Analytic Energy Gradients for Multiconfigurational Self-Consistent Field Second-Order Quasidegenerate Perturbation Theory (MC-QDPT)

An analytic energy gradient method for second-order quasidegenerate perturbation theory with multiconfigurational self-consistent field reference functions (MC-QDPT) is derived along the lines of the response function formalism (RFF). According to the RFF, the gradients are calculated without solving coupled perturbed equations. Instead, it is necessary to solve seven sets of linear equations in order to determine Lagrangian multipliers, corresponding to four sets of parameter constraining conditions and three sets of additional parameter defining conditions in the Lagrangian. Just one of these linear equations is a large scale linear equation; the others are reducible to just partial differentiations or simple equations solvable by straightforward subroutines

Interaction and Localization of One-electron Orbitals in an Organic Molecule: Fictitious Parameter Analysis for Multi-physics Simulations

We present a new methodology to analyze complicated multi-physics simulations by introducing a fictitious parameter. Using the method, we study quantum mechanical aspects of an organic molecule in water. The simulation is variationally constructed from the ab initio molecular orbital method and the classical statistical mechanics with the fictitious parameter representing the coupling strength between solute and solvent. We obtain a number of one-electron orbital energies of the solute molecule derived from the Hartree-Fock approximation, and eigenvalue-statistical analysis developed in the study of nonintegrable systems is applied to them. Based on the results, we analyze localization properties of the electronic wavefunctions under the influence of the solvent.Comment: 4 pages, 5 figures, the revised version will appear in J. Phys. Soc. Jpn. Vol.76 (No.1

Designing all-graphene nanojunctions by covalent functionalization

We investigated theoretically the effect of covalent edge functionalization, with organic functional groups, on the electronic properties of graphene nanostructures and nano-junctions. Our analysis shows that functionalization can be designed to tune electron affinities and ionization potentials of graphene flakes, and to control the energy alignment of frontier orbitals in nanometer-wide graphene junctions. The stability of the proposed mechanism is discussed with respect to the functional groups, their number as well as the width of graphene nanostructures. The results of our work indicate that different level alignments can be obtained and engineered in order to realize stable all-graphene nanodevices

A mathematical and computational review of Hartree-Fock SCF methods in Quantum Chemistry

We present here a review of the fundamental topics of Hartree-Fock theory in Quantum Chemistry. From the molecular Hamiltonian, using and discussing the Born-Oppenheimer approximation, we arrive to the Hartree and Hartree-Fock equations for the electronic problem. Special emphasis is placed in the most relevant mathematical aspects of the theoretical derivation of the final equations, as well as in the results regarding the existence and uniqueness of their solutions. All Hartree-Fock versions with different spin restrictions are systematically extracted from the general case, thus providing a unifying framework. Then, the discretization of the one-electron orbitals space is reviewed and the Roothaan-Hall formalism introduced. This leads to a exposition of the basic underlying concepts related to the construction and selection of Gaussian basis sets, focusing in algorithmic efficiency issues. Finally, we close the review with a section in which the most relevant modern developments (specially those related to the design of linear-scaling methods) are commented and linked to the issues discussed. The whole work is intentionally introductory and rather self-contained, so that it may be useful for non experts that aim to use quantum chemical methods in interdisciplinary applications. Moreover, much material that is found scattered in the literature has been put together here to facilitate comprehension and to serve as a handy reference.Comment: 64 pages, 3 figures, tMPH2e.cls style file, doublesp, mathbbol and subeqn package

Prognostic refinement of NSMP high-risk endometrial cancers using oestrogen receptor immunohistochemistry

Background: Risk-assessment of endometrial cancer (EC) is based on clinicopathological factors and molecular subgroup. It is unclear whether adding hormone receptor expression, L1CAM expression or CTNNB1 status yields prognostic refinement. Methods: Paraffin-embedded tumour samples of women with high-risk EC (HR-EC) from the PORTEC-3 trial (n = 424), and a Dutch prospective clinical cohort called MST (n = 256), were used. All cases were molecularly classified. Expression of L1CAM, ER and PR were analysed by whole-slide immunohistochemistry and CTNNB1 mutations were assessed with a next-generation sequencing. Kaplan-Meier method, log-rank tests and Cox's proportional hazard models were used for survival analysis. Results: In total, 648 HR-EC were included. No independent prognostic value of ER, PR, L1CAM, and CTNNB1 was found, while age, stage, and adjuvant chemotherapy had an independent impact on risk of recurrence. Subgroup-analysis showed that only in NSMP HR-EC, ER-positivity was independently associated with a reduced risk of recurrence (HR 0.33, 95%CI 0.15-0.75). Conclusions: We confirmed the prognostic impact of the molecular classification, age, stage, and adjuvant CTRT in a large cohort of high-risk EC. ER-positivity is a strong favourable prognostic factor in NSMP HR-EC and identifies a homogeneous subgroup of NSMP tumours. Assessment of ER status in high-risk NSMP EC is feasible in clinical practice and could improve risk stratification and treatment.Biological, physical and clinical aspects of cancer treatment with ionising radiatio