Orbital optimization in the perfect pairing hierarchy. Applications to full-valence calculations on linear polyacenes

We describe the implementation of orbital optimization for the models in the perfect pairing hierarchy [Lehtola et al, J. Chem. Phys. 145, 134110 (2016)]. Orbital optimization, which is generally necessary to obtain reliable results, is pursued at perfect pairing (PP) and perfect quadruples (PQ) levels of theory for applications on linear polyacenes, which are believed to exhibit strong correlation in the {\pi} space. While local minima and {\sigma}-{\pi} symmetry breaking solutions were found for PP orbitals, no such problems were encountered for PQ orbitals. The PQ orbitals are used for single-point calculations at PP, PQ and perfect hextuples (PH) levels of theory, both only in the {\pi} subspace, as well as in the full {\sigma}{\pi} valence space. It is numerically demonstrated that the inclusion of single excitations is necessary also when optimized orbitals are used. PH is found to yield good agreement with previously published density matrix renormalization group (DMRG) data in the {\pi} space, capturing over 95% of the correlation energy. Full-valence calculations made possible by our novel, efficient code reveal that strong correlations are weaker when larger bases or active spaces are employed than in previous calculations. The largest full-valence PH calculations presented correspond to a (192e,192o) problem.Comment: 19 pages, 4 figure

Järjestötoimijoiden ja yrittäjien välisen yhteistyön kehittäminen kulttuurirajojen yli tapahtumanjärjestämisessä

Opinnäytetyöni tarjoaa Helsingin Itäkeskuksessa sijaitsevalle Badbaado-nimiselle ruohonjuuritason toiminnan järjestölle toimintamalleja, joilla he voisivat lisätä Itäkeskuksessa sijaitsevan Puhoksen ostoskeskuksen alueen sosiaalista pääomaa PuhosXPeople-tapahtumakokonaisuuden kautta. Opinnäytetyöni kuvaa ainutlaatuista aluetta pääkaupunkiseudulla, jossa alueen toiminta pyörii maahanmuuttajataustaisten yrittäjien ympärillä. Työstäni on hyötyä tapahtumanjärjestäjälle ja järjestötyöntekijälle, jotka työskentelevät maahanmuuttajapainotteisissa alueissa ja tapahtumissa. Se käsittelee aihettaan sekä taloudellisen että sosiaalipoliittisen viitekehyksen kautta. Käytän menetelminä työssäni havaintoja tapahtuman järjestämisprosessista toukokuun 2017 alusta elokuun 2017 loppuun, strukturoituja haastatteluja alueen yrittäjien kanssa, teemahaastatteluja tapahtumanjärjestäjien kanssa, asiantuntijahaastattelua alueen pienosakkaan Maria Von Flittnerin kanssa ja aiheesta jo tehtyä tietopohjaa. Työ on tilaajan tarpeiden mukaisesti selkeä, kattava ja tiivis analyysi ja kehitysehdotus, jossa tarjotaan järjestölle tapoja kehittyä realistisesti heidän haluamaansa suuntaan. Opinnäytetyölläni on mielestäni suuri merkitys alan toimijoille: Puhoksen kaltaisista alueista ei löydy suomalaisessa viitekehyksessä paljoakaan tehtyjä tutkimuksia tai kirjallisuutta, joten opinnäytetyöni on siinä mielessä ainutlaatuinen kuvaus suomalaisesta alueesta, joka keskittyy maahanmuuttajien järjestämän toiminnan ympärille. Se on myös esimerkki tapahtuman järjestäjälle siitä, mitä tehdä tai jättää tekemättä yritysyhteistyössä pienen sosiaalisen pääoman alueella. Työn tilaaja on vuonna 2003 perustettu Badbaado ry. niminen järjestö. He toimivat alueen maa-hanmuuttajaväestön seassa ruohonjuuritason toiminnan kautta.The goal of my thesis is to offer a grassroots-organization called Badbaado, which resides in Itäkeskus neighborhood at Helsinki, operating models for increasing the social capital of an area around Puhos shopping center, which resides in Itäkeskus, through PuhosXPeople-event. My thesis describes a unique part of Helsinki Metropolitan Area, where the activities of the neighborhood revolve around entrepreneurs who own an immigrant background. My thesis is of value to those who work in event organizing and in organizations in immigrant based neighborhoods and events. It processes the subject through economical and sociopolitical frame of reference. I use various kinds of methods, such as perceptions of the event-organizing process from the end of May 2017 until the end of August 2017, structured interviews with the entrepreneurs of the area, a theme interview with the small shareholder of Puhos called Maria Von Flittner and information base already written about the subject. This work is constructed to fit with the needs of the subscriber as a clear, comprehensive and compact analysis and development proposal in which the organization is offered means to develop realistically in their wanted direction. My thesis is in my opinion of gross significance to the industry of event-organizers and organization workers: there is not a whole lot of studies or literature written about areas such as Puhos, so my thesis is in that way a unique description of a Finnish neighborhood in which the area is centered around the activities created by immigrants. It also an example for an event organizer about what to do and what not to do in organization-entrepreneur cooperation in an area which contains only a little of social capital. The subscriber of the work is an organization founded in 2003 called Badbaado. They act with the immigrant population of the area through grassroots activity

