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2. Uniqueness of the Maximal Helicoid
- Abstract
The purpose of this paper is to briefly outline the uniqueness of the helicoid and Enneper's surface among maximal surfaces in the Lorentz-Minkowski space.
- Published
- 2008
3. Uniqueness of the Maximal Helicoid
- Abstract
The purpose of this paper is to briefly outline the uniqueness of the helicoid and Enneper's surface among maximal surfaces in the Lorentz-Minkowski space.
- Published
- 2008
4. Uniqueness of the Maximal Helicoid
- Abstract
The purpose of this paper is to briefly outline the uniqueness of the helicoid and Enneper's surface among maximal surfaces in the Lorentz-Minkowski space.
- Published
- 2008
5. Uniqueness of the Maximal Helicoid
- Abstract
The purpose of this paper is to briefly outline the uniqueness of the helicoid and Enneper's surface among maximal surfaces in the Lorentz-Minkowski space.
- Published
- 2008
6. Uniqueness of the Maximal Helicoid
- Abstract
The purpose of this paper is to briefly outline the uniqueness of the helicoid and Enneper's surface among maximal surfaces in the Lorentz-Minkowski space.
- Published
- 2008
7. A convenient decontraction procedure of internally contracted state-specific multireference algorithms
- Abstract
Internally contracted state-specific multireference MR algorithms, either perturbative such as CASPT2 or NEVPT2, or nonperturbative such as contracted MR configuration interaction or MR coupled cluster, are computationally efficient but they may suffer from the internal contraction of the wave function in the reference space. The use of a low dimensional multistate model space only offers limited flexibility and is not always practicable. The present paper suggests a convenient state-specific procedure to decontract the reference part of the wave function from a series of state-specific calculations using slightly perturbed zero-order wave functions. The method provides an orthogonal valence bond reading of the ground state and an effective valence Hamiltonian, the excited roots of which are shown to be relevant. The orthogonal valence bond functions can be considered quasidiabatic states and the effective valence Hamiltonian gives therefore the quasidiabatic energies and the electronic coupling among the quasidiabatic states. The efficiency of the method is illustrated in two case problems where the dynamical correlation plays a crucial role, namely, the LiF neutral/ionic avoided crossing and the F2 ground state wave function
- Published
- 2006
8. A convenient decontraction procedure of internally contracted state-specific multireference algorithms
- Abstract
Internally contracted state-specific multireference MR algorithms, either perturbative such as CASPT2 or NEVPT2, or nonperturbative such as contracted MR configuration interaction or MR coupled cluster, are computationally efficient but they may suffer from the internal contraction of the wave function in the reference space. The use of a low dimensional multistate model space only offers limited flexibility and is not always practicable. The present paper suggests a convenient state-specific procedure to decontract the reference part of the wave function from a series of state-specific calculations using slightly perturbed zero-order wave functions. The method provides an orthogonal valence bond reading of the ground state and an effective valence Hamiltonian, the excited roots of which are shown to be relevant. The orthogonal valence bond functions can be considered quasidiabatic states and the effective valence Hamiltonian gives therefore the quasidiabatic energies and the electronic coupling among the quasidiabatic states. The efficiency of the method is illustrated in two case problems where the dynamical correlation plays a crucial role, namely, the LiF neutral/ionic avoided crossing and the F2 ground state wave function
- Published
- 2006
9. A convenient decontraction procedure of internally contracted state-specific multireference algorithms
- Abstract
Internally contracted state-specific multireference MR algorithms, either perturbative such as CASPT2 or NEVPT2, or nonperturbative such as contracted MR configuration interaction or MR coupled cluster, are computationally efficient but they may suffer from the internal contraction of the wave function in the reference space. The use of a low dimensional multistate model space only offers limited flexibility and is not always practicable. The present paper suggests a convenient state-specific procedure to decontract the reference part of the wave function from a series of state-specific calculations using slightly perturbed zero-order wave functions. The method provides an orthogonal valence bond reading of the ground state and an effective valence Hamiltonian, the excited roots of which are shown to be relevant. The orthogonal valence bond functions can be considered quasidiabatic states and the effective valence Hamiltonian gives therefore the quasidiabatic energies and the electronic coupling among the quasidiabatic states. The efficiency of the method is illustrated in two case problems where the dynamical correlation plays a crucial role, namely, the LiF neutral/ionic avoided crossing and the F2 ground state wave function
- Published
- 2006
