
Abstract
Project Summary with Interim Results
The main goal of the 4cPNMR SASPRO project is twofold:
 Development and implementation of relativistic methods for calculation of NMR on paramagnetic substances in the framework of the DiracKohnSham Hamiltonian
 Efficient implementation of the developed methods for practical calculation on systems containing few heavy atoms and up to 200 light atoms
Although both goals are complementary to each other, their achievement requires fundamentally different set of skills: code development, method development and chemical intuition for the application and analysis of the calculated data. To distinguish between these skills, in the following discussion “development” will stand for the method development or algorithm development depending on the context, “implementation” will mean implementation of the developed methods in the ReSpect program package and “application” will denote calculations of chemical systems employing the implemented methods.
The main goals of the 4cPNMR project are subdivided into the following objectives:
 Excited states: Development and implementation of the relativistic method for the calculation of lowlying excited states.
 Paramagnetic NMR (pNMR): Development and implementation of methods for the calculation of the pNMR for systems with higher than doublet character.
 Performance: Implementation of modern programing techniques designed to increase the code efficiency and thus allowing applications of the developed methods on systems with up to 200 atoms.
 Release: Providing the code to public use on ReSpect web page, including manuals, tutorials and precompiled static and dynamic binaries.
 Application: Publication of the theoretical “proof of concept” articles and application of the developed functionality in collaboration with our foreign partners.
Below the description of work and main results for each objective are provided:
Excited states: The method of choice for the calculation of excited states is timedependent density functional theory (TDDFT). This method is well established in the scientific community, successfully providing excitation spectra for wide variety of compounds. In the first part of the 4cPNMR project, we have developed and implemented into program ReSpect TDDFT method in the fourcomponent framework (4cTDDFT) for both close and openshell reference systems. In the case of openshell systems this is the first time ever implementation in the world. This is an especially remarkable result since up to now the scientific community considered this task as too challenging. Prof. W. Liu, one of the leading scientist in the field, wrote: “… whose [4cTDDFT] moment adaptation is technically rather difficult, if not impossible. …” [Mol. Phys. 111, 3741 (2013)]. To achieve this important goal it has been necessary to make significant progress in two areas: First, a new algorithm for solving large eigenvalue problems had to be developed, since the commonly used algorithm was exhibiting poor convergence or did not converge at all. Moreover, we have developed a new type of noncollinear scheme for DFT functionals, which is able to provide stable kernels for functionals depending on the gradient of spin density (so called generalized gradient approximation, GGA). Note that the GGA functionals are long accepted as more advanced in comparison with LDA (local density approximation). So far, in the framework of relativistic TDDFT methods only adiabatic LDA approximation to DFT kernels has been used (socalled ALDA approximation). As it turns out, the ALDA kernels are providing disastrous results for the zerofield splitting whereas the abovementioned new class of GGA noncollinear DFT kernels yield consistent results on the diatomic test set. Two publications describing the theory and implementation of the 4cTDDFT method are in preparation.
Paramagnetic NMR: One of the many challenges of the project is the characterization of quantum states configuration of studied paramagnetic substances. In the nonrelativistic domain, this is achieved by referring to the spin multiplicity of the system. However, this option is not available in the relativistic domain, since spin is not a good quantum number anymore. Therefore, one usually resorts to the effective spin, or equivalently, to the formal degeneracy of the ground and excited states. By coincidence, within the 4cPNMR project, we have discovered a new quantum number in the relativistic theory of manyelectron systems [Phys. Rev. A 94, 052104 (2016)]. The new quantum number has the potential to substitute the spin symmetry in the relativistic domain. In our opinion, we consider this discovery the most important theoretical result of the 4cPNMR project although it was not part of the project plan. A publication describing the efficient acquiring of the eigenvectors of the symmetry operator that defines the new quantum number is in preparation.
Performance: To reach the applicability of the developed methods to systems up to 200 atoms both computational and memory bottlenecks must be addressed. In the first phase of the 4cPNMR project, we have concentrated on the computational bottlenecks by introducing MPI parallelization of DFT kernels and CauchySchwartz (CS) screening of the fourcentre integrals. Whereas the implementation of MPI parallelization was based on our previous experiences with parallelization of DFT potentials, the CS screening involved the development of new theory tailored for the relativistic fourcomponent domain. The acquired theory for fourcomponent CS screening is formulated in the general manner and therefore it is applicable to both TDDFT and NMR kernels. A publication describing the efficient implementation of fourcomponent calculation of total energies including description of the abovementioned CS screening methodology is in preparation.
Release: The first official release of the ReSpect code is scheduled for the end of 2017. Since the old user interface is dated back to 90’s, we have performed major improvements in the input structure and run scripts. Further, the new ReSpect web page is under construction including the new manual and tutorials. We use a modern technology of constructing web pages allowing us, for example, the easy update of the static web pages or convenient browsing of the manual on smartphones.
Application: The application of developed methods has been scheduled for the next stage of the 4cPNMR project; nevertheless, unforeseen applications calculating EPR, NMR and pNMR parameters have been already performed:
 Developing new anticancer drugs (wide international collaboration of groups in USA, Austria, Saudi Arabia, and Slovakia) [Dalton Trans. 46, 11925 (2017)].
 Explanation of SpinOrbit NMR shift of light atoms near heavy atom based on perturbation theory [J. Chem. Theory Comput. 13, 3586 (2017)].
 Studying the ligand hyperfine pNMR effects [Inorg. Chem. Submitted (2017)].