Automatic Generation of Accurate and Cost-efficient Auxiliary Basis Sets

We have recently discussed an algorithm to automatically generate auxiliary basis sets (ABSs) of the standard form for density fitting (DF) or resolution-of-the-identity (RI) calculations in a given atomic orbital basis set (OBS) of any form [J. Chem. Theory Comput. 2021, 17, 6886]. In this work, we study two ways to reduce the cost of such automatically generated ABSs without sacrificing their accuracy. We contract the ABS with a singular value decomposition proposed by K\'allay [J. Chem. Phys. 2014, 141, 244113], used here in a somewhat different setting. We also drop the high-angular momentum functions from the ABS, as they are unnecessary for global fitting methods. Studying the effect of these two types of truncations on Hartree--Fock (HF) and second-order M{\o}ller--Plesset perturbation theory (MP2) calculations on a chemically diverse set of first- and second-row molecules within the RI/DF approach, we show that accurate total and atomization energies can be achieved by a combination of the two approaches with significant reductions in the size of the ABS. While the original approach yields ABSs whose number of functions $N_{\text{bf}}^{\text{ABS}}$ scales with the number of functions in the OBS, $N_{\text{OBS}}^{\text{bf}}$, as $N_{\text{ABS}}^{\text{bf}}=\gamma N_{\text{OBS}}^{\text{bf}}$ with the prefactor $\gamma\approx\mathcal{O}(10)$, the reduction schemes of this work afford results of essentially the same quality as the original unpruned and uncontracted ABS with $\gamma\approx5\text{-}6$, while an accuracy that may suffice for routine applications is achievable with a further reduced ABS with $\gamma\approx3\text{-}4$. The observed errors are similar at HF and MP2 levels of theory, suggesting that the generated ABSs are highly transferable, and can also be applied to model challenging properties with high-level methods.Comment: 20 pages, 6 figure

A call to arms: making the case for more reusable libraries

The traditional foundation of science lies on the cornerstones of theory and experiment. Theory is used to explain experiment, which in turn guides the development of theory. Since the advent of computers and the development of computational algorithms, computation has risen as the third cornerstone of science, joining theory and experiment on an equal footing. Computation has become an essential part of modern science, amending experiment by enabling accurate comparison of complicated theories to sophisticated experiments, as well as guiding by triage both the design and targets of experiments and the development of novel theories and computational methods. Like experiment, computation relies on continued investment in infrastructure: it requires both hardware (the physical computer on which the calculation is run) as well as software (the source code of the programs that performs the wanted simulations). In this Perspective, I discuss present-day challenges on the software side in computational chemistry, which arise from the fast-paced development of algorithms, programming models, as well as hardware. I argue that many of these challenges could be solved with reusable open source libraries, which are a public good, enhance the reproducibility of science, and accelerate the development and availability of state-of-the-art methods and improved software.Comment: 13 pages, 1 figur