10. A convenient decontraction procedure of internally contracted state-specific multireference algorithms
- Abstract
Internally contracted state-specific multireference MR algorithms, either perturbative such as CASPT2 or NEVPT2, or nonperturbative such as contracted MR configuration interaction or MR coupled cluster, are computationally efficient but they may suffer from the internal contraction of the wave function in the reference space. The use of a low dimensional multistate model space only offers limited flexibility and is not always practicable. The present paper suggests a convenient state-specific procedure to decontract the reference part of the wave function from a series of state-specific calculations using slightly perturbed zero-order wave functions. The method provides an orthogonal valence bond reading of the ground state and an effective valence Hamiltonian, the excited roots of which are shown to be relevant. The orthogonal valence bond functions can be considered quasidiabatic states and the effective valence Hamiltonian gives therefore the quasidiabatic energies and the electronic coupling among the quasidiabatic states. The efficiency of the method is illustrated in two case problems where the dynamical correlation plays a crucial role, namely, the LiF neutral/ionic avoided crossing and the F2 ground state wave function
- Published
- 2006
11. A convenient decontraction procedure of internally contracted state-specific multireference algorithms
- Abstract
Internally contracted state-specific multireference MR algorithms, either perturbative such as CASPT2 or NEVPT2, or nonperturbative such as contracted MR configuration interaction or MR coupled cluster, are computationally efficient but they may suffer from the internal contraction of the wave function in the reference space. The use of a low dimensional multistate model space only offers limited flexibility and is not always practicable. The present paper suggests a convenient state-specific procedure to decontract the reference part of the wave function from a series of state-specific calculations using slightly perturbed zero-order wave functions. The method provides an orthogonal valence bond reading of the ground state and an effective valence Hamiltonian, the excited roots of which are shown to be relevant. The orthogonal valence bond functions can be considered quasidiabatic states and the effective valence Hamiltonian gives therefore the quasidiabatic energies and the electronic coupling among the quasidiabatic states. The efficiency of the method is illustrated in two case problems where the dynamical correlation plays a crucial role, namely, the LiF neutral/ionic avoided crossing and the F2 ground state wave function
- Published
- 2006
12. Analysis of the magnetic coupling in binuclear complexes. I. Physics of the coupling
- Abstract
Accurate estimates of the magnetic coupling in binuclear complexes can be obtained from ab initio configuration interaction ~CI! calculations using the difference dedicated CI technique. The present paper shows that the same technique also provides a way to analyze the various physical contributions to the coupling and performs numerical analysis of their respective roles on four binuclear complexes of Cu (d9) ions. The bare valence-only description ~including direct and kinetic exchange! does not result in meaningful values. The spin-polarization phenomenon cannot be neglected, its sign and amplitude depend on the system. The two leading dynamical correlation effects have an antiferromagnetic character. The first one goes through the dynamical polarization of the environment in the ionic valence bond forms ~i.e., the M1¯M2 structures!. The second one is due to the double excitations involving simultaneously single excitations between the bridging ligand and the magnetic orbitals and single excitations of the environment. This dispersive effect results in an increase of the effective hopping integral between the magnetic orbitals. Moreover, it is demonstrated to be responsible for the previously observed larger metal-ligand delocalization occurring in natural orbitals with respect to the Hartree–Fock ones
- Published
- 2002
13. Analysis of the magnetic coupling in binuclear complexes. I. Physics of the coupling
- Abstract
Accurate estimates of the magnetic coupling in binuclear complexes can be obtained from ab initio configuration interaction ~CI! calculations using the difference dedicated CI technique. The present paper shows that the same technique also provides a way to analyze the various physical contributions to the coupling and performs numerical analysis of their respective roles on four binuclear complexes of Cu (d9) ions. The bare valence-only description ~including direct and kinetic exchange! does not result in meaningful values. The spin-polarization phenomenon cannot be neglected, its sign and amplitude depend on the system. The two leading dynamical correlation effects have an antiferromagnetic character. The first one goes through the dynamical polarization of the environment in the ionic valence bond forms ~i.e., the M1¯M2 structures!. The second one is due to the double excitations involving simultaneously single excitations between the bridging ligand and the magnetic orbitals and single excitations of the environment. This dispersive effect results in an increase of the effective hopping integral between the magnetic orbitals. Moreover, it is demonstrated to be responsible for the previously observed larger metal-ligand delocalization occurring in natural orbitals with respect to the Hartree–Fock ones
