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Closed shells

The Hiickel description of aromaticity was based in part on benzene, a cyclic fully conjugated hydrocarbon having (4n -l- 2) -electrons (ff = I) in the closed shell (ring). [Pg.55]

Kim Y S, Kim S K and Lee W D 1981 Dependence of the closed-shell repulsive interaction on the overlap of the electron densities Chem. Phys. Lett. 80 574... [Pg.213]

Pyykko P 1997 Strong closed-shell interactions in inorganic chemistry Chem. Rev. 97 597 A review of fertile ground for fiittlier research. [Pg.217]

Bartlett R J and Silver D M 1975 Many-body perturbation theory applied to eleetron pair eorrelation energies I. Closed-shell first-row diatomie hydrides J. Chem. Rhys. 62 3258-68... [Pg.2197]

The basic self-consistent field (SCF) procedure, i.e., repeated diagonalization of the Fock matrix [26], can be viewed, if sufficiently converged, as local optimization with a fixed, approximate Hessian, i.e., as simple relaxation. To show this, let us consider the closed-shell case and restrict ourselves to real orbitals. The SCF orbital coefficients are not the... [Pg.2339]

Due to the large number of variables in wavefiinction optimization problems, it may appear that fiill second-order methods are impractical. For example, the storage of the Hessian for a modest closed-shell wavefiinction with 500... [Pg.2340]

Bacskay G B 1981 A quadratically convergent Hartree-Fock (QC-SCF) method. Applications to the closed-shell case Chem. Phys. 61 385... [Pg.2356]

Figure Cl. 1.2. (a) Mass spectmm of sodium clusters (Na ), N= 4-75. The inset corresponds to A = 75-100. Note tire more abundant clusters at A = 8, 20, 40, 58, and 92. (b) Calculated relative electronic stability, A(A + 1) - A(A0 versus N using tire spherical electron shell model. The closed shell orbitals are labelled, which correspond to tire more abundant clusters observed in tire mass spectmm. Knight W D, Clemenger K, de Heer W A, Saunders W A, Chou M Y and Cohen ML 1984 Phys. Rev. Lett. 52 2141, figure 1. Figure Cl. 1.2. (a) Mass spectmm of sodium clusters (Na ), N= 4-75. The inset corresponds to A = 75-100. Note tire more abundant clusters at A = 8, 20, 40, 58, and 92. (b) Calculated relative electronic stability, A(A + 1) - A(A0 versus N using tire spherical electron shell model. The closed shell orbitals are labelled, which correspond to tire more abundant clusters observed in tire mass spectmm. Knight W D, Clemenger K, de Heer W A, Saunders W A, Chou M Y and Cohen ML 1984 Phys. Rev. Lett. 52 2141, figure 1.
One can note some interesting features from these trajectories. For example, the Mulliken population on the participating atoms in Figure 1 show that the departing deuterium canies a full electron. Also, the deuterium transferred to the NHj undergoes an initial substantial bond stretch with the up spin and down spin populations separating so that the system temporarily looks like a biradical before it settles into a normal closed-shell behavior. [Pg.237]

Electron density represents the probability of finding an electron at a poin t in space. It is calcii lated from th e elements of th e den sity matrix. The total electron density is the sum of the densities for alpha and beta electrons. In a closed-shell RUE calculation, electron densities are the same for alpha and beta electrons. [Pg.52]

Total spin den sity reflects th e excess probability of fin din g a versus P electrons in an open-shell system. Tor a system m which the a electron density is equal to the P electron density (for example, a closed-shell system), the spin density is zero. [Pg.52]

Choose LHH(spin Unrestricted Hartree-Fock) or RHF (spin Restricted Ilartree-Fock) calculations according to your molecular system. HyperChem supports UHF for both open-sh el I and closed-shell calcii lation s an d RHF for cUised-shell calculation s on ly, Th e closed-shell LHFcalculation may be useful for studyin g dissociation of m olectilar system s. ROHF(spin Restricted Open-shell Hartree-Fock) is not supported in the current version of HyperChem (for ah initio calculations). [Pg.112]

To define the state yon want to calculate, you must specify the m u Itiplicity. A system with an even ii n m ber of electron s n sn ally has a closed-shell ground state with a multiplicity of I (a singlet). Asystem with an odd niim her of electrons (free radical) nsnally has a multiplicity of 2 (a doublet). The first excited state of a system with an even ii nm ber of electron s usually has a m n Itiplicity of 3 (a triplet). The states of a given m iiltiplicity have a spectrum of states —the lowest state of the given multiplicity, the next lowest state of the given multiplicity, and so on. [Pg.218]

You can order the molecular orbitals that arc a solution to etjtia-tion (47) accordin g to th eir en ergy, Klectron s popii late the orbitals, with the lowest energy orbitals first. normal, closed-shell, Restricted Hartree hock (RHK) description has a nia.xirnuin of Lw o electrons in each molecular orbital, one with electron spin up and one w ith electron spin down, as sliowm ... [Pg.220]

I he Koothaan equations just described are strictly the equations fora closed-shell Restricted Hartrce-Fock fRHK) description only, as illustrated by the orbital energy level diagram shown earlier. To be more specific ... [Pg.226]

A closed-shell means that every occupied molecular orbital contains exactly two electrons. [Pg.226]