Computational modeling of the electron momentum density

The properties and the functionality of materials are determined to a large extent by their electronic structure. The electronic structure can be examined through the electron momentum density, which is classically equivalent to the velocity distribution of the electrons. Changes in the structure of materials induce changes on their electronic structure, which in turn are reflected as changes in the electron momentum densities that can be routinely measured using, e.g., x-ray Compton scattering. The changes in the momentum density can be linked back to the structural changes the system has experienced through the extensive use of computational modeling. This procedure naturally requires using a model matching the accuracy of the experiment, which is constantly improving as the result of the ongoing development of synchrotron radiation sources and beam line instrumentation. However, the accuracies of the current computational methods have not been hitherto established. This thesis focuses on developing the methods used to compute the electron momentum density in order to achieve an accuracy comparable to that of the experiment. The accuracies of current quantum chemical methods that can be used to model the electron momentum density are established. The completeness-optimization scheme is used to develop computationally efficient basis sets for modeling the electron momentum density at the complete basis set limit. A novel, freely available software program that can be used to perform all of the necessary electronic structure calculations is also introduced.Materiaalien ominaisuudet sekä toiminnallisuus ovat pitkälti niiden elektronisen rakenteen määräämiä. Elektronirakennetta voidaan tutkia elektroniliikemäärätiheyden avulla, joka vastaa klassisesti elektronien nopeusjakaumaa. Materiaalien rakenteessa tapahtuvat muutokset muuttavat niiden elektronirakennetta, joka puolestaan heijastuu niiden liikemäärätiheyksiin joka voidaan rutiininomaisesti mitata käyttämällä esimerkiksi röntgen-Compton-sirontaa. Liikemäärätiheydessä tapahtuvat muutokset voidaan yhdistää systeemissä tapahtuneisiin rakennemuutoksiin käyttämällä laskennallista mallinnusta. Tämä luonnollisesti vaatii sellaisen mallin käyttämistä, jonka tarkkuus on verrattavissa mittaustuloksen tarkkuuteen, joka taas paranee jatkuvasti synkrotronisäteilylähteiden ja mittauslaitteistojen kehityksen vuoksi. Nykyisten mallinnusmenetelmien tarkkuutta ei ole kuitenkaan vielä määritetty. Tässä väitöskirjassa kehitetään elektroniliikemäärätiheyden mallinnusmenetelmiä, tarkoituksena saavuttaa kokeisiin verrattavissa oleva tarkkuus. Nykyaikaisten kvanttikemiallisten menetelmien tarkkuudet määritetään. Täydellisyysoptimointimenetelmää käytetään laskennallisesti tehokkaiden, elektroniliikemäärätiheyden mallintamiseen suunnattujen kantajoukkojen muodostamiseen, joiden tulokset ovat kantajoukkorajalla. Esittelemme myös uuden, vapaasti saatavilla oleva ohjelman, jolla voidaan suorittaa kaikki mallintamisessa tarvittavat elektronirakennelaskut