- Published
- 2002
14. Analysis of the magnetic coupling in binuclear complexes. I. Physics of the coupling
- Abstract
Accurate estimates of the magnetic coupling in binuclear complexes can be obtained from ab initio configuration interaction ~CI! calculations using the difference dedicated CI technique. The present paper shows that the same technique also provides a way to analyze the various physical contributions to the coupling and performs numerical analysis of their respective roles on four binuclear complexes of Cu (d9) ions. The bare valence-only description ~including direct and kinetic exchange! does not result in meaningful values. The spin-polarization phenomenon cannot be neglected, its sign and amplitude depend on the system. The two leading dynamical correlation effects have an antiferromagnetic character. The first one goes through the dynamical polarization of the environment in the ionic valence bond forms ~i.e., the M1¯M2 structures!. The second one is due to the double excitations involving simultaneously single excitations between the bridging ligand and the magnetic orbitals and single excitations of the environment. This dispersive effect results in an increase of the effective hopping integral between the magnetic orbitals. Moreover, it is demonstrated to be responsible for the previously observed larger metal-ligand delocalization occurring in natural orbitals with respect to the Hartree–Fock ones
- Published
- 2002
15. Analysis of the magnetic coupling in binuclear complexes. I. Physics of the coupling
- Abstract
Accurate estimates of the magnetic coupling in binuclear complexes can be obtained from ab initio configuration interaction ~CI! calculations using the difference dedicated CI technique. The present paper shows that the same technique also provides a way to analyze the various physical contributions to the coupling and performs numerical analysis of their respective roles on four binuclear complexes of Cu (d9) ions. The bare valence-only description ~including direct and kinetic exchange! does not result in meaningful values. The spin-polarization phenomenon cannot be neglected, its sign and amplitude depend on the system. The two leading dynamical correlation effects have an antiferromagnetic character. The first one goes through the dynamical polarization of the environment in the ionic valence bond forms ~i.e., the M1¯M2 structures!. The second one is due to the double excitations involving simultaneously single excitations between the bridging ligand and the magnetic orbitals and single excitations of the environment. This dispersive effect results in an increase of the effective hopping integral between the magnetic orbitals. Moreover, it is demonstrated to be responsible for the previously observed larger metal-ligand delocalization occurring in natural orbitals with respect to the Hartree–Fock ones
- Published
- 2002
16. Analysis of the magnetic coupling in binuclear complexes. I. Physics of the coupling
- Abstract
Accurate estimates of the magnetic coupling in binuclear complexes can be obtained from ab initio configuration interaction ~CI! calculations using the difference dedicated CI technique. The present paper shows that the same technique also provides a way to analyze the various physical contributions to the coupling and performs numerical analysis of their respective roles on four binuclear complexes of Cu (d9) ions. The bare valence-only description ~including direct and kinetic exchange! does not result in meaningful values. The spin-polarization phenomenon cannot be neglected, its sign and amplitude depend on the system. The two leading dynamical correlation effects have an antiferromagnetic character. The first one goes through the dynamical polarization of the environment in the ionic valence bond forms ~i.e., the M1¯M2 structures!. The second one is due to the double excitations involving simultaneously single excitations between the bridging ligand and the magnetic orbitals and single excitations of the environment. This dispersive effect results in an increase of the effective hopping integral between the magnetic orbitals. Moreover, it is demonstrated to be responsible for the previously observed larger metal-ligand delocalization occurring in natural orbitals with respect to the Hartree–Fock ones
- Published
- 2002
17. Uniqueness of the Maximal Helicoid
- Author
-
I. Fernández, Francisco J. López, Rui Loja Fernandes, Roger Picken, and Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
- Subjects
Surface (mathematics) ,Helicoid ,Spacelike ,General relativity ,Mathematics::Complex Variables ,Mathematical analysis ,Uniqueness ,Mathematics::Differential Geometry ,Maximal immersion ,Space (mathematics) ,Properly embedded ,Mathematics - Abstract
The purpose of this paper is to briefly outline the uniqueness of the helicoid and Enneper's surface among maximal surfaces in the Lorentz‐Minkowski space R13.The purpose of this paper is to briefly outline the uniqueness of the helicoid and Enneper's surface among maximal surfaces in the Lorentz‐Minkowski space R13.
