## I.D.1. (VII.C.5.) |

The following glossary is adapted from: K. K. Irikura In " Computational Thermochemistry: Prediction and Estimation of Molecular Thermodynamics" (ACS Symposium Series 677); Irikura, K. K., Frurip, D. J. Eds.; American Chemical Society: Washington, DC 1998.

Glossary of Common Terms and Abbreviations in Quantum Chemistry

Physical and Chemical Properties Division, National Institute of Standards and Technology, Gaithersburg, MD 20899

The literature of quantum chemistry, covering both molecular orbital theory and density functional theory, is cluttered with abbreviations, acronyms, and jargon. Some of the more common terminology is explained in this glossary.

An extensive list of acronyms has been published recently (1),
and a major reference work is currently in preparation. The list below
is adapted from one that was developed for a brief course within the Physical
and Chemical Properties Division at NIST (2).

3-21G | A VDZ basis set. See also 6-31G. |

3-21G* | The asterisk indicates that a set of polarizing d-functions (6D) is included to supplement the 3-21G basis, but only on second-row and heavier atoms (beyond neon). Also denoted 3-21G(*) or 3-21G(d). |

5D | Indicates that five functions are used in each d-set. |

6D | Indicates that six (cartesian) functions are used in each d-set. This
includes the s-like combination (x^{2} + y^{2} + z^{2}). |

6-31G | A VDZ basis set from the Pople school. Very popular, often used with a set of heavy-atom polarization functions (see 6-31G*). The "6" indicates that each core basis function is built using six primitives. The "3" indicates that the inner valence basis functions are each built using three primitives. The "1" indicates that the outer valence basis functions are each built using a single uncontracted primitive. The "G" stands for "Gaussian", indicating the type of primitive function. (Recently-developed basis sets don't include the "G" or its equivalent since they are essentially all based upon Gaussian functions.) |

6-311G | A popular VTZ basis set similar to the small 6-31G set. Usually supplemented with polarization functions. Built like 6-31G but with a third layer of valence functions composed of a single, uncontracted primitive set. Some workers consider this basis to be less flexible than a "real" triple-zeta basis. |

6-311G* | The asterisk indicates that a set of polarization d-functions (5D) has been added to heavy atoms to supplement the 6-311G basis; also denoted 6-311G(d). |

6-311G** | The second asterisk indicates that a set of polarization p-functions has been added to hydrogen; also denoted 6-311G(d,p). |

6-311+G(3df,2p) | In addition to the 6-311G basis, the "+" indicates that diffuse s- and p-functions are added to heavy atoms, the "3df" indicates that three sets of polarization d-functions and one set of polarization f-functions are added to heavy atoms, and the "2p" indicates that two sets of polarization p-functions are added to hydrogen. |

6-31G* | A polarized VDZ basis set from the Pople school. Maybe the most popular basis set in use today. The single asterisk indicates that a set of polarizing d-functions (6D) is included on "heavy" atoms (beyond helium). Also denoted 6-31G(d). |

6-31G** | A polarized VDZ basis set from the Pople school. A set of polarizing d-functions (6D) is included on "heavy" atoms and a set of p-functions on hydrogen. Also denoted 6-31G(d,p). |

6-31+G* | Augmented 6-31G* basis; the single "+" indicates that a set of diffuse s-functions and a set of diffuse p-functions has been added to each heavy atom. Also denoted 6-31+G(d). |

6-31++G* | Augmented 6-31+G* basis; the second "+" indicates that a set of diffuse s-functions has been added to each hydrogen atom. Also denoted 6-31++G(d). |

alpha electron | An electron with spin up. |

ACES II | An ab initio software package that emphasizes coupled-cluster methods (3,4). |

ACPF | Averaged coupled-pair functional. Pretty high level of multi-reference electron correlation, requires skill to use. |

