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Correlative methods

Correlative methods have long been used as a way of dealing with the complexity of various petroleum fractions, including naphtha. Relatively easy to measure physical properties such as density (or specific gravity) (ASTM D-2935 ASTM D-3505, ASTM D-4052) are also required. Viscosity (ASTM D-88, ASTM D-445, ASTM D-2161, IP 71), density (ASTM D-287, ASTM D-891, ASTM D-941, ASTM D-1217, ASTM D-1298, ASTM D-1555, ASTM D-1657, ASTM D-2935, ASTM D-4052, ASTM D-5002, IP 160, [Pg.96]

Refractive Index kd Specific Gravity 60°/60°F Viscosity, cSt Molecular Weight [Pg.97]

IP 235, IP 365), and refractive index (ASTM D-1218) have been correlated to hydrocarbon composition (Tables 4.3 and 4.4). [Pg.97]


A very important difference between H2 and molecular orbital calculations is electron correlation. Election correlation is the term used to describe interactions between elections in the same molecule. In the hydrogen molecule ion, there is only one election, so there can be no election correlation. The designators given to the calculations in Table 10-1 indicate first an electron correlation method and second a basis set, for example, MP2/6-31 G(d,p) designates a Moeller-Plesset electron coiTclation extension beyond the Hartiee-Fock limit canied out with a 6-31G(d,p) basis set. [Pg.312]

Each of these tools has advantages and limitations. Ab initio methods involve intensive computation and therefore tend to be limited, for practical reasons of computer time, to smaller atoms, molecules, radicals, and ions. Their CPU time needs usually vary with basis set size (M) as at least M correlated methods require time proportional to at least M because they involve transformation of the atomic-orbital-based two-electron integrals to the molecular orbital basis. As computers continue to advance in power and memory size, and as theoretical methods and algorithms continue to improve, ab initio techniques will be applied to larger and more complex species. When dealing with systems in which qualitatively new electronic environments and/or new bonding types arise, or excited electronic states that are unusual, ab initio methods are essential. Semi-empirical or empirical methods would be of little use on systems whose electronic properties have not been included in the data base used to construct the parameters of such models. [Pg.519]

The disadvantage of ah initio methods is that they are expensive. These methods often take enormous amounts of computer CPU time, memory, and disk space. The HF method scales as N, where N is the number of basis functions. This means that a calculation twice as big takes 16 times as long (2" ) to complete. Correlated calculations often scale much worse than this. In practice, extremely accurate solutions are only obtainable when the molecule contains a dozen electrons or less. However, results with an accuracy rivaling that of many experimental techniques can be obtained for moderate-size organic molecules. The minimally correlated methods, such as MP2 and GVB, are often used when correlation is important to the description of large molecules. [Pg.28]

If spin contamination is small, continue to use unrestricted methods, preferably with spin-annihilated wave functions and spin projected energies. Do not use spin projection with DFT methods. When the amount of spin contamination is more significant, use restricted open-shell methods. If all else fails, use highly correlated methods. [Pg.230]

Time-dependent calculations with highly correlated methods... [Pg.259]

Correlation methods discussed include basic mathematical and numerical techniques, and approaches based on reference substances, empirical equations, nomographs, group contributions, linear solvation energy relationships, molecular connectivity indexes, and graph theory. Chemical data correlation foundations in classical, molecular, and statistical thermodynamics are introduced. [Pg.232]

Correlation Methods Vapor pressure is correlated as a function of temperature by numerous methods mainly derived from the Clapeyron equation discussed in the section on enthalpy of vaporization. The classic simple equation used for correlation of low to moderate vapor pressures is the Antoine S equation (2-27). [Pg.389]

Correlation Methods Vapor densities are not correlated as functions of temperature alone, as pressure and temperature are both important. At high temperatures and very low pressures, the ideal gas law can be applied whde at moderate temperature and low pressure, vapor density is usually correlated by the virial equation. Both methods will be discussed later. [Pg.399]

Correlation Methods This section briefly discusses methods for correlating viscosities as a function of temperature and presents the most common accurate methods for prediction of vapor and hqiiid viscosity. [Pg.406]

The Operator Action Tree (OAT) is a time reliability correlation method (NUREG/ CR-3010). specifically designed to estimate HEPs for actions requiring decision making on the part of the plant operator. It employs two steps (1) the development of an operator action tree which reflects the specific actions that may be taken by an operator faced with a particular decision, and (2) a time... [Pg.177]