- Published
- 2008
18. Accurate density functional calculations on frequency-dependent hyperpolarizabilities of small molecules
- Author
-
S. J. A. van Gisbergen, J. G. Snijders, Evert Jan Baerends, and Theoretical Chemistry
- Subjects
WAALS DISPERSION COEFFICIENTS ,Work (thermodynamics) ,Basis (linear algebra) ,COUPLED-CLUSTER ,DYNAMIC HYPERPOLARIZABILITIES ,Chemistry ,General Physics and Astronomy ,PERTURBATION-THEORY CALCULATIONS ,Coupled cluster ,Quality (physics) ,RESPONSE THEORY ,CORRECT ASYMPTOTIC-BEHAVIOR ,Ab initio quantum chemistry methods ,Quantum mechanics ,2ND HYPERPOLARIZABILITY ,Density functional theory ,EXCITATION-ENERGIES ,Statistical physics ,Physics::Chemical Physics ,Physical and Theoretical Chemistry ,Local-density approximation ,POLARIZABILITIES ,C-60 ,Adiabatic process - Abstract
In this paper we present time-dependent density functional calculations on frequency-dependent first (β) and second (γ) hyperpolarizabilities for the set of small molecules, N2, CO2, CS2, C2H4, NH3, CO, HF, H2O, and CH4, and compare them to Hartree–Fock and correlated ab initio calculations, as well as to experimental results. Both the static hyperpolarizabilities and the frequency dispersion are studied. Three approximations to the exchange-correlation (xc) potential are used: the widely used Local Density Approximation (LDA), the Becke–Lee–Yang–Parr (BLYP) Generalized Gradient Approximation (GGA), as well as the asymptotically correct Van Leeuwen–Baerends (LB94) potential. For the functional derivatives of the xc potential the Adiabatic Local Density Approximation (ALDA) is used. We have attempted to estimate the intrinsic quality of these methods by using large basis sets, augmented with several diffuse functions, yielding good agreement with recent numerical static LDA results. Contrary to claims which have appeared in the literature on the basis of smaller studies involving basis sets of lesser quality, we find that the static LDA results for β and γ are severely overestimated, and do not improve upon the (underestimated) Hartree–Fock results. No improvement is provided by the BLYP potential which suffers from the same incorrect asymptotic behavior as the LDA potential. The results are however clearly improved upon by the LB94 potential, which leads to underestimated results, slightly improving the Hartree–Fock results. The LDA and BLYP potentials overestimate the frequency dependence as well, which is once again improved by the LB94 potential. Future improvements are expected to come from improved models for asymptotically correct exchange-correlation potentials. Apart from the LB94 potential used in this work, several other asymptotically correct potentials have recently been suggested in the literature and can also be expected to improve considerably upon the relatively poor LDA and GGA results, for both the static properties and their frequency dependence.
- Published
- 1998
19. Oscillator Strengths of Electronic Excitations with Response Theory using Phase Including Natural Orbital Functionals
- Author
-
Oleg V. Gritsenko, Klaas J. H. Giesbertz, R. van Meer, Evert Jan Baerends, Theoretical Chemistry, and AIMMS
- Subjects
Density matrix ,ta114 ,Chemistry ,excitation energy ,tiheysfunktionaaliteoria ,General Physics and Astronomy ,Time-dependent density functional theory ,elektronit ,Adiabatic theorem ,Matrix (mathematics) ,Quantum mechanics ,Excited state ,Density functional theory ,eigenvalues and eigenfunctions ,Physical and Theoretical Chemistry ,Adiabatic process ,Eigenvalues and eigenvectors - Abstract
The key characteristics of electronic excitations of many-electron systems, the excitation energies ωα and the oscillator strengths fα, can be obtained from linear response theory. In one-electron models and within the adiabatic approximation, the zeros of the inverse response matrix, which occur at the excitation energies, can be obtained from a simple diagonalization. Particular cases are the eigenvalue equations of time-dependent density functional theory (TDDFT), time-dependent density matrix functional theory, and the recently developed phase-including natural orbital (PINO) functional theory. In this paper, an expression for the oscillator strengths fα of the electronic excitations is derived within adiabatic response PINO theory. The fα are expressed through the eigenvectors of the PINO inverse response matrix and the dipole integrals. They are calculated with the phaseincluding natural orbital functional for two-electron systems adapted from the work of Lowdin ¨ and Shull on two-electron systems (the phase-including Löwdin-Shull functional). The PINO calculations reproduce the reference fα values for all considered excitations and bond distances R of the prototype molecules H2 and HeH+ very well (perfectly, if the correct choice of the phases in the functional is made). Remarkably, the quality is still very good when the response matrices are severely restricted to almost TDDFT size, i.e., involving in addition to the occupied-virtual orbital pairs just (HOMO+1)-virtual pairs (R1) and possibly (HOMO+2)-virtual pairs (R2). The shape of the curves fα(R) is rationalized with a decomposition analysis of the transition dipole moments. peerReviewed