AIM | Atoms-in-molecules. An analysis method based upon the shape of the total electron density; used to define bonds, atoms, etc. (5). Atomic charges computed using this theory are often quite different from those from other analyses (e.g., from Mulliken populations). Such charges are probably the most justifiable theoretically, but meet some resistance because the values obtained may be quite different from those from older theories (6). |

AM1 | Austin model 1. One of the most popular semi-empirical MO theories. |

ANO | Atomic natural orbital. Very large basis sets derived from correlated atomic calculations. More expensive to use than the corresponding correlation consistent basis sets (e.g., cc-pVDZ) but not often significantly more accurate. |

aug-cc-pVDZ | Augmented cc-pVDZ basis (diffuse functions added). |

basis set | The set of mathematical functions (basis functions) used to describe the molecular orbitals. Gaussian functions predominate heavily, but occasional papers use the old "Slater" orbitals or functions, which are exponentials. |

beta electron | An electron with spin down. |

B3LYP | DFT using Becke exchange functional and Lee-Yang-Parr correlation functional, as well as Hartree-Fock exchange. A hybrid method; the parameters were optimized for thermochemistry, but using a different functional and numerical (basis set-free) code (7,8). Very popular. |

BAC-MP4 | Bond-additivity-corrected MP4. A method in which an MP4 energy is corrected using empirical parameters that depend upon the atoms in the molecule, bond distances, and nearest neighbors. Method developed by Carl Melius (Sandia); not well-described in the open literature. |

BD | Brueckner doubles. Very similar to CCSD and QCISD. Although BD only involves doubles, the Brueckner orbitals are those for which the singles contribution is zero. So BSD would be the same thing. |

BFGS | An optimization method often used in geometry optimization (four people with initials B, F, G, S). |

BLYP | DFT using the Becke exchange functional and the Lee-Yang-Parr correlation functional. |

bohr | One atomic unit of distance, equal to 0.5292 Å. |

bond function | Special basis functions that are centered on a bond midpoint (for example) rather that on an atomic nucleus. Not commonly used. |

BP | Becke-Perdew. A non-local DFT method employing the Becke exchange and Perdew correlation functionals. |

BSSE | Basis-set superposition error. An insidious artifact traceable to the fact that one can seldom afford to use a really big basis set. It causes an extra decrease in energy (i.e. more negative energy, greater stability) when two systems (atoms or molecules) are brought together. The energy of one fragment is lowered because its orbitals can use the basis functions on the other fragment, even if the actual electrons and nuclei on the other fragment are not included in the calculation. With a complete basis set, there is no BSSE because the other fragment's basis functions are superfluous. BSSE is usually ignored in thermochemical calculations, except for studies of weak, non-bonded interactions. See "counterpoise." |

CADPAC | Another ab initio package; acronym stands for "Cambridge analytical derivatives package." |

cartesian coordinates | The positions in space of the atoms in a molecule listed as triples (x, y, z). |

CASPT2 | Complete active space, second-order perturbation theory. This is one formulation of MP2 theory using a CASSCF reference instead of a HF reference. A high-level multireference theory. |

CASSCF | Complete active space self-consistent field. A type of MCSCF calculation in which the configurations are chosen to be all those obtainable (i.e., full CI ) using a specified number of electrons and a specified set of orbitals. The set of orbitals is called the "active space," and the specified electrons are called "active." In many cases, it requires experience and skill to select the active space correctly. |

CBS | Complete basis set. Indicates that some method of basis set extrapolation was applied in an attempt to determine the result that would have been obtained using an infinitely large basis set. The two major extrapolation methods are (1) repeating the calculation with increasingly large basis sets and making an empirical extrapolation, and (2) using analytical formulas that are correct to second-order. See the chapters by Martin and by Petersson in this book. |

cc-pVDZ | Correlation-consistent polarized valence double-zeta basis set. The smallest in a series of "correlation consistent" basis sets developed by Dunning and coworkers for high-level calculations. It has been observed that properties computed using successively larger basis sets of this series appear to converge exponentially, presumably to the corresponding CBS values. |

cc-pVTZ | Correlation-consistent polarized valence triple-zeta basis set. See cc-pVDZ. |

cc-pV(T+d)Z | Correlation-consistent polarized valence triple-zeta basis set with an additional tight d function on elements with atomic number greater than 12. |

cc-pVQZ | Correlation-consistent polarized valence quadruple-zeta basis set. See cc-pVDZ. |

cc-pV5Z | Correlation-consistent polarized valence quintuple-zeta basis set. See cc-pVDZ. |

