We present the implementation of an efficient matrix-folded formalism for the evaluation of complex response functions and the calculation of transition properties at the level of the second-order algebraic-diagrammatic construction (ADC(2)) scheme. The underlying algorithms, in combination with the adopted hybrid MPI/OpenMP parallelization strategy, enabled calculations of the UV/vis spectra of a guanine oligomer series ranging up to 1032 contracted basis functions, thereby utilizing vast computational resources from up to 32,768 CPU cores. Further analysis of the convergence behavior of the involved iterative subspace algorithms revealed the superiority of a frequency-separated treatment of response equations even for a large spectral window, including 101 frequencies. We demonstrate the applicability to general quantum mechanical operators by the first reported electronic circular dichroism spectrum calculated with a complex polarization propagator approach at the ADC(2) level of theory.

Since its beginning, the remarkable development from the first commercially available computers toward exascale supercomputers just within the span of a lifetime has been closely intertwined with the perpetual quest for the utilization of the arising computing power for the avail of theoretical chemistry. With the aim of further pushing the limits of computationally accessible molecular system sizes, this thesis includes the presentation of programming efforts, which brought forth two quantum chemical software codes, as well as a range of ab initio studies on carbon-based systems, enabled by the former.

The VeloxChem and Gator programs, developed for spectroscopy simulations at the level of density-functional theory (DFT) and correlated wave function methods, respectively, employ a hybrid message passing interface (MPI)/open multiprocessing (OpenMP) parallelization scheme embedded in a modular program structure written in a Python/C++ layered fashion for the execution in contemporary high-performance computing (HPC) environments. Included numerical solvers for the evaluation of real and complex linear response functions in combination with the parallel construction of auxiliary Fock matrices enable the efficient calculation of one-photon absorption or electronic circular dichroism (CD) spectra in the ultraviolet/visible (UV/vis) or X-ray spectral region, as well as van der Waals C₆ dispersion coefficients.

Employing the VeloxChem program in two comprehensive investigations, the C₆ dispersion coefficients of carbon fullerenes up to a system size of C₅₄₀ and the CD spectra of carbohelicenes ranging from CH[5] to CH[30] have been calculated at the DFT level of theory. The revealed non-additive scaling with respect to the number of carbon atoms of N^2.2 in the former and nontrivial CD band progressions, arguably linked to the number of overlapping layers in the helical conjugated systems, in the latter rectify the current conception in their respective fields.

In a benchmark for the Gator program on a series of guanine oligomers, the full UV/vis spectrum for a tetrad was calculated at the level of a second-order algebraic-diagrammatic construction (ADC(2)) scheme in just under 15 hours by efficient employment of 32,768 central processing unit (CPU) cores.

Exceeding the limit of 10,000 and 1,000 contracted basis functions for a treatment with the DFT and ADC(2) methods, respectively, these practical examples demonstrate the capability of VeloxChem and Gator to harness vast computational resources made available by contemporary and future HPC systems and thereby routinely address scopes of system sizes that were previously out of reach.

Den anmärkningsvärda utvecklingen som inom enbart loppet av en livstid gått från de första kommersiellt tillgängliga datorerna mot exascale superdatorer har varit nära sammanflätad med en strävan att kunna utnyttja den uppgraderade beräkningskraften för att kunna lösa mer komplexa problem inom den teoretisk kemin. I syfte att ytterligare tänja på gränserna för beräkningsmässigt tillgängliga molekylära systemstorlekar, inkluderar denna avhandling en presentation av programmeringsinsatser som ledde till utvecklingen av två kvantkemiska mjukvarukoder, såväl som en rad ab initio studier på kolbaserade system, där de två mjukvarukoderna applicerades.