In the gas correlation method, the measurement and reference signals are obtained from the same wavelength band. The temperature changes in the light source and other wavelength-related changes do not disturb the measurement. [Pg.1297]

A variety of theoretical methods have been developed which include some effects of electron correlation. Traditionally, such methods are referred to as post-SCF methods because they add correlation corrections to the basic Hartree-Fock model. As of this writing, there are many correlation methods available in Gaussian, including the following ... [Pg.114]

Prior to the widespread usage of methods based on Density Functional Theory, the MP2 method was one of the least expensive ways to improve on Hartree-Fock and it was thus often the first correlation method to be applied to new problems. It can successfully model a wide variety of systems, and MP2 geometries are usually quite accurate. Thus, MP2 remains a very useful tool in a computational chemist s toolbox. We ll see several examples of its utility in the exercises. [Pg.116]

In the last few years, methods based on Density Functional Theory have gained steadily in popularity. The best DFT methods achieve significantly greater accuracy than Harttee-Fock theory at only a modest increase in cost (far less than MP2 for medium-size and larger molecular systems). They do so by including some of the effects of electron correlation much less expensively than traditional correlated methods. [Pg.118]

These SVWN5 results are somewhat fortuitous. Be careful not to overgeneralize from their agreement to experiment. We will see a different result in Exercise 6.7. Several other excerises will also include comparisons of DFT methods to Hartree-Fock theory, MP2 and other electron correlation methods. [Pg.121]

I even the higher order electron correlation methods. [Pg.136]

The UHF curve is much higher than those for the correlation methods Hartree-Fock theory does a relatively poor job of describing this process. The MP2 curve is somewhat higher than those for the MP3 and MP4(SDTQ) levels, which appear to have converged. [Pg.188]

Any method which goes beyond SCF in attempting to treat this phenomenon properly is known as an electron correlation method (despite the fact that Hartree-Fock theory does include some correlation effects) or a post-SCT method. We will look briefly at two different approaches to the electron correlation problem in this section. [Pg.265]

Chapter 6, Selecting an Appropriate Theoretical Method, discusses the model chemistry concept introduced in Chapter 1 in detail. It covers the strengths, computational cost and limitations of a variety of popular methods, beginning with semi-empirical models and continuing through Hartree-Fock, Density Functional Theory, and electron correlation methods. [Pg.317]

The HF method determines the best one-determinant trial wave function (within the given basis set). It is therefore clear that in order to improve on HF results, the starting point must be a trial wave function which contains more than one Slater Determinant (SD). This also means that the mental picture of electrons residing in orbitals has to be abandoned, and the more fundamental property, the electron density, should be considered. As the HF solution usually gives 99% of the correct answer, electron correlation methods normally use the HF wave function as a starting point for improvements. [Pg.99]


See other pages where Correlative methods is mentioned: [Pg.725]    [Pg.1419]    [Pg.1460]    [Pg.2184]    [Pg.2185]    [Pg.2226]    [Pg.2227]    [Pg.390]    [Pg.131]    [Pg.136]    [Pg.136]    [Pg.138]    [Pg.139]    [Pg.167]    [Pg.259]    [Pg.285]    [Pg.49]    [Pg.49]    [Pg.49]    [Pg.1591]    [Pg.360]    [Pg.101]    [Pg.189]    [Pg.265]    [Pg.265]    [Pg.267]    [Pg.271]    [Pg.273]    [Pg.275]    [Pg.98]   
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Ab initio electron correlation methods

