Electronic correlationElectronic correlation is the interaction between electrons in the electronic structure of a quantum system. The correlation energy is a measure of how much the movement of one electron is influenced by the presence of all other electrons. Within the Hartree–Fock method of quantum chemistry, the antisymmetric wave function is approximated by a single Slater determinant. Exact wave functions, however, cannot generally be expressed as single determinants.
PurinePurine is a heterocyclic aromatic organic compound that consists of two rings (pyrimidine and imidazole) fused together. It is water-soluble. Purine also gives its name to the wider class of molecules, purines, which include substituted purines and their tautomers. They are the most widely occurring nitrogen-containing heterocycles in nature. Purines are found in high concentration in meat and meat products, especially internal organs such as liver and kidney. In general, plant-based diets are low in purines.
NucleobaseNucleobases (nitrogenous bases or simply bases) are nitrogen-containing biological compounds that form nucleosides, which, in turn, are components of nucleotides, with all of these monomers constituting the basic building blocks of nucleic acids. The ability of nucleobases to form base pairs and to stack one upon another leads directly to long-chain helical structures such as ribonucleic acid (RNA) and deoxyribonucleic acid (DNA). Five nucleobases—adenine (A), cytosine (C), guanine (G), thymine (T), and uracil (U)—are called primary or canonical.
AdenineAdenine (ˈædᵻnᵻn) (symbol A or Ade) is a purine nucleobase. It is one of the four nucleobases in the nucleic acids of DNA, the other three being guanine (G), cytosine (C), and thymine (T). Adenine derivatives have various roles in biochemistry including cellular respiration, in the form of both the energy-rich adenosine triphosphate (ATP) and the cofactors nicotinamide adenine dinucleotide (NAD), flavin adenine dinucleotide (FAD) and Coenzyme A. It also has functions in protein synthesis and as a chemical component of DNA and RNA.
PyrimidinePyrimidine (; pɪˈɹɪ.mɪˌdiːn,_paɪˈɹɪ.mɪˌdiːn) is an aromatic, heterocyclic, organic compound similar to pyridine (). One of the three diazines (six-membered heterocyclics with two nitrogen atoms in the ring), it has nitrogen atoms at positions 1 and 3 in the ring. The other diazines are pyrazine (nitrogen atoms at the 1 and 4 positions) and pyridazine (nitrogen atoms at the 1 and 2 positions). In nucleic acids, three types of nucleobases are pyrimidine derivatives: cytosine (C), thymine (T), and uracil (U).
Basis set (chemistry)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 are expanded within the basis set as a linear combination of the basis functions , where the expansion coefficients are given by .
Nucleotide salvageA salvage pathway is a pathway in which a biological product is produced from intermediates in the degradative pathway of its own or a similar substance. The term often refers to nucleotide salvage in particular, in which nucleotides (purine and pyrimidine) are synthesized from intermediates in their degradative pathway. Nucleotide salvage pathways are used to recover bases and nucleosides that are formed during degradation of RNA and DNA. This is important in some organs because some tissues cannot undergo de novo synthesis.
NucleotideNucleotides are organic molecules composed of a nitrogenous base, a pentose sugar and a phosphate. They serve as monomeric units of the nucleic acid polymers – deoxyribonucleic acid (DNA) and ribonucleic acid (RNA), both of which are essential biomolecules within all life-forms on Earth. Nucleotides are obtained in the diet and are also synthesized from common nutrients by the liver. Nucleotides are composed of three subunit molecules: a nucleobase, a five-carbon sugar (ribose or deoxyribose), and a phosphate group consisting of one to three phosphates.
Conical intersectionIn quantum chemistry, a conical intersection of two or more potential energy surfaces is the set of molecular geometry points where the potential energy surfaces are degenerate (intersect) and the non-adiabatic couplings between these states are non-vanishing. In the vicinity of conical intersections, the Born–Oppenheimer approximation breaks down and the coupling between electronic and nuclear motion becomes important, allowing non-adiabatic processes to take place.
Nucleic acidNucleic acids are biopolymers, macromolecules, essential to all known forms of life. They are composed of nucleotides, which are the monomer components: a 5-carbon sugar, a phosphate group and a nitrogenous base. The two main classes of nucleic acids are deoxyribonucleic acid (DNA) and ribonucleic acid (RNA). If the sugar is ribose, the polymer is RNA; if the sugar is deoxyribose, a version of ribose, the polymer is DNA. Nucleic acids are chemical compounds that are found in nature.
