anisiraj/SmolLM3-3B-compchem-sft-lora
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Ab initio quantum chemistry methods are a class of computational chemistry techniques based on quantum chemistry that aim to solve the electronic Schrödinger equation. Ab initio means "from first principles" or "from the beginning", meaning using only physical constants and the positions and number of electrons in the ... |
The ability to run these calculations has enabled theoretical chemists to solve a range of problems and their importance is highlighted by the awarding of the 1998 Nobel prize to John Pople and Walter Kohn. The term ab initio was first used in quantum chemistry by Robert Parr and coworkers, including David Craig in a s... |
== Accuracy and scaling == |
Ab initio electronic structure methods aim to calculate the many-electron function which is the solution of the non-relativistic electronic Schrödinger equation (in the Born–Oppenheimer approximation). The many-electron function is generally a linear combination of many simpler electron functions with the dominant func... |
One needs to consider the computational cost of ab initio methods when determining whether they are appropriate for the problem at hand. When compared to much less accurate approaches, such as molecular mechanics, ab initio methods often take larger amounts of computer time, memory, and disk space, though, with modern ... |
=== Linear scaling approaches === |
The problem of computational expense can be alleviated through simplification schemes. In the density fitting scheme, the four-index integrals used to describe the interaction between electron pairs are reduced to simpler two- or three-index integrals, by treating the charge densities they contain in a simplified way. ... |
== Classes of methods == |
The most popular classes of ab initio electronic structure methods: |
=== Hartree–Fock methods === |
Hartree–Fock – Approximation method in quantum physicsPages displaying short descriptions of redirect targets (HF) |
Restricted open-shell Hartree–Fock (ROHF) |
Unrestricted Hartree–Fock – Method for calculating open-shell systems (UHF) |
=== Post-Hartree–Fock methods === |
Møller–Plesset perturbation theory – Method in ab initio Quantum Chemistry (MPn) |
Configuration interaction – Concept in computational chemistry (CI) |
Coupled cluster – Method for approximating many-body systems (CC) |
Quadratic configuration interaction (QCI) |
Quantum chemistry composite methods – Combining multiple simulation methods |
Sign learning kink-based (SiLK) quantum Monte Carlo |
=== Multi-reference methods === |
Multi-configurational self-consistent field – Method in quantum chemistry (MCSCF including CASSCF and RASSCF) |
Multi-reference configuration interaction (MRCI) |
n-electron valence state perturbation theory (NEVPT) |
Complete active space perturbation theory (CASPTn) |
State universal multi-reference coupled-cluster theory (SUMR-CC) |
== Methods in detail == |
=== Hartree–Fock and post-Hartree–Fock methods === |
The simplest type of ab initio electronic structure calculation is the Hartree–Fock (HF) scheme, in which the instantaneous Coulombic electron-electron repulsion is not specifically taken into account. Only its average effect (mean field) is included in the calculation. This is a variational procedure; therefore, the o... |
Example |
Is the bonding situation in disilyne Si2H2 the same as in acetylene (C2H2)? |
A series of ab initio studies of Si2H2 is an example of how ab initio computational chemistry can predict new structures that are subsequently confirmed by experiment. They go back over 20 years, and most of the main conclusions were reached by 1995. The methods used were mostly post-Hartree–Fock, particularly configur... |
Al2H2 and Ga2H2 have exactly the same isomers, in spite of having two electrons less than the Group 14 molecules. |
The only difference is that the four-membered ring ground state is planar and not bent. The cis-mono-bridged and vinylidene-like isomers are present. Experimental work on these molecules is not easy, but matrix isolation spectroscopy of the products of the reaction of hydrogen atoms and silicon and aluminium surfaces h... |
=== Valence bond methods === |
Valence bond (VB) methods are generally ab initio although some semi-empirical versions have been proposed. Current VB approaches are: |
Generalized valence bond – Quantum chemistry method extending valence bond theory (GVB) |
Modern valence bond theory (MVBT) |
=== Quantum Monte Carlo methods === |
A method that avoids making the variational overestimation of HF in the first place is Quantum Monte Carlo (QMC), in its variational, diffusion, and Green's function forms. These methods work with an explicitly correlated wave function and evaluate integrals numerically using a Monte Carlo integration. Such calculation... |
Sign Learning Kink-based (SiLK) Quantum Monte Carlo (website): The Sign Learning Kink (SiLK) based Quantum Monte Carlo (QMC) method is based on Feynman's path integral formulation of quantum mechanics, and can reduce the minus sign problem when calculating energies in atomic and molecular systems. |