CCD | Coupled-cluster, doubles. A theory of electron correlation that is complete to infinite order but only for a subset of possible excitations (doubles, for CCD). See " CI ." |

CCSD | Coupled-cluster, singles and doubles. (See CCD.) |

CCSD(T) | Coupled-cluster, singles and doubles with approximate triples. (See CCD.) Triples contributions are determined perturbatively. CCSD(T) is the cheapest of the usual approximations to full CCSDT, but appears to be the best. The most popular high-level (i.e., lots of electron correlation) method. Size-consistent. Very expensive. |

CCSDT | Coupled-cluster, singles and doubles and triples. (See CCD.) Extra-high level of electron correlation: incredibly expensive, rarely used. |

CEPA | Coupled electron pair approximation. An approximate coupled-cluster-type method. Pretty high level. |

cGTO | Contracted gaussian-type orbital. The usual basis function; it's a
linear combination of gaussian functions with the linear coefficients fixed,
then multiplied by an angular function. So one set of p-functions contains
three cGTO's (p_{x}, p_{y}, and p_{z}), i.e, three
basis functions. See "primitives." |

CI | Configuration interaction. A theory of electron correlation. A large set of Hartree-Fock-type configurations (Slater determinants) is used as a many-electron basis set. The coefficient of each configuration is determined variationally so as to minimize the total energy of this wavefunction. Recovers the "dynamic" electron correlation important in bonding. Reliability and expense depend upon the size of the CI, e.g., CISD was popular before coupled-cluster methods caught on. Ordinary, truncated CI (CIS, CISD, etc.) is not size-consistent, so determining bond energies requires "supermolecule" calculations. |

CID | Configuration interaction, doubles. A CI that only includes those determinants that correspond to double excitations from the reference (which is usually Hartree-Fock). |

CIS | Configuration interaction, singles. (See CID.) The simplest method for calculating electronically excited states; limited to singly-excited states. Contains no electron correlation and has no effect on the ground state (Hartree-Fock) energy. |

CISD | Configuration interaction, singles and doubles. A CI that only includes those determinants that correspond to single or double excitations from the reference (which is usually Hartree-Fock). Declining popularity. |

CNDO | A semi-empirical method ("complete neglect of differential overlap"). |

contraction | Refers to the particular choice of scheme for generating the linear combinations of gaussian functions that constitute a contracted basis set. (See cGTO.) A "generally-contracted" basis set is one in which each primitive is used in many basis functions. A "segmented" basis set, in contrast, is one in which each primitive is used in only one (or maybe two) contracted function. |

correlation effects | The effect upon the quantity of interest attributable to the inclusion of dynamic electron correlation. |

correlation energy | The difference between the Hartree-Fock energy and the FCI energy for a given basis set. Most of this energy is attributable to the correlation among the positions of electrons of opposite spin, caused by their coulombic repulsion. See dynamic and non-dynamic correlation. |

counterpoise | The most common, but still controversial, correction for BSSE. The BSSE is approximated as the energy difference between (1) an isolated fragment and (2) the fragment accompanied by the basis functions, but not the atoms, of its companion fragment(s). |

coupled cluster | In diagrammatic perturbation theory, an excited configuration that is "coupled" to the reference configuration. |

Davidson correction | A correction sometimes made to some types of correlated calculations (esp. CISD and MR-CISD) to estimate higher-order contributions to the energy and correct approximately for size-inconsistency. |

