204]
3. Compounds for quantum information processing [see e.g. 193]
4. Isotope effects in NMR spectra [see e.g. 22, 26, 32, 34, 36, 49, 77, 84, 93]
5. How the motion of the nuclei in a molecule influences its NMR spectrum [see e.g. 11, 20, 22, 26, 28, 32, 34, 36, 42, 43, 49, 69, 93, 126, 154, 160]
6. Structure and spectra of heavy metal (Cd, Hg, Pt) complexes [see e.g. 45, 60, 112, 117, 118, 125, 155, 164, 167, 200]
7. Molecular processes leading to radiation damage of biomolecules [see e.g. 70, 80, 88, 90, 91, 99, 110, 116, 149, 152, 159]
8. Radiation damage to other molecules [see e.g. 128, 140, 151, 161, 165, 170, 172, 179, 181, 184, 185, 187, 189, 199]
9. The effect of the breakdown of the Born-Oppenheimer approximation and hyperfine interactions on vibration-rotation spectra of diatomic molecules [seee.g.3, 8, 14, 15, 18, 19, 21, 44, 61, 64, 65, 67, 96, 104, 129]
10. New compounds for optical data storage materials [see e.g. 39, 41, 50]
11. Chiral discrimination via NMR spectroscopy [see e.g. 108, 120, 176]
12. Optical rotation of chiral molecules [see e.g.143, 202]
13. Photochemistry of organic molecules [see e.g. 139, 162, 166, 198]
14. Reaction of organic molecules [see e.g. 146, 149, 152, 180]

We develop and test quantum chemical methods and corresponding computer programs for the calculation of molecular spectra with special emphasis on 

1. The effect of the environment on molecular spectra, e.g. the solvent for a molecule in solution or the protein environment of an active site, using continuum solvation and QM/MM approaches [see e.g. 46, 57, 85, 100, 113, 122, 133, 144, 159, 171, 178, 198 ]
2. Møller-Plesset perturbation theory or Coupled Cluster theory based methods like RPA(D), SOPPA(CCSD), SOPPA(CC2) and our newest method HRPA(D) [see e.g. 23, 25, 30, 37, 95, 105, 122, 141, 144, 163, 177, 186, 188]
3. Benchmarking of Density Functional Theory and wavefunction methods for the calculation of NMR, ESR and UV/Vis spectra [see e.g. 71, 73, 76, 78, 83, 87, 92, 97, 105, 106, 120, 126, 132, 133, 134, 150, 182, 186, 195, 196, 197, 205 ]
4. Benchmarking of Density Functional Theory and wavefunction methods for the calculation of other electromagnetic properties [see e.g. 27, 63, 72, 79, 127, 158, 190, 192, 201, 202, 203]
5. Development of specialized basis sets for the calculation of NMR and ESR spectra [see e.g. 9, 30, 38, 47, 54, 62, 89, 94, 114, 115, 135, 138, 168, 174, 207]
6. Alternative formulations of NMR parameters [see e.g. 7, 9, 13, 54, 71, 153]
7. Born-Oppenheimer-breakdown effects in rotational and vibrational spectra [see e.g. 29, 63, 84]

Proposals for Projects 

(research projects, bachelor & masters or other projects)

Development of quantum chemical methods for quantum computers (funded by the Novo Nordisk Foundation)

In this project you will take part in the effort to make use of present and future quantum computers for quantum chemical calculations. This involves rederivation and reimplementation of many of the known quantum chemical methods as well as new ones, which are more advantageous on quantum computers. Working on these projects you will gain experience with  programing quantum computers in general.
See also here for more details.

Implementation of the second order polarization propagator approximation (SOPPA) in the relativistic DIRAC program

Spectroscopic parameters can be determined using linear response theory, where the parameters are calculated from the response of a system to a perturbation by an external electromagnetic field. Many approaches based on the non-relativistic electronic Schrödinger equation, where the speed of light is assumed to be infinite and where the electrons are thus considered non-relativistically, exist for lighter atoms. 