VeloxChem- och Gator-programmen som är utvecklade för spektroskopi-simuleringar på nivån för density-functional theory (DFT) respektive korrelerade vågfunktionsmetoder, använder ett hybrid-message passing interface (MPI)/open multiprocessing (OpenMP) parallelliseringsschema som är inbäddat i en modulär programstruktur skriven i lager av  Python/C++ för exekvering i nutida hög-prestandaberäkningsmiljöer (HPC). De inkluderade numeriska lösningsalgoritmerna för utvärdering av reella och komplexa linjära responsfunktioner i kombination med den parallella konstruktionen av extra Fock-matriser möjliggör effektiv beräkning av både en-fotonabsorption eller elektronisk cirkulär dikroism (CD)-spektra i ultravioletta/synliga (UV/vis) eller röntgen områden, samt beräkningar av van der Waals C₆ dispersionskoefficienter.

Genom att använda VeloxChem-programmet i två omfattande undersökningar har dispersionskoefficienterna C₆ för kolfullerener upp till en systemstorlek på C₅₄₀ och CD-spektra av kolhelicener från CH[5] till CH[30] varit beräknade på DFT-nivå. Den första undersökningen avslöjade en icke-additiv skalning med avseende på antalet kolatomer av N^2,2. Den andra identifierade icke-triviala CD-bandprogressioner, som förmodligen är kopplat till antalet överlappande lager i de spiralformade konjugerade systemen. Resultaten från dessa studier utmanar den nuvarande uppfattningen inom undersökningarnas respektive områden.

I en jämförelse på en serie guanin-oligomerer utförda med Gator-programmet, beräknades hela UV/vis-spektrumet för en tetrad på nivån av ett andra-ordningens algebraic-diagrammatic construction (ADC(2)) scheme på mindre än 15 timmar genom effektivt nyttjande av 32 768 kärnor för centralprocessorer (CPU).

Genom att överskrida gränsen på 10 000 och 1 000 kontrakterade basfunktioner för en behandling med DFT- respektive ADC(2)-metoderna, visar dessa applicerade exempel på VeloxChems och Gators förmåga att utnyttja enorma beräkningsresurser som görs tillgängliga av både nutida och framtida HPC-system och därmed tillåter rutinmässiga beräkningar av systemstorlekar som tidigare var utom räckhåll.

We demonstrate that contemporary computational resources allow for accurate theoretical studies of systems matching recent advances in experimental helicene chemistry. Concerned with first-principles calculations of carbohelicenes, our work surpasses CH[12] as the largest system investigated to date and unravels trends in the electronic structure of the low-lying states of the homologous series. Utilizing a highly efficient implementation of linear response algorithms, we present electronic circular dichroism (CD) spectra of carbohelicenes ranging from CH[5] to CH[30] at the level of Kohn-Sham density-functional theory. Our results for a systematic increase in system size show the emergence of new CD bands that subsequently rise to intensities dominating the spectrum. The spectral band progressions exhibit a periodicity directly linked to the number of overlapping layers of conjugation. While our findings rectify the current understanding of the electronic structure of carbohelicenes, they also serve as a general call for caution regarding the extrapolation of trends from small system ranges.

Within the self-consistent field approximation, computationally tractable expressions for the isotropic second-order hyperpolarizability have been derived and implemented for the calculation of two-photon absorption cross sections. The novel tensor average formulation presented in this work allows for the evaluation of isotropic damped cubic response functions using only similar to 3.3% (one-photon off-resonance regions) and similar to 10% (one-photon resonance regions) of the number of auxiliary Fock matrices required when explicitly calculating all the needed individual tensor components. Numerical examples of the two-photon absorption cross section in the one-photon off-resonance and resonance regions are provided for alanine-tryptophan and 2,5-dibromo-1,4-bis(2-(4-diphenylaminophenyl)vinyl)-benzene. Furthermore, a benchmark set of 22 additional small- and medium-sized organic molecules is considered. In all these calculations, a quantitative assessment is made of the reduced and approximate forms of the cubic response function in the one-photon off-resonance regions and results demonstrate a relative error of less than similar to 5% when using the reduced expression as compared to the full form of the isotropic cubic response function.

