The method of dispersion correction as an add-on to standard Kohn-Sham density functional theory (DFT-D) has been refined regarding higher accuracy, broader range of applicability, and less empiricism. The main new ingredients are atom-pairwise specific dispersion coefficients and cutoff radii that are both computed from first principles. The coefficients for new eighth-order dispersion terms are computed using established recursion relations. System (geometry) dependent information is used for the first time in a DFT-D type approach by employing the new concept of fractional coordination numbers (CN). They are used to interpolate between dispersion coefficients of atoms in different chemical environments. The method only requires adjustment of two global parameters for each density functional, is asymptotically exact for a gas of weakly interacting neutral atoms, and easily allows the computation of atomic forces. Three-body nonadditivity terms are considered. The method has been assessed on standard benchmark sets for inter- and intramolecular noncovalent interactions with a particular emphasis on a consistent description of light and heavy element systems. The mean absolute deviations for the S22 benchmark set of noncovalent interactions for 11 standard density functionals decrease by 15%-40% compared to the previous (already accurate) DFT-D version. Spectacular improvements are found for a tripeptide-folding model and all tested metallic systems. The rectification of the long-range behavior and the use of more accurate C(6) coefficients also lead to a much better description of large (infinite) systems as shown for graphene sheets and the adsorption of benzene on an Ag(111) surface. For graphene it is found that the inclusion of three-body terms substantially (by about 10%) weakens the interlayer binding. We propose the revised DFT-D method as a general tool for the computation of the dispersion energy in molecules and solids of any kind with DFT and related (low-cost) electronic structure methods for large systems.

http://dns2.asia.edu.tw/~ysho/YSHO-English/1000%20WC/PDF/J%20Che%20Phy132,%20154104.pdf

A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu

Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

Fast parallel algorithms for short-range molecular dynamics

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

It is shown by an extensive benchmark on molecular energy data that the mathematical form of the damping function in DFT-D methods has only a minor impact on the quality of the results. For 12 different functionals, a standard "zero-damping" formula and rational damping to finite values for small interatomic distances according to Becke and Johnson (BJ-damping) has been tested. The same (DFT-D3) scheme for the computation of the dispersion coefficients is used. The BJ-damping requires one fit parameter more for each functional (three instead of two) but has the advantage of avoiding repulsive interatomic forces at shorter distances. With BJ-damping better results for nonbonded distances and more clear effects of intramolecular dispersion in four representative molecular structures are found. For the noncovalently-bonded structures in the S22 set, both schemes lead to very similar intermolecular distances. For noncovalent interaction energies BJ-damping performs slightly better but both variants can be recommended in general. The exception to this is Hartree-Fock that can be recommended only in the BJ-variant and which is then close to the accuracy of corrected GGAs for non-covalent interactions. According to the thermodynamic benchmarks BJ-damping is more accurate especially for medium-range electron correlation problems and only small and practically insignificant double-counting effects are observed. It seems to provide a physically correct short-range behavior of correlation/dispersion even with unmodified standard functionals. In any case, the differences between the two methods are much smaller than the overall dispersion effect and often also smaller than the influence of the underlying density functional.

Effect of the damping function in dispersion corrected density functional theory

6.2.2. Definition of Effective Properties 3064 6.3. Response Properties to Magnetic Fields 3066 6.3.1. Nuclear Shielding 3066 6.3.2. Indirect Spin−Spin Coupling 3067 6.3.3. EPR Parameters 3068 6.4. Properties of Chiral Systems 3069 6.4.1. Electronic Circular Dichroism (ECD) 3069 6.4.2. Optical Rotation (OR) 3069 6.4.3. VCD and VROA 3070 7. Continuum and Discrete Models 3071 7.1. Continuum Methods within MD and MC Simulations 3072

/pdf/quantum-mechanical-continuum-solvation-models-3edv963g14.pdf

Quantum mechanical continuum solvation models.