Notably, the Second-Order-Polarization-Propagator-Approximation (SOPPA) has proven to be very useful, as it yields results in good agreement with experiment while being computationally less demanding than the high-accuracy Coupled Cluster (CC) methods. For heavy elements, the available methods based on the Schrödinger equation often become insufficient. Heavy elements are interesting both as central components in catalysts as well as solar cells and as highly toxic pollutants that need to be removed from the environment.

 Due to larger nuclear charges, electrons close to the nucleus can move at speeds close to that of light, giving rise to relativistic effects such as spin–orbit coupling, the Darwin term and the mass–velocity correction, which can all severely affect spectroscopic properties. Effects on nuclear magnetic resonance (NMR) parameters, for instance, can already be observed for the third period of the periodic table. The fairly large contribution from relativistic effects implies the need for a four-component version of SOPPA.

The goal of this project is thus to start the implementation of SOPPA method in the relativistic quantum chemistry program DIRAC.

Implementation of the third order polarization propagator method (TOPPA) in our new atomic integral direct program

Python program for the calculation of vibrational corrections to spectroscopic properties

All molecules vibrate even at 0K. However, in the Born-Oppenheimer approximation the motion of the electrons and nuclei is separated and one solves the electronic Schrödinger equation for a fixed nuclear geometry. This implies that in a normal quantum chemical calculation of NMR spin-spin coupling constants or chemical shifts at the equilibrium geometry of a given molecule, the contribution of the vibration of the molecule is ignored. However, the vibrational contributions are the sole reason for the temperature dependence or isotope shifts of these properties. Therefore it is important to study these contributions.
In this project an existing Python program for the calculation of vibrational corrections will be extended to treat more molecular properties.

Implementation of the calculation of the stopping power for low ion velocities

Our calculations of stopping powers of molecules were so far based on the simplest description of ion-molecule interactions, the Bethe-Born stopping theory, which is only valid for ions at high velocities. In this project we will extend the approach to include also to the low velocity range of the Bragg-peak where the biological damage is highest. For this we want to base our calculations directly on the generalized oscillator strength, which are a generalization of the normal dipole oscillator strengths of UV/Vis spectroscopy. Primarily, we have to automatize the calculation of the stopping power from generalized oscillator strengths in the DALTON program. Having done this we want to investigate whether it is possible to calculate generalized oscillator strengths with the necessary accuracy with modern basis sets, e.g. center-of-mass based Rydberg functions.

Computational Chemistry

The influence of solvent molecules on the electrochemical potential of tetrasubstituted p-phenylenediamines

N,N,N’,N’ tetrasubstituted p-phenylenediamines are electron-rich compounds that are easily oxidized to persistent radical cations by, for instance, electrochemical oxidation. A famous member of the group is N,N,N’,N’-tetramethyl-p-phenylenediamine (TMePD) the radical cation of which (Wurster's blue) was reported as early as 1879. Since then the radical cations of TMePD and related pphenylenediamines have featured in numerous investigations including studies of the optical, vibrational, and ESR spectra, electronic, mixed-valence and selfexchange properties, reorganization energies, and radical cation dimerizations.
In the current project we want to investigate the influence of the solvent on calculations of the redox potentials of these compounds. In particular we want to investigate, whether including explicit solvent molecules in the calculations will improve the agreement with experimental values.

Photochemistry of tetrasubstituted p-phenylenediamines

N,N,N’,N’ tetrasubstituted p-phenylenediamines are electron-rich compounds that are easily oxidized to persistent radical cations by, for instance, electrochemical oxidation. A famous member of the group is N,N,N’,N’-tetramethyl-p-phenylenediamine (TMePD) the radical cation of which (Wurster's blue) was reported as early as 1879. Since then the radical cations of TMePD and related pphenylenediamines have featured in numerous investigations including studies of the optical, vibrational, and ESR spectra, electronic, mixed-valence and selfexchange properties, reorganization energies, and radical cation dimerizations.
In the current project we want to find a suitable computational protocol, which allows to reproduce and thus predict the photochemistry of this compounds. This involves choosing an optimal DFT functional, basis set and solvent model by comparing to the measured UV-Vis spectra.

