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The 20 most cited articles over time based on CrossRef data.
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Density‐functional thermochemistry. III. The role of exact exchange J. Chem. Phys. 98, 5648 (1993); http://dx.doi.org/10.1063/1.464913 (5 pages) | Cited 24652 times
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Despite the remarkable thermochemical accuracy of Kohn–Sham density‐functional theories with gradient corrections for exchange‐correlation [see, for example, A. D. Becke, J. Chem. Phys. 96, 2155 (1992)], we believe that further improvements are unlikely unless exact‐exchange information is considered. Arguments to support this view are presented, and a semiempirical exchange‐correlation functional containing local‐spin‐density, gradient, and exact‐exchange terms is tested on 56 atomization energies, 42 ionization potentials, 8 proton affinities, and 10 total atomic energies of first‐ and second‐row systems. This functional performs significantly better than previous functionals with gradient corrections only, and fits experimental atomization energies with an impressively small average absolute deviation of 2.4 kcal/mol. |
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Equation of State Calculations by Fast Computing Machines J. Chem. Phys. 21, 1087 (1953); http://dx.doi.org/10.1063/1.1699114 (6 pages) | Cited 8745 times Online Publication Date: 23 December 2004
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A general method, suitable for fast computing machines, for investigating such properties as equations of state for substances consisting of interacting individual molecules is described. The method consists of a modified Monte Carlo integration over configuration space. Results for the two‐dimensional rigid‐sphere system have been obtained on the Los Alamos MANIAC and are presented here. These results are compared to the free volume equation of state and to a four‐term virial coefficient expansion. |
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J. Chem. Phys. 90, 1007 (1989); http://dx.doi.org/10.1063/1.456153 (17 pages) | Cited 8153 times
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In the past, basis sets for use in correlated molecular calculations have largely been taken from single configuration calculations. Recently, Almlöf, Taylor, and co‐workers have found that basis sets of natural orbitals derived from correlated atomic calculations (ANOs) provide an excellent description of molecular correlation effects. We report here a careful study of correlation effects in the oxygen atom, establishing that compact sets of primitive Gaussian functions effectively and efficiently describe correlation effects if the exponents of the functions are optimized in atomic correlated calculations, although the primitive (sp) functions for describing correlation effects can be taken from atomic Hartree–Fock calculations if the appropriate primitive set is used. Test calculations on oxygen‐containing molecules indicate that these primitive basis sets describe molecular correlation effects as well as the ANO sets of Almlöf and Taylor. Guided by the calculations on oxygen, basis sets for use in correlated atomic and molecular calculations were developed for all of the first row atoms from boron through neon and for hydrogen. As in the oxygen atom calculations, it was found that the incremental energy lowerings due to the addition of correlating functions fall into distinct groups. This leads to the concept of correlation consistent basis sets, i.e., sets which include all functions in a given group as well as all functions in any higher groups. Correlation consistent sets are given for all of the atoms considered. The most accurate sets determined in this way, [5s4p3d2f1g], consistently yield 99% of the correlation energy obtained with the corresponding ANO sets, even though the latter contains 50% more primitive functions and twice as many primitive polarization functions. It is estimated that this set yields 94%–97% of the total (HF+1+2) correlation energy for the atoms neon through boron. |
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Comparison of simple potential functions for simulating liquid water J. Chem. Phys. 79, 926 (1983); http://dx.doi.org/10.1063/1.445869 (10 pages) | Cited 6087 times
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Classical Monte Carlo simulations have been carried out for liquid water in the NPT ensemble at 25 °C and 1 atm using six of the simpler intermolecular potential functions for the water dimer: Bernal–Fowler (BF), SPC, ST2, TIPS2, TIP3P, and TIP4P. Comparisons are made with experimental thermodynamic and structural data including the recent neutron diffraction results of Thiessen and Narten. The computed densities and potential energies are in reasonable accord with experiment except for the original BF model, which yields an 18% overestimate of the density and poor structural results. The TIPS2 and TIP4P potentials yield oxygen–oxygen partial structure functions in good agreement with the neutron diffraction results. The accord with the experimental OH and HH partial structure functions is poorer; however, the computed results for these functions are similar for all the potential functions. Consequently, the discrepancy may be due to the correction terms needed in processing the neutron data or to an effect uniformly neglected in the computations. Comparisons are also made for self‐diffusion coefficients obtained from molecular dynamics simulations. Overall, the SPC, ST2, TIPS2, and TIP4P models give reasonable structural and thermodynamic descriptions of liquid water and they should be useful in simulations of aqueous solutions. The simplicity of the SPC, TIPS2, and TIP4P functions is also attractive from a computational standpoint. |
