共查询到20条相似文献,搜索用时 46 毫秒
1.
F. G. Pashaev 《Journal of mathematical chemistry》2009,45(4):891-890
An efficient method for computing overlap integral over Slater type orbitals based on the B Filter-Steinborn and Guseinov auxiliary functions is presented. The final results are expressed through the binomial coefficients with the help of which
the overlap integrals can be evaluated efficiently and accurately. The results of calculation are in good agreement with those
obtained by other method for arbitrary principal quantum numbers and different screening constants.
An erratum to this article can be found at 相似文献
2.
Tomislav P. Živković 《Journal of mathematical chemistry》2008,43(2):518-600
Interaction of a finite quantum system that contains ρ eigenvalues and eigenstates with an infinite quantum system that contains a single one-parameter eigenvalue band is considered. A new approach for the treatment of the combined system
is developed. This system contains embedded eigenstates with continuous eigenvalues , and, in addition, it may contain isolated eigenstates with discrete eigenvalues . Two ρ × ρ eigenvalue equations, a generic eigenvalue equation and a fractional shift eigenvalue equation are derived. It is shown that all properties of the system that interacts with the system can be expressed in terms of the solutions to those two equations. The suggested method produces correct results, however
strong the interaction between quantum systems and . In the case of the weak interaction this method reproduces results that are usually obtained within the formalism of the
perturbation expansion approach. However, if the interaction is strong one may encounter new phenomena with much more complex
behavior. This is also the region where standard perturbation expansion fails. The method is illustrated with an example of
a two-dimensional system that interacts with the infinite system that contains a single one-parameter eigenvalue band. It is shown that all relevant completeness relations are satisfied,
however strong the interaction between those two systems. This provides a strong verification of the suggested method. 相似文献
3.
On the example of the molecular ion, we show that spherically distorted s-type orbitals possessing angular dependent orbital exponents, even in a minimal basis may lead to total energies the accuracy
of which is comparable with the ones obtained by fully numerical (‘complete basis’) calculations. 相似文献
4.
Radosław Szmytkowski 《Journal of mathematical chemistry》2009,46(1):231-260
The derivative of the associated Legendre function of the first kind of integer degree with respect to its order, , is studied. After deriving and investigating general formulas for μ arbitrary complex, a detailed discussion of , where m is a non-negative integer, is carried out. The results are applied to obtain several explicit expressions for the associated
Legendre function of the second kind of integer degree and order, . In particular, we arrive at formulas which generalize to the case of (0 ≤ m ≤ n) the well-known Christoffel’s representation of the Legendre function of the second kind, Q
n
(z). The derivatives and , all with m > n, are also evaluated. 相似文献
5.
Tomislav P. ivkovi 《Journal of mathematical chemistry》2009,45(4):1060-1101
Mathematical formalism of the Low Rank Perturbation method (LRP) is applied to the vibrational isotope effect in the harmonic
approximation with a standard assumption that force field does not change under isotopic substitutions. A pair of two n-atom isotopic molecules A and B which are identical except for isotopic substitutions at ρ atomic sites is considered. In the LRP approach vibrational frequencies ω
k
and normal modes of the isotopomer B are expressed in terms of the vibrational frequencies ν
i
and normal modes of the parent molecule A. In those relations complete specification of the normal modes is not required. Only amplitudes at sites τ affected by the isotopic substitutions and in the coordinate direction s (s = x, y, z) are needed. Out-of-plane vibrations of the (H,D)-benzene isotopomers are considered. Standard error of the LRP frequencies
with respect to the DFT frequencies is on average . This error is due to the uncertainty of the input data (± 0.5 cm−1) and in the absence of those uncertainties and in the harmonic approximation it should disappear. In comparing with experiment,
one finds that LRP frequencies reproduces experimental frequencies of (H,D)-benzene isotopomers better () than scaled DFT frequencies () which are designed to minimize (by frequency scaling technique) this error. In addition, LRP is conceptually and numerically
simple and it also provides a new insight in the vibrational isotope effect in the harmonic approximation. 相似文献
6.
Tomislav P. Živković 《Journal of mathematical chemistry》2006,39(1):151-176
Time-dependent properties of a state
that interacts with an infinite dimensional quantum system
containing several one-parameter eigenvalue bands
are considered. This is done by a new mathematical method that produces correct results, however strong the interaction between
the state
and the system
. It is shown that in the case of the weak interaction one obtains standard results that are usually obtained within the formalism
of the perturbation expansion method. In particular, if the eigenvalue E of the state
is embedded inside the range
of the unperturbed eigenvalues, time evolution of the state
that is initially prepared in the state
has typical exponential decay behavior. One also reproduces standard results concerning probabilities of the transition of
the state
at infinite time (t=∞) into various eigenvalue bands. However, if the interaction is strong, one finds much more complex and much more complicated
behavior. 相似文献
7.