Understanding the trend in carbon chemical shifts in RuCAuL complexes

Carbide-bridged ruthenium gold complexes of the general formula trans-((C6H11)3P)2Cl2Ru=C−Au-L show a linear correlation between the carbon chemical shift and the Au-C bond length when changing the ligands L.
The goal of this project is to get a better understanding of the underlying mechanisms which are responsible for this trend. For this purpose relativistic density functional theory calculations will be carried out to investigate the inductive effects of the ligands and the effect of the Au-C bond length as well to analyse which molecular orbitals are responsible for the changes in the chemical shift.

Understanding the NMR properties of organofluoride compounds

Growing interest in organofluorine compounds has led to a rapid development of this area of chemistry, driving the attention of several fields as medicinal chemistry, pharmaceutical industry, material chemistry and agrochemistry, to name a few. Their range of applications is thus very wide, stretching from fluorinated drugs (due to the important biological role of these compounds), to solar cells (where the fluorination of the polymer improves the performance of the devices), to quantum computers (where the implementation of fluoroaromatic heterocyclic compounds is seen as very promising). The reason for the success of organofluorine compounds lies in the peculiar characteristics of F, being regarded to as a unique element across the periodic table. These particular properties arise from the combination of its small size, its electron-rich configuration, and its unmatched electronegativity. The singular properties of F also extend to nuclear magnetic resonance (NMR) spectroscopy: the ¹⁹F nucleus has 100% natural abundance, a high gyromagnetic ratio, and very desirable broad chemical shift ranges, meaning well-separated signals. ¹⁹F NMR spectroscopy is thus a very important characterization tool.

The influence of the molecular geometry on the calculation of NMR spin-spin coupling constants

Calculations of NMR spin-spin coupling constants are often plagued by so-called triplet instabilities or near-instabilities, which means that the lowest excited triplet state is errorneously calculated to have a lower energy than the singlet ground state or an energy close to it. The standard approach to solve this problem is to employ a higher-order method. This is of course limit to smaller molecules. In the literature, there are some hints that the choice of geometry also could have an influence on this. In this project we want to investigate this more generally in order to provide better guidance for the general user.

Mapping the dependence of Hg(II) electric field gradients on the coordinating ligands

The coordination chemistry of Hg(II) is important in its own right, and, in particular, because mercury ions may substitute native metal ions in metalloproteins, probably giving rise to the well known toxic effects of this heavy metal ion. ¹⁹⁹Hg NMR spectroscopy has become a powerful tool in this context due to the sensitivity of the ¹⁹⁹Hg NMR shielding constants and chemical shifts to the first coordination sphere of Hg(II). In this project it is the goal to systematically map the dependence of the ¹⁹⁹Hg chemical shifts and electric field gradients on the coordination number and ligands surrounding the ¹⁹⁹Hg nucleus.

Performance and turning of the new srDFT methods for the calculation of

NMR spin-spin coupling constants

electronic excitation energies

One of the most promising new computational methods are the short-range density functional theory methods (srDFT), where a DFT treatment for the correlation between electrons a short distances is combined with various wave function method treatments for the correlation at larger distances. In this project we want to explore the potential of this new method by investigating various DFT functionals as well as wave function methods. For each of these these combinations, one has to investigate also which is the optimal value of the range-separation parameter.