- Published
- 2013
20. Accurate interaction energies at density functional theory level by means of an efficient dispersion correction
- Author
-
Christian Van Alsenoy, Tamás Veszprémi, Alisa Krishtal, Kenno Vannomeslaeghe, Paul Geerlings, András Olasz, Chemistry, Pathology/molecular and cellular medicine, Mathematics, General Chemistry, Quantum Chemistry - Molecular Modelling, and Analytical Chemistry and Pharmaceutical Technology
- Subjects
General Physics and Astronomy ,Sensitivity and Specificity ,Quality (physics) ,coupled cluster calculations ,Polarizability ,Linear regression ,Dispersion (optics) ,Physics::Atomic and Molecular Clusters ,Limit (mathematics) ,Physics::Chemical Physics ,Physical and Theoretical Chemistry ,molecular configurations ,Anisotropy ,Basis set ,density functional theory ,Physics ,polarisability ,Symmetry (physics) ,Computational physics ,Chemistry ,Linear Models ,Quantum Theory ,Thermodynamics ,organic compounds ,Algorithms - Abstract
This paper presents an approach for obtaining accurate interaction energies at the density functional theory level for systems where dispersion interactions are important. This approach combines Becke and Johnson's [J. Chem. Phys. 127, 154108 (2007)] method for the evaluation of dispersion energy corrections and a Hirshfeld method for partitioning of molecular polarizability tensors into atomic contributions. Due to the availability of atomic polarizability tensors, the method is extended to incorporate anisotropic contributions, which prove to be important for complexes of lower symmetry. The method is validated for a set of 18 complexes, for which interaction energies were obtained with the B3LYP, PBE, and TPSS functionals combined with the aug-cc-pVTZ basis set and compared with the values obtained at the CCSD(T) level extrapolated to a complete basis set limit. It is shown that very good quality interaction energies can be obtained by the proposed method for each of the examined functionals, the overall performance of the TPSS functional being the best, which with a slope of 1.00 in the linear regression equation and a constant term of only 0.1 kcal/mol allows to obtain accurate interaction energies without any need of a damping function for complexes close to their exact equilibrium geometry.
- Published
- 2009
21. Analysis of the magnetic coupling in binuclear complexes. I. Physics of the coupling
- Author
-
Carmen J. Calzado, Jean-Paul Malrieu, Rosa Caballol, Jesús Cabrero, and Universidad de Sevilla. Departamento de Química Física
- Subjects
Physics ,Coupling (physics) ,Atomic orbital ,Ab initio quantum chemistry methods ,Ab initio ,General Physics and Astronomy ,Ionic bonding ,Valence bond theory ,Physical and Theoretical Chemistry ,Configuration interaction ,Atomic physics ,Inductive coupling - Abstract
Accurate estimates of the magnetic coupling in binuclear complexes can be obtained from ab initio configuration interaction ~CI! calculations using the difference dedicated CI technique. The present paper shows that the same technique also provides a way to analyze the various physical contributions to the coupling and performs numerical analysis of their respective roles on four binuclear complexes of Cu (d9) ions. The bare valence-only description ~including direct and kinetic exchange! does not result in meaningful values. The spin-polarization phenomenon cannot be neglected, its sign and amplitude depend on the system. The two leading dynamical correlation effects have an antiferromagnetic character. The first one goes through the dynamical polarization of the environment in the ionic valence bond forms ~i.e., the M1¯M2 structures!. The second one is due to the double excitations involving simultaneously single excitations between the bridging ligand and the magnetic orbitals and single excitations of the environment. This dispersive effect results in an increase of the effective hopping integral between the magnetic orbitals. Moreover, it is demonstrated to be responsible for the previously observed larger metal-ligand delocalization occurring in natural orbitals with respect to the Hartree–Fock ones
- Published
- 2002
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