Multicentre multipole expansions in principle should allow one to solve theshape' con- vergence problem arising in the calculation of long-range interaction energies between large non-spherical molecules via point-multipole expansions. In part I of this series (1996, Molec. Phys., 88, 69) it was shown that this indeed is the case for ® rst-order electrostatic and second- order induction energies when employing distributed multipole moments and static polar- izabilities generated from the topological partitioning of the molecular volume as provided by Bader'satoms-in-molecules' theory. Their generalization to frequency-dependent, topologically partitioned polarizabilities is used in the present contribution to compare the convergence behaviour of one-centre and multicentre multipole expansions of the second- order dispersion energy for homomolecular dimers of the water, carbon monoxide, cyanogen and urea molecules. The ® ndings are similar to those for the induction energy; the radial `extension' convergence problem, which already exists for point-multipole expanded inter- action energies between atoms, necessarily persists, but the angular convergence problems linked to the shape of the interacting molecules can successfully be treated by multicentre multipole expansions of the dispersion energy.

Intermolecular interaction energies by topologically partitioned electric properties II. Dispersion energies in one-centre and multicentre multipole expansions

An ab initio investigation of the electric-field-gradient-induced birefringence of H2, N2, C2H2, and CH4 is presented. All linear and nonlinear optical properties contributing to the induced anisotropy of the refractive index are computed by means of coupled cluster singles and doubles response theory. For systems of cubic or icosahedral symmetry, the only nonvanishing contribution to the induced birefringence within the semiclassical approach is due to the frequency-dependent dipole–dipole–quadrupole and dipole–dipole–magnetic dipole hyperpolarizabilities. These hyperpolarizabilities are important for accurate experimental determinations of the molecular quadrupole moment from electric-field-gradient-induced birefringence measurements.

Coupled cluster investigation of the electric-field-gradient-induced birefringence of h2, n2, c2h2, and ch4

The implementation of two-photon transition moments is described for the hierachy of coupled cluster models CCS, CC2 and CCSD and applications are reported for the two-photon transition probability rate constants for transitions from the ground state to the first excited 1Se state in helium and to the lowest 1De and 1Se states in neon and argon. At the CCSD level the rate constant for the 1De transition in argon is in good agreement with the experimental rate constant and also with a recent MCSCF calculation.

Coupled cluster response calculations of two-photon transition probability rate constants for helium, neon and argon

An improved formulation of pair natural orbital (PNO)–based explicitly correlated Moller–Plesset second-order perturbation theory is presented. Increased efficiency has been achieved by modifying the representation of the strong orthogonality projector used in the evaluation of the F12 intermediates. We demonstrate two simple relationships between the truncation errors arising from PNOs in the virtual space and those arising from the PNOs in the strong orthogonality operators. This permits robust error control through a single parameter.

Pair natural orbitals in explicitly correlated second-order moller-plesset theory

We report an implementation of the linear response function for singlet excited states for the coupled cluster models CCS, CC2 and CCSD The implementation is based on the derivation of excited state response functions as derivatives of excited state quasienergy Lagrangians Secular divergencies are explicitly eliminated and response equations and response functions therefore are numerical stable in the static limit Calculations are performed for the polarizabilities of pyrimidine and s-tetrazine in their lowest singlet excited states We find that the results for the excited state polarizabilities are sensitive to the accuracy of the excitation energies and that a qualitative correct description of the dispersion is first obtained at a correlated level

Christof Hättig

Papers

Intermolecular interaction energies by topologically partitioned electric properties II. Dispersion energies in one-centre and multicentre multipole expansions

Coupled cluster investigation of the electric-field-gradient-induced birefringence of h2, n2, c2h2, and ch4

Coupled cluster response calculations of two-photon transition probability rate constants for helium, neon and argon

Pair natural orbitals in explicitly correlated second-order moller-plesset theory

Static and frequency-dependent polarizabilities of excited singlet states using coupled cluster response theory