Y-sukupolven johtaminen Airpro Oy:ssä

Y-sukupolvi on jo hämmentämässä työelämää. Näitä 1980−1990 -luvuilla syntyneitä ihmisiä kuvaillaan kärsimättömäksi sukupolveksi, joka ei auktoriteetteja kunnioita. Monissa yrityksissä ollaan hieman hämillään näiden nuorien työntekijöiden kanssa, sillä heitä tuntuvat motivoivan erilaiset asiat kuin aikaisempia sukupolvia. Airpro Oy:n turvatarkastusyksikkö muodostaa yrityksen liikevaihdollisesti suurimman yksikön. Sen 336 työntekijästä suurin osa kuuluu y-sukupolveen. Yrityksessä on huomattu, että y-sukupolveen kuuluvien henkilöiden maailma poikkeaa aikaisempien sukupolvien maailmasta, joten heidän johtamiseensa on kiinnitettävä erityistä huomiota. Tutkimuksen tavoitteena oli muodostaa käsitys siitä, mitä y-sukupolveen kuuluvat odottavat työelämältä, mitä he odottavat esimiestoiminnalta ja mitkä asiat vaikuttavat heidän sitoutu-miseensa työnantajaan. Jotta y-sukupolveen kuuluvia nuoria voidaan johtaa menestyksekkäästi, tarvitaan tietoa siitä, mikä heitä motivoi ja ajaa eteenpäin työelämässä. Tutkimustuloksia hyödynnetään Airpro Oy:n turvatarkastusyksikön esimiestoiminnan kehittämiseen. Työn sisältämä tutkimus suoritettiin kvalitatiivisia menetelmiä käyttäen. Tutkimusmenetelminä olivat puolistrukturoitu haastattelu sekä dokumenttianalyysi. Tutkimuksessa haastateltiin seitsemää toimeksiantajayrityksen y-sukupolveen kuuluvaa henkilöä. Haastatteluista saatua tietoa verrattiin myös koosteeseen turvatarkastusyksiköstä irtisanoutuneiden henkilöiden irtisanoutumiseen johtaneista syistä. Työn teoreettinen osuus painottuu johtamiseen, valmentavaan johtamiseen ja y-sukupolven ominaisuuksiin. Tutkimuksesta saatua tietoa verrattiin teoriapohjaan, jonka perusteella voitiin tehdä päätelmiä tutkimusongelman selvittämiseksi. Tutkimuksen tulokset osoittivat, että y-sukupolveen kuuluvat henkilöt edellyttävät työltään runsaasti motivaatiotekijöitä. Heille tärkeintä työssä on, että se tarjoaa riittävästi etenemis- ja kehittymismahdollisuuksia. Työilmapiirin täytyy olla myös hyvä ja työtä halutaan tehdä mieluiten tiimeissä hyvien työkavereiden ympäröimänä. Työn pitää olla myös merkityksellistä. Heitä tulisi johtaa keskustelevalla otteella, jossa esimies pyrkii kehittämään työntekijöitä jatkuvasti. Heidän motivointinsa onnistuu parhaiten palautetta antamalla ja siihen tulisikin kiinnittää erityistä huomiota. Y-sukupolven sitoutuminen työnantajaan liittyy vahvasti motivaatiotekijöihin. Kun heille järjestetään esimerkiksi erilaisia kehitysohjelmia, saadaan heidät sitoutettua tehokkaasti yrityksen palvelukseen. Jatkotutkimusaiheita nousi tämänkin tutkimuksen myötä luonnollisesti esiin. Kun tässä tutki-muksessa on selvitetty y-sukupolveen kuuluvien työntekijöiden johtamista toimeksiantajayri-tyksessä, olisi mielenkiintoista selvittää, miten esimiehet näkevät y-sukupolven johtamisen.Managing generation Y at Airpro Oy Generation Y causes confusion in today’s working life. It has been said that people of this generation, born in the 1980—1990s, are impatient and do not respect any authorities. Employers may often be perplexed with these young adults since their motivations in life seem to be quite different from that of previous generations. The security unit of Airpro Oy is the biggest unit of the company measured by turnover. Most of its 336 employees belong to generation Y. In the company it has been noted that generation Y appear to have different values compared to older members of the workforce. For this reason particular attention should be paid to the management of this group. The purpose of the study was to understand what people of this age group expect from work, from management and what produces commitment to the employer. In order to manage gen-eration Y successfully, it is necessary to research how they can be motivated. The results of this study will be made use of in the development of management practices. Research for this study was conducted using qualitative methods. Seven individuals were in-terviewed through semi-structured interviews. The data gathered from the interviews was also compared to a summary of employees’ reasons for resigning from the company. The theoretical framework consists of three elements which were management, coaching as a management model and the special characteristics of generation Y. The information that was received from the empirical research was compared to the theoretical knowledge base. On the basis of this comparison it was possible to make conclusions to clarify the research problem. The results of the study showed that the persons who belong to the generation Y require plenty of motivation factors from their work. It is most important to them that the work provides opportunities for progress and sufficient self-development. The working atmosphere must also be good and they want to work preferably in teams surrounded by good colleagues. The work must also be significant. They should be managed using a consultative management style in which the superior tries to develop the workers continuously. Motivating them succeeds best by giving feedback and therefore special attention should be paid to this. The commitment of the generation Y to the employer is strongly connected to the motivation factors. When, for example, different development programmes are arranged for them, they will become more committed to the company. Topics for further research also arose from this research. Since the special characteristics of the workers who belong to the generation Y have been clarified, it would be interesting to examine the management’s view of the subject

Meta-GGA density functional calculations on atoms with spherically symmetric densities in the finite element formalism