DCI | See CID. In very recent papers, "DCI" may mean "direct" (see) CI . |

DFT | Density-functional theory. Ab initio method not based upon a wavefunction. Instead, the energy is computed as a functional of the electron density. Sometimes called Kohn-Sham theory. The correct functional has not yet been found, but many approximations are in use. |

diffuse | Diffuse basis functions are typically of low angular momentum (unlike polarization functions) but with much smaller exponents, so that they spread more thinly over space. Usually essential for calculations involving negative ions or Rydberg states. |

dihedral angle | The angle between two intersecting planes. In a molecule with atoms A-B-C-D, the dihedral angle (A-B-C-D) is the angle between the planes defined by (A, B, C) and by (B, C, D). By convention, the angle is positive for a right-handed rotation from the first plane to the second, i.e., for a right-handed twist along the sequence A-B-C-D. |

DIIS | Direct inversion in the iterative subspace. An extrapolation procedure used to accelerate the convergence of SCF calculations. |

direct | Indicates that integrals are not pre-computed and then written to disk, but instead are computed as needed. Done to save I/O time during a calculation. |

dynamic correlation | All the correlation energy or correlation effect that is not considered "nondynamic" or "static." |

DZ | Double-zeta. A basis set for which there are twice as many basis functions as are minimally necessary (see "MBS"). "Zeta" (Greek letter ) is the usual name for the exponent that characterizes a Gaussian function. |

DZP | Double-zeta with polarization. DZ with polarization basis functions added. A polarization set generally has an angular momentum one unit higher than the highest valence function. So a polarization set on carbon is a set of d-functions. |

ECP | Effective core potential. The core electrons have been replaced by an effective potential. Saves computational expense. May sacrifice some accuracy, but can include some relativistic effects for heavy elements (see RECP). |

ESP | Electrostatic potential. The electrical potential due to the nuclei and electrons in the molecule, as experienced by a test charge. |

exchange energy | Also called "exchange correlation energy." The energy associated with the correlation among the positions of electrons of like spin. This is included in Hartree-Fock calculations. |

expensive | Requiring large resources: cpu time, memory, and/or disk space. |

FCI | Full configuration interaction. A CI that includes all possible determinants. FCI is the best wavefunction (and provides the lowest variational energy) obtainable using a given basis set. Almost never affordable. |

frozen | Indicates that some orbitals were not included in the treatment. Usually used as "frozen-core," to indicate that the core orbitals were left uncorrelated in a correlated calculation. Sometimes (esp. in some DFT programs) it means that core orbitals were fixed as taken from calculations on isolated atoms. |

G1 | Gaussian-1. A composite method for computing thermochemistry, involving extrapolations and a few parameters (9). Effectively superseded by G2 and G2(MP2). |

G2 | Gaussian-2. A composite method for computing thermochemistry, involving extrapolations and a few parameters (10). Very popular but quite expensive; practical for up to seven "heavy" atoms (i.e., non-hydrogen) on a Cray supercomputer. |

G2(MP2) | Gaussian-2, second-order variant. A composite method for computing thermochemistry, involving extrapolations and a few parameters (11). Less-expensive alternative to G2, of comparable accuracy. |

GAMESS | General Atomic and Molecular Electronic Structure System. A free ab initio software package that emphasizes multi-reference calculations (12). There is also a British program with the same name, distinguished as GAMESS-UK (vs. GAMESS-US). |

Gaussian | A popular package in the ab initio software industry is by Gaussian Inc (13). The name refers to the common use of gaussian functions as basis functions in quantum chemistry. |

gaw | Group additivity method as implemented in the NIST Chemistry Webbook. See http://webbook.nist.gov/chemistry/grp-add/ for a group additivity method that predicts enthalpies of formation and entropies. Group additivity methods assume that a molecule can be broken down into separate parts (groups), each of which contributes additively to the total enthalpy or entropy. For example acetone is composed of two methyl groups (each adds -42.7 kJ/mol) and a carbonyl group (which adds -131 kJ/mol) for an estimated enthalpy of formation of -216.4 kJ/mol. |

generally contracted | See "contraction." |

GGA | See "nonlocal." |

ghost function | A basis function that is not accompanied by an atomic nucleus, usually for counterpoise corrections for BSSE. |