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J. Chem. Phys. 82, 299 (1985); http://dx.doi.org/10.1063/1.448975 (12 pages) | Cited 3710 times
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Ab initio effective core potentials (ECP’s) have been generated to replace the innermost core electron for third‐row (K–Au), fourth‐row (Rb–Ag), and fifth‐row (Cs–Au) atoms. The outermost core orbitals—corresponding to the ns2np6 configuration for the three rows here—are not replaced by the ECP but are treated on an equal footing with the nd, (n+1)s and (n+1)p valence orbitals. These ECP’s have been derived for use in molecular calculations where these outer core orbitals need to be treated explicitly rather than to be replaced by an ECP. The ECP’s for the forth and fifth rows also incorporate the mass–velocity and Darwin relativistic effects into the potentials. Analytic fits to the potentials are presented for use in multicenter integral evaluation. Gaussian orbital valence basis sets are developed for the (3s, 3p, 3d, 4s, 4p), (4s, 4p, 4d, 5s, 5p), and (5s, 5p, 5d, 6s, 6p) ortibals of the three respective rows. |
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Gaussian‐Type Functions for Polyatomic Systems. I J. Chem. Phys. 42, 1293 (1965); http://dx.doi.org/10.1063/1.1696113 (10 pages) | Cited 3564 times Online Publication Date: 2 July 2004
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In view of rapid progress of computer capability, it is very desirable to have a reliable assessment of the usefulness of Gaussian‐type orbitals as basis functions for large‐scale molecular calculations. In the present paper several attempts are made to answer this question mainly at the level of atomic Hartree—Fock calculations. The necessary number of terms of Gaussian‐type basis functions in the analytical Hartree—Fock expansion calculation is apparently more than twice as much as the number of terms needed in the expansion with Slater‐type basis functions. However, this fact does not necessarily suggest a definite choice of Slater‐type orbitals. Discussions pertinent to this point are presented in the latter part of the present paper. |
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J. Chem. Phys. 56, 2257 (1972); http://dx.doi.org/10.1063/1.1677527 (5 pages) | Cited 3544 times Online Publication Date: 18 September 2003
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Two extended basis sets (termed 5–31G and 6–31G) consisting of atomic orbitals expressed as fixed linear combinations of Gaussian functions are presented for the first row atoms carbon to fluorine. These basis functions are similar to the 4–31G set [J. Chem. Phys. 54, 724 (1971)] in that each valence shell is split into inner and outer parts described by three and one Gaussian function, respectively. Inner shells are represented by a single basis function taken as a sum of five (5–31G) or six (6–31G) Gaussians. Studies with a number of polyatomic molecules indicate a substantial lowering of calculated total energies over the 4–31G set. Calculated relative energies and equilibrium geometries do not appear to be altered significantly. |
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Electronic Population Analysis on LCAO☒MO Molecular Wave Functions. I J. Chem. Phys. 23, 1833 (1955); http://dx.doi.org/10.1063/1.1740588 (8 pages) | Cited 3323 times Online Publication Date: 29 December 2004
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With increasing availability of good all‐electron LCAO MO (LCAO molecular orbital) wave functions for molecules, a systematic procedure for obtaining maximum insight from such data has become desirable. An analysis in quantitative form is given here in terms of breakdowns of the electronic population into partial and total ``gross atomic populations,'' or into partial and total ``net atomic populations'' together with ``overlap populations.'' ``Gross atomic populations'' distribute the electrons almost perfectly among the various AOs (atomic orbitals) of the various atoms in the molecule. From these numbers, a definite figure is obtained for the amount of promotion (e.g., from 2s to 2p) in each atom; and also for the gross charge Q on each atom if the bonds are polar. The total overlap population for any pair of atoms in a molecule is in general made up of positive and negative contributions. If the total overlap population between two atoms is positive, they are bonded; if negative, they are antibonded. Tables of gross atomic populations and overlap populations, also gross atomic charges Q, computed from SCF (self‐consistent field) LCAO‐MO data on CO and H2O, are given. The amount of s‐p promotion is found to be nearly the same for the O atom in CO and in H2O (0.14 electron in CO and 0.15e in H2O). For the C atom in CO it is 0.50e. For the N atom in N2 it is 0.26e according to calculations by Scherr. In spite of very strong polarity in the π bonds in CO, the σ and π overlap populations are very similar to those in N2. In CO the total overlap population for the π electrons is about twice that for the σ electrons. The most easily ionized electrons of CO are in an MO such that its gross atomic population is 94% localized on the carbon atom; these electrons account for the (weak) electron donor properties of CO. A comparison between changes of bond lengths observed on removal of an electron from one or another MO of CO and H2, and corresponding changes in computed overlap populations, shows good correlation. Several other points of interest are discussed. |
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Kinetics of Phase Change. I General Theory J. Chem. Phys. 7, 1103 (1939); http://dx.doi.org/10.1063/1.1750380 (10 pages) | Cited 3318 times Online Publication Date: 22 December 2004
