Some calculations on the ground and lowest-triplet state of the helium isoelectronic sequence with the nucleus in motion

The method described in the preceding paper for the solution of two-electron atoms, which was used to calculate the 1 1S and 2 3S states of helium and heliumlike atoms within the fixed-nucleus approximation, has been applied to the case where all three particles are in relative motion. The solutions in the present case automatically include the effects of the mass polarization term and are compared with the results obtained for the term by using first-order perturbation theory with the fixed-nucleus wave functions. The input data for a particular atom consist of the atomic number, as before, but now the corresponding mass of the nucleus must be given also. Nonrelativistic energies with the nuclear mass included in the calculation have been obtained for the 1 1S and 2 3S states for Z ranging from 1 to 10. The energy with the nucleus in motion can be expressed only to eight significant figures (SF's) given the accuracy with which the relevant physical constants are known at present. All the results given here are computed as if these constants were known to ten SF's so that errors not incurred due to rounding. Convergence of the energies to ten SF's for both the singlet and triplet state was reached with a matrix of size 444 for Z values from 2 to 10. Convergence for the H- ion was a little slower

On Factorization of Molecular Wavefunctions

Recently there has been a renewed interest in the chemical physics literature of factorization of the position representation eigenfunctions \{$\Phi$\} of the molecular Schr\"odinger equation as originally proposed by Hunter in the 1970s. The idea is to represent $\Phi$ in the form $\varphi\chi$ where $\chi$ is \textit{purely} a function of the nuclear coordinates, while $\varphi$ must depend on both electron and nuclear position variables in the problem. This is a generalization of the approximate factorization originally proposed by Born and Oppenheimer, the hope being that an `exact' representation of $\Phi$ can be achieved in this form with $\varphi$ and $\chi$ interpretable as `electronic' and `nuclear' wavefunctions respectively. We offer a mathematical analysis of these proposals that identifies ambiguities stemming mainly from the singularities in the Coulomb potential energy.Comment: Manuscript submitted to Journal of Physics A: Mathematical and Theoretical, May 2015. Accepted for Publication August 24 201

Comment on `On the Quantum Theory of Molecules' [J. Chem.Phys. {\bf 137}, 22A544 (2012)]

In our previous paper [J. Chem.Phys. {\bf 137}, 22A544 (2012)] we argued that the Born-Oppenheimer approximation could not be based on an exact transformation of the molecular Schr\"{o}dinger equation. In this Comment we suggest that the fundamental reason for the approximate nature of the Born-Oppenheimer model is the lack of a complete set of functions for the electronic space, and the need to describe the continuous spectrum using spectral projection.Comment: 2 page

On the Quantum Theory of Molecules

Transition state theory was introduced in the 1930s to account for chemical reactions. Central to this theory is the idea of a potential energy surface (PES). It was assumed that such a surface could be constructed using eigensolutions of the Schr\"{o}dinger equation for the molecular (Coulomb) Hamiltonian but at that time such calculations were not possible. Nowadays quantum mechanical ab-initio electronic structure calculations are routine and from their results PESs can be constructed which are believed to approximate those assumed derivable from the eigensolutions. It is argued here that this belief is unfounded. It is suggested that the potential energy surface construction is more appropriately regarded as a legitimate and effective modification of quantum mechanics for chemical purpose

SeqCode: a nomenclatural code for prokaryotes described from sequence data

Most prokaryotes are not available as pure cultures and therefore ineligible for naming under the rules and recommendations of the International Code of Nomenclature of Prokaryotes (ICNP). Here we summarize the development of the SeqCode, a code of nomenclature under which genome sequences serve as nomenclatural types. This code enables valid publication of names of prokaryotes based upon isolate genome, metagenome-assembled genome or single-amplified genome sequences. Otherwise, it is similar to the ICNP with regard to the formation of names and rules of priority. It operates through the SeqCode Registry (https://seqco.de/), a registration portal through which names and nomenclatural types are registered, validated and linked to metadata. We describe the two paths currently available within SeqCode to register and validate names, including Candidatus names, and provide examples for both. Recommendations on minimal standards for DNA sequences are provided. Thus, the SeqCode provides a reproducible and objective framework for the nomenclature of all prokaryotes regardless of cultivability and facilitates communication across microbiological disciplines.Funding was provided by the US National Science Foundation (DEB 1841658, DEB 1557042 and EAR 1516680) to B.H., A.-L.R. and A.M.; the US National Institute of General Medical Sciences (GM103440) from the National Institutes of Health to B.H.; the Spanish Ministry of Science, Innovation and Universities (PGC2018-096956-B-C41 and PID2021-126114NB-C42) to R.R.; the Australian Research Council (FL150100038) to P.H.; the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation, SFB 1439/1 2021—426547801) and European Regional Development Funds (FEDER) to A.P.; and the International Society for Microbial Ecology (ISME) to all authors

Development of the SeqCode: A proposed nomenclatural code for uncultivated prokaryotes with DNA sequences as type