GIAO | Gauge-independent atomic orbitals. A method specially designed for calculation of NMR shifts. Currently used with methods such as HF, MP2, or DFT. Research codes can handle CCSD. |

GTO | Gaussian-type orbital. Basis function consisting of a Gaussian function,
i.e., exp(-r^{2}), multiplied by an angular function. If the angular
function is "cartesian", there are six d-functions, ten f-functions, etc.
(6d, 10f). If the angular function is spherical, there will the usual number
of functions (5d, 7f). |

GVB | Generalized valence bond. A limited type of MCSCF, in which excitations are taken within an electron pair but not between orbitals in different pairs. Dissociation-consistent. If restricted to doubles, is called "perfect pairing" (GVB-PP). If includes both singles and doubles, is called "restricted configuration interaction" (GVB-RCI). |

hartree | One atomic unit of energy, equal to 2625.5 kJ/mol, 627.5 kcal/mol,
27.211 eV, and 219474.6 cm^{-1}. |

heavy atom | An atom beyond helium, i.e., Z > 2. |

Hartree-Fock | Simplest and least expensive ab initio wavefunction. Involves only a single Slater determinant (a single electron configuration). Orbitals that contain electrons are "occupied," those that are vacant are called "virtual." |

HF | Hartree-Fock. In the Gaussian programs, HF denotes RHF for closed-shell molecules and UHF for open-shell. |

HFS | Hartree-Fock Slater. An older DFT method involving only local, Slater-style exchange. Often synonymous with the X alpha method. |

HONDO | An ab initio program package; genealogically related to GAMESS. |

HOMO | Highest occupied molecular orbital. The energy of this orbital approximates the ionization energy of the molecule (Koopmans' theorem). |

HOMO-1 | The second-highest occupied molecular orbital. |

instability | A wavefunction is expressed as a long list of parameters (basis-set expansion) that are adjusted to minimize the total energy. Sometimes the global minimum is not obtained; the local minimum that is obtained may be unstable with respect to various perturbations or liberalization of constraints. Such a wavefunction is said to be unstable. One of the more common instabilities is an RHF to UHF instability, which indicates that the UHF solution (different alpha and beta orbitals) is of lower energy than the RHF solution (identical alpha and beta orbitals) for a closed-shell system. This may be encountered, for example, when a bond is stretched. |

internal coordinates | Bond lengths, bond angles, and dihedral (torsional) angles; sometimes called "natural coordinates." |

IRC | Intrinsic reaction coordinate. An optimized reaction path that is followed downhill, starting from a transition state, to approximate the course (mechanism) of an elementary reaction step. |

isodesmic | Refers to a chemical reaction that conserves types of chemical bond.
Due to better cancellation of systematic errors, energy changes computed
using such reactions are expected to be more accurate than those computed
using reactions that do not conserve bond types. Example: CH_{3}CH_{2}F
+ CH_{4} = CH_{3}CH_{3} + CH_{3}F for computing
the C-F bond strength in fluoroethane. |

isogyric | Refers to a chemical reaction that conserves net spin. Due to better
cancellation of systematic errors, energy changes computed using such reactions
are expected to be more accurate than those computed using reactions that
do not conserve spin. Example: CH_{3}CH_{2}F + H = CH_{3}CH_{2}
+ HF for computing the C-F bond strength in fluoroethane. |

Koopmans | His theorem for approximate ionization energies (see HOMO) and poor electron affinities (see LUMO). |

LDA | see LSDA. |

local | In DFT, a functional that depends only upon the value of the density, f[rho]. This is the simplest and least expensive type of functional. |