Density functional calculations on atoms are often used for determining accurate initial guesses as well as generating various types of pseudopotential approximations and efficient atomic-orbital basis sets for polyatomic calculations. To reach the best accuracy for these purposes, the atomic calculations should employ the same density functional as the polyatomic calculation. Atomic density functional calculations are typically carried out employing spherically symmetric densities, corresponding to the use of fractional orbital occupations. We have described their implementation for density functional approximations (DFAs) belonging to the local density approximation (LDA) and generalized gradient approximation (GGA) levels of theory as well as Hartree-Fock (HF) and range-separated exact exchange [S. Lehtola, Phys. Rev. A 2020, 101, 012516]. In this work, we describe the extension to meta-GGA functionals using the generalized Kohn-Sham scheme, in which the energy is minimized with respect to the orbitals, which in turn are expanded in the finite element formalism with high-order numerical basis functions. Furnished with the new implementation, we continue our recent work on the numerical well-behavedness of recent meta-GGA functionals [S. Lehtola and M. A. L. Marques, J. Chem. Phys. 2022, 157, 174114]. We pursue complete basis set (CBS) limit energies for recent density functionals, and find many to be ill-behaved for the Li and Na atoms. We report basis set truncation errors (BSTEs) of some commonly used Gaussian basis sets for these density functionals and find them to be strongly functional dependent. We also discuss the importance of density thresholding in DFAs and find that all of the functionals studied in this work yield total energies converged to $0.1\ \mu E_{h}$ when densities smaller than $10^{-11}a_{0}^{-3}$ are screened out.Comment: 30 pages, 2 figure

Assessment of Initial Guesses for Self-Consistent Field Calculations. Superposition of Atomic Potentials : Simple yet Efficient

Electronic structure calculations, such as in the Hartree-Fock or Kohn-Sham density functional approach, require an initial guess for the molecular orbitals. The quality of the initial guess has a significant impact on the speed of convergence of the self-consistent field (SCF) procedure. Popular choices for the initial guess include the one-electron guess from the core Hamiltonian, the extended Huckel method, and the superposition of atomic densities (SAD). Here, we discuss alternative guesses obtained from the superposition of atomic potentials (SAP), which is easily implementable even in real-space calculations. We also discuss a variant of SAD which produces guess orbitals by purification of the density matrix that could also be used in real-space calculations, as well as a parameter-free variant of the extended Huckel method, which resembles the SAP method and is easy to implement on top of existing SAD infrastructure. The performance of the core Hamiltonian, the SAD, and the SAP guesses as well as the extended Huckel variant is assessed in nonrelativistic calculations on a data set of 259 molecules ranging from the first to the fourth periods by projecting the guess orbitals onto precomputed, converged SCF solutions in single- to triple-zeta basis sets. It is shown that the proposed SAP guess is the best guess on average. The extended Huckel guess offers a good alternative, with less scatter in accuracy.Peer reviewe

Importance profiles. Visualization of basis set superposition errors

Recent developments in fully numerical methods promise interesting opportunities for new, compact atomic orbital (AO) basis sets that maximize the overlap to fully numerical reference wave functions, following the pioneering work of Richardson and coworkers from the early 1960s. Motivated by this technique, we suggest a way to visualize the importance of AO basis functions in polyatomic calculations, employing fully numerical calculations at the complete basis set (CBS) limit: the importance of a normalized AO basis function $|\alpha\rangle$ centered on some nucleus can be visualized by projecting $|\alpha\rangle$ on the set of numerically represented occupied orbitals $|\psi_{i}\rangle$ as $I(\alpha)=\sum_{i}\langle\alpha|\psi_{i}\rangle\langle\psi_{i}|\alpha\rangle$. Choosing $\alpha$ to be a continuous parameter describing the orbital basis, such as the exponent of a Gaussian-type orbital (GTO) or Slater-type orbital (STO) basis function, one is then able to visualize the importance of various functions on various centers in various molecules. The proposed visualization $I(\alpha)$ has the important property $0\leq I(\alpha)\leq1$ which allows unambiguous interpretation. We exemplify the method with importance profiles computed for atoms from the first three rows in a set of chemically diverse diatomic molecules. We find that the method offers a good way to visualize basis set superposition errors: the non-orthonormality of AO basis functions on different atomic centers is unambiguously revealed by the importance profiles computed for the ghost atom in an atomic calculation performed in the numerical basis set for a diatomic molecule.Comment: 10 pages, 3 figure