Basis set (chemistry) | EPFL Graph Search

In theoretical and computational chemistry, a basis set is a set of functions (called basis functions) that is used to represent the electronic wave function in the Hartree–Fock method or density-functional theory in order to turn the partial differential equations of the model into algebraic equations suitable for efficient implementation on a computer. The use of basis sets is equivalent to the use of an approximate resolution of the identity: the orbitals |\psi_i\rangle are expanded within the basis set as a linear combination of the basis functions |\psi_i\rangle \approx \sum_\mu c_{\mu i} |\mu\rangle, where the expansion coefficients c_{\mu i} are given by c_{\mu i} = \sum_\nu \langle \mu|\nu \rangle^{-1} \langle \nu |\psi_i \rangle. The basis set can either be composed of atomic orbitals (yielding the linear combination of atomic orbitals approach), which is the usual choice within the quant

Efficient Treatment of Correlation Energies at the Basis-Set Limit by Monte Carlo Summation of Continuum States

Martin Peter Bircher, Ursula Röthlisberger, Justin Villard

The calculation of electron correlation is vital for the description of atomistic phenomena in physics, chemistry, and biology. However, accurate wavefunction-based methods exhibit steep scaling and often sluggish convergence with respect to the basis set at hand. Because of their delocalization and ease of extrapolation to the basis-set limit, plane waves would be ideally suited for the calculation of basis-set limit correlation energies. However, the routine use of correlated wavefunction approaches in a plane-wave basis set is hampered by prohibitive scaling due to a large number of virtual continuum states and has not been feasible for all but the smallest systems, even if substantial computational resources are available and methods with comparably beneficial scaling, such as the Moller-Plesset perturbation theory to second order (MP2), are used. Here, we introduce a stochastic sampling of the MP2 integrand based on Monte Carlo summation over continuum orbitals, which allows for speedups of up to a factor of 1000. Given a fixed number of sampling points, the resulting algorithm is dominated by a flat scaling of similar to O(N-2). Absolute correlation energies are accurate to

AMER CHEMICAL SOC2020

Photophysics and Photochemistry from First Principles

Matteo Guglielmi

Quantum chemical methods are important tools for the predictions of electronic structure and energetics of molecules providing the interpretation of spectroscopic experiments and reaction mechanisms. In this thesis, density functional theory (DFT) and wavefunction-based methods are used in order to evaluate their ability in predicting experimental data with a particular attention to photoprocesses occurring in both gas and condensed phase systems. The cases studied in this work are inspired by problems both from biology and material science. In the first study, the photoexcitation properties of the molecule 7-hydroxyquinoline·(NH3)3, a prototypical molecular wire, are investigated. A concerted mechanism according to which all protons are transferred simultaneously in a fast process (∼ 100 fs) that amounts to the net transport of one proton from the oxygen to the nitrogen of 7-hydroxyquinoline is observed. In addition, the proton transfer pathway involves all three ammonia molecules and not only two as previously proposed. The presence of potential energy surface crossings with a dark-state is responsible for the low experimentally observed quantum-yield. To better understand the complex photophysics of the amino acid tryptophan, which is widely used as a probe of protein structure, we performed DFT and TDDFT calculations of gas phase tryptophan solvated with a controlled number of water molecules. The addition of two water molecules sufficiently lengthens the excited state lifetime enabling vibrationally resolved spectra. Quantum chemical calculations at the RI-CC2/aug-cc-pVDZ level, together with TDDFT/pw based first-principles MD simulations of the excited state dynamics, clearly demonstrate how interactions with water destabilize the photodissociative states and increase the excited state lifetime. Due to the availability of high-resolution experimental data, this system is ideally suited as benchmark model for the evaluation of the performance of different quantum chemical methods. An extensive low-energy isomer search was carried out for [TrpH·(H2O)n=0,1,2]+ using a hierarchy of theoretical methods ranging from classical force fields to a variety of DFT methods (BLYP, B3LYP, M05, M05-2X, M06, M06-2X and M06-HF with different basis sets) up to the CBS-C level. For the low-energy structures, the harmonic vibrational frequencies are calculated and compared with high resolution experimental IR spectra. It turns out that in all three cases, CBS-C is able to predict the lowest energy isomers that are in agreement with the experimentally observed vibrational spectra. In most cases, M06 provides energetics in close agreement with the CBS-C results. On the other hand, M05-2X is the only functional that yields highly-reliable predictions of the vibrational spectra. A natural extension of the tryptophan model to condensed phase was performed by an investigation of the [Trp-Lys]+ motif studied in the protein Human Serum Albumin via QM/MM simulations. Like in the case of gas phase [TrpH]+, solvation effects lead to an increase of the σN-H orbital energies. As a result, the first photoaccessible state of sW K+ is primarily a photostable π orbital, while in dW K+, photoexcitation leads to a dissociative pathway. The last application of this work concerns the optical properties of a novel dye for the sensitization of titanium dioxyde nanoparticles in Grätzel solar cells. The presence of a new absorption band in the visible region opens the way for a rational design of new dyes with improved properties.

EPFL2010

Wannier90 as a community code: new features and applications

Marco Gibertini, Hyungjun Lee, Daniel John Gilles Marchand, Antimo Marrazzo, Nicola Marzari, Lorenzo Paulatto, Giovanni Pizzi, Samuel Poncé, Junfeng Qiao

Wannier90 is an open-source computer program for calculating maximally-localised Wannier functions (MLWFs) from a set of Bloch states. It is interfaced to many widely used electronic-structure codes thanks to its independence from the basis sets representing these Bloch states. In the past few years the development of Wannier90 has transitioned to a community-driven model; this has resulted in a number of new developments that have been recently released in Wannier90 v3.0. In this article we describe these new functionalities, that include the implementation of new features for wannierisation and disentanglement (symmetry-adapted Wannier functions, selectively-localised Wannier functions, selected columns of the density matrix) and the ability to calculate new properties (shift currents and Berry-curvature dipole, and a new interface to many-body perturbation theory); performance improvements, including parallelisation of the core code; enhancements in functionality (support for spinor-valued Wannier functions, more accurate methods to interpolate quantities in the Brillouin zone); improved usability (improved plotting routines, integration with high-throughput automation frameworks), as well as the implementation of modern software engineering practices (unit testing, continuous integration, and automatic source-code documentation). These new features, capabilities, and code development model aim to further sustain and expand the community uptake and range of applicability, that nowadays spans complex and accurate dielectric, electronic, magnetic, optical, topological and transport properties of materials.

2020

Photophysics and Photochemistry from First Principles

Matteo Guglielmi

EPFL2010