The energy of a graph is defined as the sum of the absolute values of all the eigenvalues of the graph. Let
denote the set of trees on n vertices and diameter d,
. Yan and Ye [Appl. Math. Lett. 18 (2005) 1046–1052] have recently determined the unique tree in
with minimal energy. In this article, the trees in
with second-minimal energy are characterizedAMS Subject Classification: 05C50, 05C35 相似文献
8.
Denote by the set of trees of order 2k with perfect matchings. GUO [Guo, Linear Algebra Appl. 368:379–385, 2003.] determined the largest value of Laplacian spectral
radii μ(T) of the trees T in and gave the corresponding tree T in whose μ(T) reaches this largest value. In this paper, we determine the second to the sixth largest values of μ(T) of the trees T in and also give the corresponding trees T in whose μ(T) reach these values. 相似文献
9.
Tomislav P. Živković 《Journal of mathematical chemistry》2006,39(2):295-344
A new method for the exact solution of the interaction of an isolated state
with an infinite dimensional quantum system §∞ b
containing several one-parameter eigenvalue bands
is developed. Unlike standard perturbation expansion approach, this method produces correct results however strong the interaction
between the state
and the system
. It is shown that in the case of the weak interaction this method correctly reproduces standard results obtained within the
formalism of the perturbation expansion method. In particular, due to the interaction with the system
, eigenvalue E of the state
shifts to a new position. In addition, if this eigenvalue is embedded inside the range
of the unperturbed eigenvalues, this shifted eigenvalue broadens and spectral distribution of the state
has the shape of the universal resonance curve. However, if the interaction is strong, one finds much more complex and much
more complicated behavior 相似文献
10.
Let λ1 (G) and Δ (G), respectively, denote the largest eigenvalue and the maximum degree of a graph G. Let
be the set of trees with perfect matchings on 2m vertices, and
. Among the trees in
, we characterize the tree which alone minimizes the largest eigenvalue, as well as the tree which alone maximizes the largest
eigenvalue when
. Furthermore, it is proved that, for two trees T
1 and T
2 in
(m≥ 4), if
and Δ (T
1) > Δ (T
2), then λ1 (T
1) > λ1 (T
2). 相似文献
11.
Extremal Polyomino Chains on k-matchings and k-independent Sets 总被引:3,自引:0,他引:3
Denote by the set of polyomino chains with n squares. For any , let m
k
(T
n
) and i
k
(T
n
) be the number of k-matchings and k-independent sets of T
n
, respectively. In this paper, we show that for any polyomino chain and any , and , with the left equalities holding for all k only if T
n
=L
n
, and the right equalities holding for all k only if T
n
=Z
n
, where L
n
and Z
n
are the linear chain and the zig-zag chain, respectively.
This work is supported by NNSFC (10371102). 相似文献
12.
Wen-Huan Wang An Chang Lian-Zhu Zhang Dong-Qiang Lu 《Journal of mathematical chemistry》2006,39(1):231-241
The minimal energy of unicyclic Hückel molecular graphs with Kekulé structures, i.e., unicyclic graphs with perfect matchings,
of which all vertices have degrees less than four in graph theory, is investigated. The set of these graphs is denoted by
such that for any graph in , n is the number of vertices of the graph and l the number of vertices of the cycle contained in the graph. For a given n(n ≥ 6), the graphs with minimal energy of
have been discussed.
MSC 2000: 05C17, 05C35 相似文献
13.
In this article, we derived several new recurrence relations of the rotation matrix elements by using Gauss’ recurrence formulas
for hypergeometric functions and auxiliary functions , and . The aim of this contribution is to obtain general algorithm to compute the rotation matrix elements, paying attention to
the use recurrence relationships of the auxiliary functions that allow the treatment of the functions with high angular momentum
quantum numbers. 相似文献
14.
May Nyman Todd M. Alam François Bonhomme Mark A. Rodriguez Colleen S. Frazer Margaret E. Welk 《Journal of Cluster Science》2006,17(2):197-219
The hexaniobate Lindqvist ion
has long been known as the dominant specie in alkaline niobium oxide solutions. Recent advances in heteropolyniobate chemistry continue to be greatly aided by use of
alkali salts as soluble precursors; in particular, potassium, sodium and lithium hexaniobate salts. We report here the solid-state characterization and solution behavior of Li, K, Rb and Cs Lindqvist
salts. Synthesis and single-crystal X-ray diffraction data is reported for nine new hexaniobate salts. These structures differ in the number of charge-balancing alkali cations, protonation of the clusters, relative arrangement of the clusters and alkali metal cations, amount of lattice water and its mode of interaction with other lattice species. Trends of alkali-cluster bonding are observed as a function of alkali radius. Protonation of the clusters in the solid-state is influenced by the method of crystallization of the
salt. Lability of the cluster oxygens is observed by solution 17O NMR experiments. Rates of isotopic enrichment of the bridging oxygen, terminal oxygen and bridging hydroxyl cluster sites are compared for aqueous solutions of Li, K, Rb and Cs hexaniobate salts. Parameters influencing the oxo-ligand exchange rates of the salts are discussed relative to their use as heteropolyniobate precursors.This paper is dedicated to Professor Michael T. Pope on the event of his retirement to acknowledge his fruitful career in polyoxometalate chemistry. 相似文献
15.