Performance of DFT functionals and our own wavefunction methods in the calculation of

molecular polarizabilities

optical rotation of chiral molecules

NMR spin-spin coupling constants

Most calculations of spectral parameters are today carried out at the level of density functional theory (DFT) because DFT can be employed to study larger systems, as it is often the case for organic molecules, while higher-theory methods quickly become unfeasible. However, the weakness of DFT lies in the non-universal description of the electron correlation. Consequently, the results are often largely dependent on the chosen functional, and benchmark studies need to be performed to establish the suitability of DFT methods for a given calculation.
In this project the performance of the most common DFT functionals versus experimental values or highly correlated wavefunction methods will be investigated in calculations of the above mentioned molecular properties.

Performance of the SOPPA method in the calculation of polarizabilities compared to other second order methods

The dipole polarizability is an important optical property of every molecule, which is e.g. the molecular property behind the refractive index or the property which determines the intensity of the lines Raman spectra. We have recently implemented the SOPPA method (based on Møller-Plesset 2nd order perturbation theory) in our new atomic integral direct program, which will allow calculations on larger organic molecules than previously. It is there time to investigate how well this level of theory performs compare to other methods. This project involves a literature study in order to choose suitable molecules, a basis set study in order to find a sufficiently converged basis set for this property and then to carry out calculations of polarizabilities with several methods including of course SOPPA.

Intermolecular bromine-bromine interactions in substituted dibromobenzenes in crystals

The crystal structure of different 2,5-disubstituerede-1,4-dibromobenzenes differ from the known types found for other halogen substituted compounds. In this project we want to investigate the energetics of the bromine-bromine intermolecular interactions in these compounds. As relativistic and in particular spin-orbit effects possibly play a role for bromine-bromine interactions, we will investigate in the first part of the project how large relativistic effects are and which method is suitable for describing them.

Radiation damage and radiation therapy with ion beams

The aim of these projects is to advance the understanding of radiation damage in biomolecules. The interaction of ion and gamma rays can be used to treat, or cause, cancers, depending on the point of application and the nature of the radiation. Understanding the basic physics and chemistry of the interaction of radiation with biological targets becomes ever more important as one seeks to protect healthy cells from radiation damage and to target therapeutic radiation (e.g. protons and C6+ ion beams have recently become viable modes of radiotherapy) selectively on pathologic cells. In our work, we apply quantum mechanical molecular electronic structure theory to the most basic level of the problem, namely the collisions of swift ions with biomolecules and the following chemical changes of the biomolecules.

Calculation of mean excitation energies of ions

The first step is to study the fundamental physics of the initial energy deposition of swift ions into biomolecules, which is characterized by a quantity called stopping power, or energy deposition per unit length along a pathway. This stopping power for ions at very high velocities is determined solely by the mean excitation energy of Bethe-Born stopping theory. The purpose of this project is to calculate mean excitation energies of ions as they are found in plasmas.

Calculation of the stopping power for low ion velocities

The first step is to study the fundamental physics of the initial energy deposition of swift ions into biomolecules, which is characterized by a quantity called stopping power, or energy deposition per unit length along a pathway. So far our work was based on the simplest description of ion-molecule interactions, the Bethe-Born stopping theory, which is only valid for ions at high velocities. In this project we will extend the approach to include also to the low velocity range of the Bragg-peak where the biological damage is highest. For this we want to base our calculations directly on the generalized oscillator strength, which are a generalization of the normal dipole oscillator strengths of UV/Vis spectroscopy. However, in the first step we have to investigate whether it is possible to calculate generalized oscillator strengths with the necessary accuracy with modern basis sets, e.g. center-of-mass based Rydberg functions.

Fragmentation following direct ionization or electron attachment

The second step is to investigate ionization and fragmentation of biomolecules as a consequence of direct hits by the ion beam. We want to study the possible chemical reactions, e.g. fragmentation, following direct ionization or electron attachment of nucleobases and will employ the full power of modern electronic structure theory to these reactions in the gas phase. The main issues to be investigated are what the dominant fragmentation channels are and whether any of the nucleobases is more susceptible for these reactions than others.