Angular Correlation of Annihilation Radiation (ACAR) Method

Block correlated coupled cluster method

Calibration methods regression and correlation

Centroid methods time correlation functions

Cluster expansion methods pair-correlation

Cluster expansion methods particle correlations

Correlated methods

Correlated sampling method

Correlating functions correlated methods

Correlation Averaging Method

Correlation Methods for Kinetic Data Linear Free Energy Relations

Correlation and Similarity Based Methods

Correlation by Multiconfigurational SCF Methods

Correlation diagram method

Correlation energy methods

Correlation function first-zero method

Correlation function maximum entropy method

Correlation length method

Correlation methods

Correlation methods

Correlation methods, macroscopic

Correlation methods, molecular similarity

Correlation methods, molecular similarity measurements

Correlation spectroscopy, COSY which method

Correlation, between analytical methods

Correlation, multivariate methods

Correlation-diagram method symmetry-forbidden reactions

Correlations and Correction Methods

Counting methods time-correlated single-photon

Cross-Correlation Method

Direct electron correlation methods

Dynamic electron correlation energy accurate estimation method

Dynamic methods molecular model correlation

Dynamical correlation methods

Dynamical correlations coupled cluster methods

Electrocyclic reactions correlation-diagram method

Electron Correlation and Post-SCF Methods

Electron Correlation---Post-Hartree-Fock Methods

Electron correlation coupled-cluster methods

Electron correlation localized methods

Electron correlation method Density-functional theory Mpller-Plesset

Electron correlation method, Density-functional theory

Electron correlation methods

Electron correlation methods Mpller-Plesset perturbation theory

Electron correlation methods accuracy

Electron correlation methods beryllium atom

Electron correlation methods configuration interaction

Electron correlation methods convergence

Electron correlation methods coupled cluster theory

Electron correlation methods dissociation

Electron correlation methods excited Slater determinants

Electron correlation methods excited states

Electron correlation methods interelectronic distance

Electron correlation methods size consistency

Electron correlation methods size extensivity

Electron correlation methods spin contamination

Electron correlation multiconfiguration-based methods

Electronic structure methods exchange-correlation functional

Embrittlement correlation methods

Embrittlement correlation methods Europe

Embrittlement correlation methods Japan

Embrittlement correlation methods USA

Embrittlement correlation methods metal

Embrittlement correlation methods method

Embrittlement correlation methods pressure vessels

Embrittlement correlation methods surveillance data

Exchange-correlation potential method

Excited electron correlation methods

Explicitly correlated methods

Explicitly correlated methods Hylleraas function

Explicitly correlated methods correlating functions

Fluorescence correlation spectroscopy relaxation methods

Fractionation methods photon correlation spectroscopy

Gaussian methods correlated calculations

Generalized pairwise correlation method

Graphical correlation method

Hamiltonian operators electron correlation methods

Hammett correlation method

Hartree-Fock theory electron correlation methods

Heat Transfer Correlation Method

Heat transfer correlating methods

Heteronuclear Chemical Shift Correlation Methods

Heteronuclear long-range shift correlation method

Heteronuclear multiple bond correlation method

Illustrating correlation methods for the beryllium atom

Intensity correlation method, lifetime

Intensity correlation method, lifetime measurement

Local MP2 Electron-correlation Method for Nonconducting Crystals

Local correlation method

Local electron-correlation method

Localized correlation methods

Method development, levels correlation with clinical

Method of correlated vectors

Methods of accounting for correlation effects

Molecular mechanics force field correlated methods

Molecular orbital methods electron correlation

Monte Carlo method time correlation function

Multi-coefficient correlation methods

Multi-coefficient correlation methods MCCM)

Multi-configuration self-consistent field electron correlation methods

Multi-determinant wave functions electron correlation methods

Multi-reference methods correlation

Multicoefficient correlation method

Near-neighbour correlations Bethes method

New Long-Range Heteronuclear Shift Correlation Methods

Nondynamic correlated methods

Orbital symmetry correlation diagram method

Outlook on Electron Correlation Methods for Large Systems

Pair correlation function method

Parameterized correlation methods

Post Dirac-Fock-Methods - Electron Correlation

Pressure correlating methods

Proton-detected correlation methods

Proton-detected correlation methods pulse sequences

Quantum Monte Carlo method correlation energy

Quantum chemistry methods correlation models

Quantum mechanics electron correlation methods

Reactor pressure vessel embrittlement correlation methods

Restricted Hartree-Fock method electron correlation methods

Restricted open-shell Hartree-Fock electron correlation methods

Scaling electron correlation methods

Schrodinger equation electron correlation methods

Self-consistent field method correlation interactions

Self-consistent field methods, correlation

Self-consistent field methods, correlation coefficients

Self-consistent field theory electron correlation methods

Slater determinants electron correlation methods

Statistical methods correlation between many data sets

Structure analysis methods molecular correlation time

Structure correlation method

Summary of Electron Correlation Methods

Tensor Correlation Methods

The Correlation Method

The correlation between different normalisation methods

Time correlator method

Time-correlated single-photon counting TCSPC) method

Unrestricted Hartree-Fock method electron correlation methods

Wave functions, molecular, correlated methods

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