LSDA | Local spin-density approximation. A DFT method involving only local functionals (i.e., no dependence upon the gradient of the electron density). In the Gaussian programs "LSDA" is equivalent to the "SVWN" keyword. |

LST | Linear synchronous transit. An interpolative method used to guess a transition state structure given the structures of the products and of the reactants. |

LUMO | Lowest unoccupied molecular orbital. The energy of this orbital is sometimes used to approximate the electron affinity of the molecule, but this usually works badly. |

MBPT | Many-body perturbation theory. Synonymous with MP (Møller-Plesset) perturbation theory. |

MBS | Minimal basis set. Only enough basis functions are supplied to put all the electrons somewhere; the number of basis functions is equal to the number of orbitals. The most common of these is "STO-3G". Qualitative results at best. |

MCPF | Modified coupled-pair functional. Pretty high-level theory. |

MCSCF | Multi-configuration self-consistent field. More than one configuration (Hartree-Fock-type determinant) is used to describe the wavefunction. Both the coefficients of the configurations and the orbital coefficients are optimized. This is a limited type of CI (configuration interaction), with the added feature of orbital optimization. See CASSCF. |

MNDO | A semi-empirical method ("minimal neglect of differential overlap"). |

MO | Molecular orbital. |

MOLCAS | An ab initio software package that emphasizes electron correlation, esp. CASPT2 (14). |

MOLPRO | An ab initio software package that emphasizes electron correlation, esp. very large MRCI (15). |

MOPAC | The most popular package for semiempirical MO calculations (16). |

MP2 | Second-order Møller-Plesset perturbation theory. Standard Rayleigh-Schrödinger perturbation theory taken to second order. The least-expensive traditional method for including electron correlation. For open-shell cases with a UHF reference, MP2 is sometimes denoted "UMP2." |

MP2=fc | Frozen-core MP2 calculation in Gaussian-style notation. (See "Frozen" and "MP2.") |

MP2=fu | MP2=full. |

MP2=full | MP2 calculation in which the core orbitals are active and not frozen. |

MP4 | Fourth-order MBPT. (See MP2.) At the heart of the BAC-MP4 method. |

MRCI | Multi-reference configuration interaction. CI using more that one reference determinant, instead of the usual single Hartree-Fock reference. Among multi-reference theories, MR-CISD (singles and doubles CI) is popular and high-level (but not dissociation consistent). |

Mulliken population | A procedure for assigning net atomic charges within a molecule. It includes an arbitrary choice involving overlap populations, and more seriously is very sensitive (values varying by more than 100%) to the choice of basis set. Still used mostly for convenience, since it has no cost and is included in all ab initio program packages. Superseded by NPA and AIM methods of population analysis. |

NO | Natural orbital. |

NBO | Natural bond order. See NPA. |

natural orbital | The natural orbitals are those for which the first-order density matrix is diagonal; each will contain some non-integer number of electrons between 0 and 2. Usually discussed in the context of a correlated calculation. RHF calculations give molecular orbitals that are also natural orbitals. The NOs are the orbitals for which the CI expansion converges fastest. |

nondynamic correlation | Also called "static" correlation. The part of the correlation that
is ascribed to the "multireference" nature of the problem at hand, i.e.,
to the qualitative failure of Hartree-Fock theory to describe the system.
The best-known stable molecule with important nondynamic correlation is
singlet methylene, CH_{2} (ã ^{1}A_{1}),
for which two configurations are important: (a_{1})^{2}(b_{1})^{0}
and (a_{1})^{0}(b_{1})^{2}. In many cases, the distinction between
nondynamic and dynamic correlation is rather arbitrary. When nondynamic
correlation is important, single-reference theories may be unreliable. |

nonlocal | In DFT, indicates that a functional of the density gradient (i.e., f[grad rho]) is included in addition to a local functional. The most popular NL exchange functional is that by Becke. Popular NL correlation functionals are those by Lee/Yang/Parr and by Perdew. A functional that includes nonlocal terms is sometimes called "gradient-corrected" or a "GGA," which stands for "generalized-gradient approximation." |