Fragmentation of nucleobases following reaction with an OH radical

The second step is to investigate the reactions of biomolecules with the fragmentation products of the main ingredient of a cell: water. So far we have studied the first reactions of OH radicals with individual nucleobases in the gas phase and in a simple water models. Now we want to study what happens after the OH radical has either abstracted a hydrogen atom or has added itself to one of the double bonds in the nucleobases. We will employ the full power of modern electronic structure theory to study these reactions in the gas phase and in different models for a water environment. The main issues to be investigated are what the dominant fragmentation channels are after the first hydrogen abstraction or OH addition.

Born-Oppenheimer Breakdown effects in rotation and vibration spectra

Calculation of the rotational and vibrational g-tensors

The theoretical description of matter is normally based on the Born-Oppenheimer approximation, which allows treating the motion of electrons and nuclei independently. However, this is only an approximation, although in general a very good one, and in certain situations deviations from it can be observed. In the analysis of high-resolution rotation or vibration-rotation spectra one includes therefore correction terms accounting for this, the so-called Born-Oppenheimer-breakdown (BOB) parameters and calculated values for the BOB parameters are useful or sometimes necessary for the analysis. There is therefore a constant need for high-level calculations of the BOB parameters, rotational and vibrational g-tensor, for small molecules.

Department of Chemistry, University of Copenhagen

Assoc. Prof. Lars Hemmingsen
on calculations of spectral parameters of heavy metals in biological systems

Prof. Leila Lo Leggio
on calculations of spectral parameters of metalloproteins

Prof. Jesper Bendix
on calculations of spectral parameters of transition metal complexes

Assoc. Prof. Michael Pittelkow
on calculations of the energetics and reactions of Biotin[6]uril

Assoc. Prof. Christian Marcus Pedersen
on the calculation of NMR parameters of carbohydrates

Assoc. Prof. Ole Hammerich
on the calculation of NMR parameters and redox potentials

Prof. Dr. Kurt Mikkelsen
on common interests

Department of Science and Environment, Roskilde University

Prof. Dr. Poul Erik Hansen
on the calculation of NMR paramete

Department of Physics and Chemistry, University of Southern Denmark, Odense

Prof. Dr. Jens Oddershede
on hadron radiation therapy, i.e. the interaction of atoms, molecules and biomolecules with fast ions

Prof. Jacob Kongsted
on QM/MM calculations of NMR spectra

Faculty of Chemistry, University of Opole, Poland

Prof. Dr. Teobald Kupka
on studies of NMR parameters

Instituto de Química Médica, Consejo Superior de Investigaciones Científicas, Madrid, Spain

Prof. Dr. Ibon Alkorta
on the calculation of chiroptical properties and properties of molecular clusters

Quantum Theory Project, University of Florida, Gainesville, USA

Prof. Dr. John R. Sabin
on hadron radiation therapy, i.e. the interaction of atoms, molecules and biomolecules with fast ions

Institute of Physics, Universidade de São Paulo, Brazil 

Prof. Dr. Sylvio Canuto and Prof. Dr. Kaline Coutinho
on solvent effects on molecular spectra

Institute of Chemistry, University of Campinas, Brazil

Prof. Dr. Rodrigo A. Cormanich
on NMR parameters of flourinated compounds

Department of Chemistry, University of Lavras, Brazil

Prof. Dr. Teodorico Castro Ramalho
on molecules for quantum information processing

Departamento de Fisica, University of Buenos Aires, Argentina 

Prof. Dr. Marta B. Ferraro
on the calculation of chiroptical properties

Assoc. Prof. Cristina Caputo
on NMR properties of molecular clusters

Departamento de Fisica, Universidad National del Nordeste, Corrientes, Argentina 

Assoc. Prof. Dr. Patricio F. Provasi
on the calculation of NMR indirect nuclear spin-spin coupling constants