The Gator program has been developed for computational spectroscopy and calculations of molecular properties using real and complex propagators at the correlated level of wave function theory. Currently, the focus lies on methods based on the algebraic diagrammatic construction (ADC) scheme up to the third order of perturbation theory. An auxiliary Fock matrix-driven implementation of the second-order ADC method for excitation energies has been realized with an underlying hybrid MPI/OpenMP parallelization scheme suitable for execution in high-performance computing cluster environments. With a modular and object-oriented program structure written in a Python/C++ layered fashion, Gator additionally enables time-efficient prototyping of novel scientific approaches, as well as interactive notebook-driven training of students in quantum chemistry. This article is categorized under: Computer and Information Science > Computer Algorithms and Programming Electronic Structure Theory > Ab Initio Electronic Structure Methods Software > Quantum Chemistry.

While the anomalous non-additive size-dependencies of static dipole polarizabilities and van der Waals C-6 dispersion coefficients of carbon fullerenes are well established, the widespread reported scalings for the latter (ranging from N-2.2 to N-2.8) call for a comprehensive first-principles investigation. With a highly efficient implementation of the linear complex polarization propagator, we have performed Hartree-Fock and Kohn-Sham density functional theory calculations of the frequency-dependent polarizabilities for fullerenes consisting of up to 540 carbon atoms. Our results for the static polarizabilities and C-6 coefficients show scalings of N-1.2 and N-2.2, respectively, thereby deviating significantly from the previously reported values obtained with the use of semi-classical/empirical methods. Arguably, our reported values are the most accurate to date as they represent the first ab initio or first-principles treatment of fullerenes up to a convincing system size.

An open-source program named VeloxChem has been developed for the calculation of electronic real and complex linear response functions at the levels of Hartree–Fock and Kohn–Sham density functional theories. With an object-oriented program structure written in a Python/C++ layered fashion, VeloxChem enables time-efficient prototyping of novel scientific approaches without sacrificing computational efficiency, so that molecular systems involving up to and beyond 500 second-row atoms (or some 10,000 contracted and in part diffuse Gaussian basis functions) can be routinely addressed. In addition, VeloxChem is equipped with a polarizable embedding scheme for the treatment of the classical electrostatic interactions with an environment that in turn is modeled by atomic site charges and polarizabilities. The underlying hybrid message passing interface (MPI)/open multiprocessing (OpenMP) parallelization scheme makes VeloxChem suitable for execution in high-performance computing cluster environments, showing even slightly beyond linear scaling for the Fock matrix construction with use of up to 16,384 central processing unit (CPU) cores. An efficient—with respect to convergence rate and overall computational cost—multifrequency/gradient complex linear response equation solver enables calculations not only of conventional spectra, such as visible/ultraviolet/X-ray electronic absorption and circular dichroism spectra, but also time-resolved linear response signals as due to ultra-short weak laser pulses. VeloxChem distributed under the GNU Lesser General Public License version 2.1 (LGPLv2.1) license and made available for download from the homepage https://veloxchem.org. This article is categorized under: Software > Quantum Chemistry Electronic Structure Theory > Density Functional Theory Theoretical and Physical Chemistry > Spectroscopy.

We present the derivation and implementation of an efficient matrix-folded formalism for the evaluation of complex response functions at the level of the second-order algebraic-diagrammatic construction ADC(2) scheme. The adopted hybrid MPI/OpenMP parallelization strategy enables the utilization of vast computational resources without significant performance losses as demonstrated by consistent size-scalings for the computationally most demanding steps obtained from calculations of the UV/vis spectra of a guanine oligomer series ranging up to 1,032 contracted basis functions. Further analysis of the convergence behavior of the involved iterative subspace algorithm revealed the superiority of a frequency-separated treatment of response equations even for a large spectral window including 101 frequencies. We demonstrate the applicability to general quantum mechanical operators by the first reported electric circular dichroism spectrum calculated with the complex polarization propagator approach at the ADC(2) level of theory.