RNA worldThe RNA world is a hypothetical stage in the evolutionary history of life on Earth, in which self-replicating RNA molecules proliferated before the evolution of DNA and proteins. The term also refers to the hypothesis that posits the existence of this stage. Alexander Rich first proposed the concept of the RNA world in 1962, and Walter Gilbert coined the term in 1986. Alternative chemical paths to life have been proposed, and RNA-based life may not have been the first life to exist.
Outer spaceOuter space, commonly referred to simply as space, is the expanse that exists beyond Earth and its atmosphere and between celestial bodies. Outer space is not completely empty; it is a near-perfect vacuum containing a low density of particles, predominantly a plasma of hydrogen and helium as well as electromagnetic radiation, magnetic fields, neutrinos, dust, and cosmic rays. The baseline temperature of outer space, as set by the background radiation from the Big Bang, is .
DNADeoxyribonucleic acid (diːˈɒksᵻˌraɪboʊnjuːˌkliːᵻk,_-ˌkleɪ-; DNA) is a polymer composed of two polynucleotide chains that coil around each other to form a double helix. The polymer carries genetic instructions for the development, functioning, growth and reproduction of all known organisms and many viruses. DNA and ribonucleic acid (RNA) are nucleic acids. Alongside proteins, lipids and complex carbohydrates (polysaccharides), nucleic acids are one of the four major types of macromolecules that are essential for all known forms of life.
Multi-configurational self-consistent fieldMulti-configurational self-consistent field (MCSCF) is a method in quantum chemistry used to generate qualitatively correct reference states of molecules in cases where Hartree–Fock and density functional theory are not adequate (e.g., for molecular ground states which are quasi-degenerate with low-lying excited states or in bond-breaking situations). It uses a linear combination of configuration state functions (CSF), or configuration determinants, to approximate the exact electronic wavefunction of an atom or molecule.
Gröbner basisIn mathematics, and more specifically in computer algebra, computational algebraic geometry, and computational commutative algebra, a Gröbner basis is a particular kind of generating set of an ideal in a polynomial ring K[x1, ..., xn] over a field K. A Gröbner basis allows many important properties of the ideal and the associated algebraic variety to be deduced easily, such as the dimension and the number of zeros when it is finite.
Basis (linear algebra)In mathematics, a set B of vectors in a vector space V is called a basis (: bases) if every element of V may be written in a unique way as a finite linear combination of elements of B. The coefficients of this linear combination are referred to as components or coordinates of the vector with respect to B. The elements of a basis are called . Equivalently, a set B is a basis if its elements are linearly independent and every element of V is a linear combination of elements of B.
Dynamical mean-field theoryDynamical mean-field theory (DMFT) is a method to determine the electronic structure of strongly correlated materials. In such materials, the approximation of independent electrons, which is used in density functional theory and usual band structure calculations, breaks down. Dynamical mean-field theory, a non-perturbative treatment of local interactions between electrons, bridges the gap between the nearly free electron gas limit and the atomic limit of condensed-matter physics.
Nucleic acid sequenceA nucleic acid sequence is a succession of bases within the nucleotides forming alleles within a DNA (using GACT) or RNA (GACU) molecule. This succession is denoted by a series of a set of five different letters that indicate the order of the nucleotides. By convention, sequences are usually presented from the 5' end to the 3' end. For DNA, with its double helix, there are two possible directions for the notated sequence; of these two, the sense strand is used.
Space habitatA space habitat (also called a space settlement, space colony, spacestead, space city, orbital habitat, orbital settlement, orbital colony, orbital stead or orbital city) is a more advanced form of living quarters than a space station or habitation module, in that it is intended as a permanent settlement or green habitat rather than as a simple way-station or other specialized facility. No space habitat has been constructed yet, but many design concepts, with varying degrees of realism, have come both from engineers and from science-fiction authors.
Base pairA base pair (bp) is a fundamental unit of double-stranded nucleic acids consisting of two nucleobases bound to each other by hydrogen bonds. They form the building blocks of the DNA double helix and contribute to the folded structure of both DNA and RNA. Dictated by specific hydrogen bonding patterns, "Watson–Crick" (or "Watson–Crick–Franklin") base pairs (guanine–cytosine and adenine–thymine) allow the DNA helix to maintain a regular helical structure that is subtly dependent on its nucleotide sequence.