NPA | Natural population analysis. Considered better than Mulliken populations for assigning atomic charges; results are fairly independent of the basis set. Theory based upon chemical concepts of bonds, lone pairs, etc. |

orbital | Usually an eigenfunction of a one-electron hamiltonian, e.g., from Hartree-Fock theory. A spin orbital has an explicit spin and a spatial orbital does not. Orbitals are probably the most useful concept from quantum chemistry: one can think of an atom or molecule as having a set of orbitals that are filled with electrons (occupied) or vacant (unoccupied or "virtual"). |

PES | Potential energy surface. The 3N-6 (or 3N-5, for linear molecules) dimensional function that indicates how the molecule's energy depends upon its geometry. (Not to be confused with experimental photoelectron spectroscopy.) |

PM3 | A semi-empirical method. |

PMP2 | Spin-projected MP2 energy. Analog of PUHF, but for UMP2 energy instead of UHF energy. Likewise, the PMP3 and PMP4 energies are the UMP3 and UMP4 analogs. |

polarized | A "polarized" basis set includes functions that are of higher angular momentum than is minimally required. For example, carbon atoms have 1s, 2s, and 2p orbitals, so a polarized basis set would also include at least a set of d-functions. The added functions are often called "polarization functions." Polarization functions help to account for the fact that atoms within molecules are not spherical. |

primitives | Also called "primitive functions." The individual gaussian functions that are summed to produce a contracted basis function (cGTO). So a set of p-functions is three basis functions, but may be many primitives (3n, where there are n primitives in the cGTO). |

pseudopotential | see ECP. |

PUHF | Spin-projected UHF energy. An approximation intended to provide the energy that would result from a UHF calculation if it did not suffer spin-contamination. The PUHF energy is usually lower than the UHF energy because the contributions of higher-multiplicity states, which usually have high energies, have been (approximately) subtracted. |

QCI | Quadratic configuration interaction. A CI method to which terms have been added to confer size-consistency. May also be considered to be an approximation to coupled-cluster theory. |

QCISD | Quadratic configuration interaction, singles and doubles. (See QCI.) |

QCISD(T) | QCISD with a correction for triples. This method is at the core of the popular G2 theory. Usually gives similar results as CCSD(T), of which it is a truncation. |

RECP | Relativistic effective core potential. The core electrons have been replaced by an effective potential that is based upon relativistic quantum calculations of the free atoms. Saves cost because of fewer explicit electrons and also includes some relativistic effects, especially the contraction of core s- and p-orbitals. |

redundant internal coordinates | Internal coordinates that overdetermine the molecular geometry, i.e., are more numerous than 3N-6 for non-linear molecules or 3N-5 for linear molecules. |

reference | As in "single-reference" or "multi-reference," refers to the number of configurations (or really Slater determinants) in the 0th-order description of the wavefunction. Most methods that don't begin with "MR," "MC," or "CAS" are single-reference methods. |

RHF | Spin-restricted Hartree-Fock. Closed-shell singlet with two electrons in each occupied orbital. |

ROHF | Spin-restricted open-shell Hartree-Fock. For open-shell molecules. Except for the odd electron(s), there are two electrons in each occupied orbital. (See UHF.) |

SCF | Self-consistent field. The orbitals (i.e., the coefficients of the atomic basis functions in each molecular orbital) are adjusted until they are optimal in the mean electric field that they imply. Implicit for Hartree-Fock calculations. Sometimes the term "SCF" is used interchangeably with "HF," but it also applies to most DFT calculations and to all MCSCF calculations. |

SCRF | Self-consistent reaction field. A continuum method for treating solvation. The simplest formulation involves placing the molecule in a spherical hole in a polarizable (dielectric) continuum. The molecule polarizes the solvent, which in turn affects the electron distribution in the molecule; this is iterated to self-consistency. |

scaling | Multiplying calculated results by an empirical fudge factor in the hope of getting a more accurate prediction. Very often done for vibrational frequencies computed at the HF/6-31G* level, for which the accepted scaling factor is 0.893 (17). |