IlyperChcm semi-empirical methods usually let you request a calculation on the lowest energy stale of a given multiplicity or the next lowest state of a given spin m ultipliriiy. Sin ce m osl m olecu les with an even num her of electron s are closed-shell singlets without... [Pg.232]

Closed-shell Systems and the Roothaan-Hall Equations... [Pg.76]

We shall initially consider a closed-shell system with N electroris in N/2 orbitals. The derivation of the Hartree-Fock equations for such a system was first proposed by Roothaan [Roothaan 1951] and (independently) by Hall [Hall 1951]. The resulting equations are known as the Roothaan equations or the Roothaan-Hall equations. Unlike the integro-differential form of the Hartree-Fock equations. Equation (2.124), Roothaan and Hall recast the equations in matrix form, which can be solved using standard techniques and can be applied to systems of any geometry. We shall identify the major steps in the Roothaan approach. [Pg.76]

The Fock matrix elements for a closed-shell system can be expanded as follows by substituting the expression for the Fock operator ... [Pg.77]

P is the total spinless density matrix (P = P + P ) and P is the spin density matrix (P = p" + P ). For a closed-shell system Mayer s definition of the bond order reduces to ... [Pg.103]

In a closed-shell system, P = P) = P and the Fock matrix elements can be obtained by making this substitution. If a basis set containing s, p orbitals is used, then many of the one-centre integrals nominally included in INDO are equal to zero, as are the core elements Specifically, only the following one-centre, two-electron integrals are non-zero (/x/x /x/x), (pit w) and (fti/lfM/). The elements of the Fock matrix that are affected can then be written a." Uxllow s ... [Pg.113]

I he results of their calculations were summarised in two rules. The first rule states that at least one isomer C with a properly closed p shell (i.e. bonding HOMO, antibonding I. U.MO) exists for all n = 60 - - 6k (k = 0,2,3,..., but not 1). Thus Qg, C72, Cyg, etc., are in lhi-< group. The second rule is for carbon cylinders and states that a closed-shell structure is lound for n = 2p(7 - - 3fc) (for all k). C70 is the parent of this family. The calculations Were extended to cover different types of structure and fullerenes doped with metals. [Pg.121]

The sum of the zeroth-order and first-order energies thus corresponds to the Hartree-Fock energy (compare with Equation (2.110), which gives the equivalent result for a closed-shell system) ... [Pg.135]


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Ab initio Closed Shell Formalism

Atomic interactions closed-shell

Atomic orbitals closed-shell configuration

Atomic-shell closing

Atoms alkali clusters, shell closing

Atoms with closed shells

Barrier means a cost of opening the closed-shells

Chemistry closed shell

Close-shell interactions

Closed shell SCF calculation

Closed shell bonding

Closed shell case

Closed shell configuration

Closed shell determinant

Closed shell electronic configuration

Closed shell metalloporphyrins

Closed shell molecule

Closed shell repulsion

Closed shell structure

Closed shell, definition

Closed shells - unrestricted Hartree-Fock (UHF)

Closed shells and negative ions

Closed shells summary

Closed-shell atoms

Closed-shell colloids

Closed-shell complexes

Closed-shell compounds

Closed-shell compounds calculations

Closed-shell compounds electron transfer

Closed-shell compounds radicals

Closed-shell compounds systems

Closed-shell confined helium

Closed-shell ground states

Closed-shell hydrocarbons

Closed-shell interaction

Closed-shell ion

Closed-shell mode

Closed-shell molecular orbitals

Closed-shell molecular orbitals calculations

Closed-shell molecular systems

Closed-shell molecule, self-consistent

Closed-shell molecule, self-consistent field configuration, calculation

Closed-shell molecules reference functions

Closed-shell molecules spin contamination

Closed-shell normalization constant

Closed-shell principle

Closed-shell singlet

Closed-shell singlet ground states

Closed-shell singlet state

Closed-shell solutes

Closed-shell state

Closed-shell systems

Closed-shell systems definition

Closed-shell transition metal atom states

Closed-shell wave function

Closed-shells CCSD method

Closed-shells calculations

Closed-shells restricted Hartree-Fock

Closed-shells total energy

Clusters closed shell

Collective motion in closed shells

Coupled-cluster theory closed shell

Diatomic molecules closed shells

Dirac-Hartree-Fock Total Energy of Closed-Shell Atoms

Early Examples of Surface Calculations for Closed-shell Systems

Electron closed shell

Electron transfer radical closed-shell structures

Electronic shell alkali atom clusters, closing

Energy expression closed-shell system

Energy levels in closed shell nuclei

Energy of closed-shell system

Finite-basis approximations. Closed-shell systems

Generation from Closed-Shell Species

Hartree-Fock equations/theory closed-shell

Hartree-Fock function closed shell single determinant

Icosahedral shell-closings

Integral, Closed Shell, and Restricted Chemistry

Local-density approximation closed-shell

Metallocenes closed-shell

Molecular beam electric resonance of closed shell molecules

Molecular beam magnetic resonance of closed shell molecules

Nucleus closed shells

Organic molecules closed/open shell

Photoionization closed shell atom

Pseudo-closed-shell structures

Roothaan-Hall equations closed-shell systems

Second- and third-order MBPT for closed-shell atoms

Self interaction correction closed-shell

Shell closed versus open

Spherical jellium model closed-shell clusters

Spherical shell-closing

The Luminescence of Closed-Shell Transition-Metal Complexes

The Periodic System. Closed Shells

The closed shell atom

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