Over the last fifteen years, genomics has become fully integrated into prokaryotic systematics. The genomes of most type strains have been sequenced, genome sequence similarity is widely used for delineation of species, and phylogenomic methods are commonly used for classification of higher taxonomic ranks. Additionally, environmental genomics has revealed a vast diversity of as-yet-uncultivated taxa. In response to these developments, a new code of nomenclature, the Code of Nomenclature of Prokaryotes Described from Sequence Data (SeqCode), has been developed over the last two years to allow naming of Archaea and Bacteria using DNA sequences as the nomenclatural types. The SeqCode also allows naming of cultured organisms, including fastidious prokaryotes that cannot be deposited into culture collections. Several simplifications relative to the International Code of Nomenclature of Prokaryotes (ICNP) are implemented to make nomenclature more accessible, easier to apply and more readily communicated. By simplifying nomenclature with the goal of a unified classification, inclusive of both cultured and uncultured taxa, the SeqCode will facilitate the naming of taxa in every biome on Earth, encourage the isolation and characterization of as-yet-uncultivated taxa, and promote synergies between the ecological, environmental, physiological, biochemical, and molecular biological disciplines to more fully describe prokaryotes.Funding was provided by the US National Science Foundation (DEB 1841658 and EAR 1516680), the US National Institute of General Medical Sciences (P20 GM103440) from the National Institutes of Health, the Spanish Ministry of Science, Innovation and Universities (PID2021-126114NB-C42), the Australian Research Council (FL150100038), the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation, SFB 1439/1 2021 – 426547801) also supported with European Regional Development Funds (FEDER), and the International Society for Microbial Ecology (ISME

A genome-wide scan for common alleles affecting risk for autism

Although autism spectrum disorders (ASDs) have a substantial genetic basis, most of the known genetic risk has been traced to rare variants, principally copy number variants (CNVs). To identify common risk variation, the Autism Genome Project (AGP) Consortium genotyped 1558 rigorously defined ASD families for 1 million single-nucleotide polymorphisms (SNPs) and analyzed these SNP genotypes for association with ASD. In one of four primary association analyses, the association signal for marker rs4141463, located within MACROD2, crossed the genome-wide association significance threshold of P < 5 × 10−8. When a smaller replication sample was analyzed, the risk allele at rs4141463 was again over-transmitted; yet, consistent with the winner's curse, its effect size in the replication sample was much smaller; and, for the combined samples, the association signal barely fell below the P < 5 × 10−8 threshold. Exploratory analyses of phenotypic subtypes yielded no significant associations after correction for multiple testing. They did, however, yield strong signals within several genes, KIAA0564, PLD5, POU6F2, ST8SIA2 and TAF1C

Development of the SeqCode: A proposed nomenclatural code for uncultivated prokaryotes with DNA sequences as type

Over the last fifteen years, genomics has become fully integrated into prokaryotic systematics. The genomes of most type strains have been sequenced, genome sequence similarity is widely used for delineation of species, and phylogenomic methods are commonly used for classification of higher taxonomic ranks. Additionally, environmental genomics has revealed a vast diversity of as-yet-uncultivated taxa. In response to these developments, a new code of nomenclature, the Code of Nomenclature of Prokaryotes Described from Sequence Data (SeqCode), has been developed over the last two years to allow naming of Archaea and Bacteria using DNA sequences as the nomenclatural types. The SeqCode also allows naming of cultured organisms, including fastidious prokaryotes that cannot be deposited into culture collections. Several simplifications relative to the International Code of Nomenclature of Prokaryotes (ICNP) are implemented to make nomenclature more accessible, easier to apply and more readily communicated. By simplifying nomenclature with the goal of a unified classification, inclusive of both cultured and uncultured taxa, the SeqCode will facilitate the naming of taxa in every biome on Earth, encourage the isolation and characterization of as-yet-uncultivated taxa, and promote synergies between the ecological, environmental, physiological, biochemical, and molecular biological disciplines to more fully describe prokaryotes

SeqCode: a nomenclatural code for prokaryotes described from sequence data

Most prokaryotes are not available as pure cultures and therefore ineligible for naming under the rules and recommendations of the International Code of Nomenclature of Prokaryotes (ICNP). Here we summarize the development of the SeqCode, a code of nomenclature under which genome sequences serve as nomenclatural types. This code enables valid publication of names of prokaryotes based upon isolate genome, metagenome-assembled genome or single-amplified genome sequences. Otherwise, it is similar to the ICNP with regard to the formation of names and rules of priority. It operates through the SeqCode Registry (https://seqco.de/), a registration portal through which names and nomenclatural types are registered, validated and linked to metadata. We describe the two paths currently available within SeqCode to register and validate names, including Candidatus names, and provide examples for both. Recommendations on minimal standards for DNA sequences are provided. Thus, the SeqCode provides a reproducible and objective framework for the nomenclature of all prokaryotes regardless of cultivability and facilitates communication across microbiological disciplines

Multiple Recurrent De Novo CNVs, Including Duplications of the 7q11.23 Williams Syndrome Region, Are Strongly Associated with Autism

SummaryWe have undertaken a genome-wide analysis of rare copy-number variation (CNV) in 1124 autism spectrum disorder (ASD) families, each comprised of a single proband, unaffected parents, and, in most kindreds, an unaffected sibling. We find significant association of ASD with de novo duplications of 7q11.23, where the reciprocal deletion causes Williams-Beuren syndrome, characterized by a highly social personality. We identify rare recurrent de novo CNVs at five additional regions, including 16p13.2 (encompassing genes USP7 and C16orf72) and Cadherin 13, and implement a rigorous approach to evaluating the statistical significance of these observations. Overall, large de novo CNVs, particularly those encompassing multiple genes, confer substantial risks (OR = 5.6; CI = 2.6–12.0, p = 2.4 × 10-7). We estimate there are 130–234 ASD-related CNV regions in the human genome and present compelling evidence, based on cumulative data, for association of rare de novo events at 7q11.23, 15q11.2-13.1, 16p11.2, and Neurexin 1