SDCI | See CISD. |

segmented | See "contraction." |

semi-empirical | An approximate version of Hartree-Fock theory in which the more computationally expensive integrals are replaced by adjustable parameters, which are determined by fitting experimental atomic and molecular data. Different choices of parameterization lead to different specific theories (e.g., MNDO, AM1, PM3). Semiempirical calculations are much faster than ab initio calculations. |

size-consistent | Describes a calculation that gives the same energy for two atoms (or
molecular fragments) separated by a large distance as is obtained from
summing the energies for the atoms (or molecular fragments) computed separately.
So for a size-consistent method, the bond energy in N_{2} is D_{e}
= 2E(N) - E(N_{2}). For a method that is not size-consistent, a
"supermolecule" calculation with a big distance
(e.g., 100 Å) is required:
D_{e} = E(N......N) - E(N_{2}). |

SOMO | Singly-occupied molecular orbital (for radicals). |

spin-contamination | See UHF. |

spin density | The amount of excess alpha (over beta) spin; useful for identifying the location of unpaired electrons in radicals and for interpreting ESR experiments. |

spin-polarized | See UHF. |

spin-unrestricted | See UHF. |

split-valence | Refers to a basis set that is more than minimal (see MBS) for the valence orbitals, i.e., at least VDZ. 3-21G is one example of a split-valence basis. 6-311G might be called a triple-split-valence basis. |

static correlation | See "nondynamic correlation." |

STO | Slater-type orbital. Basis function with an exponential radial function, i.e., exp(- zeta r). Also used to denote a fit to such a function using other functions, such as gaussians. For example, STO-3G is an MBS that uses 3 gaussians to fit an exponential. Exponentials are probably better basis functions than gaussians, but are so much more difficult computationally that they were abandoned by most people a long time ago. |

STO-3G | The most popular MBS (see MBS and STO). |

supermolecule | A system composed of two or more atoms or molecules separated by large distances. See "size-consistent." |

SVWN | Slater exchange functional, Vosko-Wilk-Nusair correlation functional. A local DFT method. |

T1 diagnostic | An indication of how far the usual HF orbitals differ from the Brueckner orbitals. It has been used as an indicator of multi-reference character and therefore of the reliability of coupled cluster calculations (18,19), although this usage has been challenged. |

TDA | Tamm-Dancoff approximation. Synonymous with CIS. |

TZ | Triple-zeta. See "DZ." |

TZ2P | Triple-zeta with two sets of polarization functions. See "DZP." |

TZP | Triple-zeta with polarization. See "DZP." |

UHF | Spin-unrestricted Hartree-Fock. For open-shell molecules. There are separate orbitals for spin-up (alpha) and for spin-down (beta) electrons. UHF wavefunctions are usually not eigenfunctions of spin, and are often contaminated by states of higher spin multiplicity (which usually raises the energy; see PUHF). |

UMP2 | MP2 theory using a UHF reference. Likewise UMP3, UMP4, UCCSD, etc. |

unrestricted | See UHF. |

unstable | See instability. |

virtual | An unoccupied orbital. |

VDZ | Valence double-zeta. A minimal basis is used to describe core electrons, but the valence electrons have twice the minimum number of functions (see "DZ"). |

VTZ | Valence triple-zeta. A minimal basis is used to describe core electrons, but the valence electrons have three times the minimum number of functions (see "DZ"). |

X alpha | X-alpha. A venerable, local DFT method in which the coefficient alpha is taken as an adjustable parameter, usually 0.7. |

Z-matrix | A common format for specifying molecular geometry in terms of internal coordinates. |

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2. Certain commercial materials and equipment are identified in this paper in order to specify procedures completely. In no case does such identification imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that the material or equipment identified is necessarily the best available for the purpose.

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