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 eff... |
The use of basis sets is equivalent to the use of an approximate resolution of the identity: the atomic 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 quantum chemistry community; plane waves which are typically used within the solid state community, or real-space approaches. Several types of atomic orbitals can b... |
== Introduction == |
In modern computational chemistry, quantum chemical calculations are performed using a finite set of basis functions. When the finite basis is expanded towards an (infinite) complete set of functions, calculations using such a basis set are said to approach the complete basis set (CBS) limit. In this context, basis fun... |
Within the basis set, the wavefunction is represented as a vector, the components of which correspond to coefficients of the basis functions in the linear expansion. In such a basis, one-electron operators correspond to matrices (a.k.a. rank two tensors), whereas two-electron operators are rank four tensors. |
When molecular calculations are performed, it is common to use a basis composed of atomic orbitals, centered at each nucleus within the molecule (linear combination of atomic orbitals ansatz). The physically best motivated basis set are Slater-type orbitals (STOs), |
which are solutions to the Schrödinger equation of hydrogen-like atoms, and decay exponentially far away from the nucleus. It can be shown that the molecular orbitals of Hartree–Fock and density-functional theory also exhibit exponential decay. Furthermore, S-type STOs also satisfy Kato's cusp condition at the nucleus,... |
Unfortunately, calculating integrals with STOs is computationally difficult and it was later realized by Frank Boys that STOs could be approximated as linear combinations of Gaussian-type orbitals (GTOs) instead. Because the product of two GTOs can be written as a linear combination of GTOs, integrals with Gaussian bas... |
Dozens of Gaussian-type orbital basis sets have been published in the literature. Basis sets typically come in hierarchies of increasing size, giving a controlled way to obtain more accurate solutions, however at a higher cost. |
The smallest basis sets are called minimal basis sets. A minimal basis set is one in which, on each atom in the molecule, a single basis function is used for each orbital in a Hartree–Fock calculation on the free atom. For atoms such as lithium, basis functions of p type are also added to the basis functions that corre... |
A minimal basis set may already be exact for the gas-phase atom at the self-consistent field level of theory. In the next level, additional functions are added to describe polarization of the electron density of the atom in molecules. These are called polarization functions. For example, while the minimal basis set for... |
Another common addition to basis sets is the addition of diffuse functions. These are extended Gaussian basis functions with a small exponent, which give flexibility to the "tail" portion of the atomic orbitals, far away from the nucleus. Diffuse basis functions are important for describing anions or dipole moments, bu... |
== STO hierarchy == |
The most common minimal basis set is STO-nG, where n is an integer. The STO-nG basis sets are derived from a minimal Slater-type orbital basis set, with n representing the number of Gaussian primitive functions used to represent each Slater-type orbital. Minimal basis sets typically give rough results that are insuffic... |
STO-3G |
STO-4G |
STO-6G |
STO-3G* – Polarized version of STO-3G |
There are several other minimum basis sets that have been used such as the MidiX basis sets. |
== Split-valence basis sets == |
During most molecular bonding, it is the valence electrons which principally take part in the bonding. In recognition of this fact, it is common to represent valence orbitals by more than one basis function (each of which can in turn be composed of a fixed linear combination of primitive Gaussian functions). Basis sets... |
=== Pople basis sets === |
The notation for the split-valence basis sets arising from the group of John Pople is typically X-YZg. In this case, X represents the number of primitive Gaussians comprising each core atomic orbital basis function. The Y and Z indicate that the valence orbitals are composed of two basis functions each, the first one c... |
Polarization functions are denoted by two different notations. The original Pople notation added "*" to indicate that all "heavy" atoms (everything but H and He) have a small set of polarization functions added to the basis (in the case of carbon, a set of 3d orbital functions). The "**" notation indicates that all "li... |
In all cases, diffuse functions are indicated by either adding a + before the letter G (diffuse functions on heavy atoms only) or ++ (diffuse functions are added to all atoms). |
Here is a list of commonly used split-valence basis sets of this type: |
3-21G |
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