Codon Adaptation Index (CAI), Effective Number of Codons as well as its modifications , can be used to measure gene codon bias. In this article, we prove is more efficient and unbiased than and by revisiting correlations of them with CAI in the level of individual amino acid’s codon bias. Correlations are studied
by mathematical expressions rather than statistic methods, because the latter unavoidably depend on the data set used. Additionally,
the immediate cause of correlations of with CAI (as well as those of RSCU with CAI) are also described in mathematical language. Perhaps, mathematics provides us
a new way to study correlations between biological indexes. 相似文献
16.
I. I. Guseinov 《Journal of mathematical chemistry》2008,44(3):839-848
Using the properties of tensor spherical harmonics introduced by the author in previous paper (Guseinov, Phys Lett A 372:44,
2007) and complete orthonormal scalar basis sets of nonrelativistic -exponential type orbitals ( -ETO), - momentum space orbitals ( -MSO) and z
α-hyperspherical harmonics (z
α-HSH) for particles with spin s = 0 the new analytical relations for the quasirelativistic and relativistic spinor wave functions
and Slater spinor orbitals in coordinate, momentum and four-dimensional spaces are derived, where α = 1, 0, −1, −2,.... The
2-component quasirelativistic and 4-component relativistic spinor wave functions obtained are complete without the inclusion
of the continuum. The relativistic spinor wave function sets and Slater spinor orbitals are expressed through the corresponding
quasirelativistic spinor wave functions and Slater spinor orbitals, respectively. The analytical formulas for overlap integrals
over quasirelativistic and relativistic Slater spinor orbitals with the same screening constants in coordinate space are also
derived. 相似文献
17.
I. I. Guseinov 《Journal of mathematical chemistry》2008,44(1):197-205
The new formulas are obtained for complete orthonormal sets of exponential type vector orbitals of a particle with spin 1
in coordinate, momentum and four-dimensional spaces using the properties of spherical vectors and complete orthonormal scalar
basis sets of -exponential type orbitals ( -ETO), -momentum space orbitals ( -MSO) and -hyperspherical harmonics ( -HSH) introduced by the author for particles with spin s = 0, where These vector orbitals are complete without the inclusion of the continuum and, therefore, their group of transformation is
the four-dimensional rotation group of O(4). For overlap integrals over vector Slater orbitals with the same screening constant
the analytical relations in coordinate space are also derived. It should be noted that the new idea presented in this study
is the combination of spherical vectors with complete orthonormal scalar sets for radial parts of -orbitals. 相似文献
18.
Let G be an unicycle graph and d
v
the degree of the vertex v. In this paper, we investigate the following topological indices for an unicycle graph ,
, where m ≥ 2 is an integer. All unicycle graphs with the largest values of the three topological indices are characterized.
This research is supported by the National Natural Science Foundation of China(10471037)and the Education Committee of Hunan
Province(02C210)(04B047). 相似文献
19.
In this paper, we study the spectral radius of graphs of order n with κ(G) ≤ k. We show that among those graphs, the maximal spectral radius is obtained uniquely at , which is the graph obtained by joining k edges from k vertices of K
n-1 to an isolated vertex. We also show that the spectral radius of will be very close to n − 2 for a fixed k and a sufficiently large n. 相似文献
20.
Hongbo Hua 《Journal of mathematical chemistry》2008,43(2):831-844
The Hosoya index z(G) of a (molecular) graph G is defined as the total number of subsets of the edge set, in which any two edges are mutually independent, i.e., the total
number of independent-edge sets of G. By G(n, l, k) we denote the set of unicyclic graphs on n vertices with girth and pendent vertices being resp. l and k. Let be the graph obtained by identifying the center of the star S
n-l+1 with any vertex of C
l
. By we denote the graph obtained by identifying one pendent vertex of the path P
n-l-k+1 with one pendent vertex of . In this paper, we show that is the unique unicyclic graph with minimal Hosoya index among all graphs in G(n, l, k).
相似文献