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The theory of the kinetics of phase change is developed with the experimentally supported assumptions that the new phase is nucleated by germ nuclei which already exist in the old phase, and whose number can be altered by previous treatment. The density of germ nuclei diminishes through activation of some of them to become growth nuclei for grains of the new phase, and ingestion of others by these growing grains. The quantitative relations between the density of germ nuclei, growth nuclei, and transformed volume are derived and expressed in terms of a characteristic time scale for any given substance and process. The geometry and kinetics of a crystal aggregate are studied from this point of view, and it is shown that there is strong evidence of the existence, for any given substance, of an isokinetic range of temperatures and concentrations in which the characteristic kinetics of phase change remains the same. The determination of phase reaction kinetics is shown to depend upon the solution of a functional equation of a certain type. Some of the general properties of temperature‐time and transformation‐time curves, respectively, are described and explained. |
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J. Chem. Phys. 82, 270 (1985); http://dx.doi.org/10.1063/1.448799 (14 pages) | Cited 3176 times
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Ab initio effective core potentials (ECP’s) have been generated to replace the Coulomb, exchange, and core‐orthogonality effects of the chemically inert core electron in the transition metal atoms Sc to Hg. For the second and third transition series relative ECP’s have been generated which also incorporate the mass–velocity and Darwin relativistic effects into the potential. The ab initio ECP’s should facilitate valence electron calculations on molecules containing transition‐metal atoms with accuracies approaching all‐electron calculations at a fraction of the computational cost. Analytic fits to the potentials are presented for use in multicenter integral evaluation. Gaussian orbital valence basis sets are developed for the (3d,4s,4p), (4d,5s,5p), and (5d,6s,6p) orbitals of the first, second, and third transition series atoms, respectively. All‐electron and valence‐electron atomic excitation energies are also compared for the low‐lying states of Sc–Hg, and the valence‐electron calculations are found to reproduce the all‐electron excitation energies (typically within a few tenths of an eV). |
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Kinetics of Phase Change. II Transformation‐Time Relations for Random Distribution of Nuclei J. Chem. Phys. 8, 212 (1940); http://dx.doi.org/10.1063/1.1750631 (13 pages) | Cited 2621 times Online Publication Date: 29 December 2004
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Following upon the general theory in Part I, a considerable simplification is here introduced in the treatment of the case where the grain centers of the new phase are randomly distributed. Also, the kinetics of the main types of crystalline growth, such as result in polyhedral, plate‐like and lineal grains, are studied. A relation between the actual transformed volume V and a related extended volume V1 ex is derived upon statistical considerations. A rough approximation to this relation is shown to lead, under the proper conditions, to the empirical formula of Austin and Rickett. The exact relation is used to reduce the entire problem to the determination of V1 ex, in terms of which all other quantities are expressed. The approximate treatment of the beginning of transformation in the isokinetic range is shown to lead to the empirical formula of Krainer and to account quantitatively for certain relations observed in recrystallization phenomena. It is shown that the predicted shapes for isothermal transformation‐time curves correspond well with the experimental data. |
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Dispersion and Absorption in Dielectrics I. Alternating Current Characteristics J. Chem. Phys. 9, 341 (1941); http://dx.doi.org/10.1063/1.1750906 (11 pages) | Cited 2588 times Online Publication Date: 29 December 2004
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The dispersion and absorption of a considerable number of liquid and dielectrics are represented by the empirical formula  If a distribution of relaxation times is assumed to account for Eq. (1), it is possible to calculate the necessary distribution function by the method of Fuoss and Kirkwood. It is, however, difficult to understand the physical significance of this formal result. If a dielectric satisfying Eq. (1) is represented by a three‐element electrical circuit, the mechanism responsible for the dispersion is equivalent to a complex impedance with a phase angle which is independent of the frequency. On this basis, the mechanism of interaction has the striking property that energy is conserved or ``stored'' in addition to being dissipated and that the ratio of the average energy stored to the energy dissipated per cycle is independent of the frequency. |
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J. Chem. Phys. 82, 284 (1985); http://dx.doi.org/10.1063/1.448800 (15 pages) | Cited 2553 times
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A consistent set of ab initio effective core potentials (ECP) has been generated for the main group elements from Na to Bi using the procedure originally developed by Kahn. The ECP’s are derived from all‐electron numerical Hartree–Fock atomic wave functions and fit to analytical representations for use in molecular calculations. For Rb to Bi the ECP’s are generated from the relativistic Hartree–Fock atomic wave functions of Cowan which incorporate the Darwin and mass–velocity terms. Energy‐optimized valence basis sets of (3s3p) primitive Gaussians are presented for use with the ECP’s. Comparisons between all‐electron and valence‐electron ECP calculations are presented for NaF, NaCl, Cl2, Cl2−, Br2, Br2−, and Xe2+. The results show that the average errors introduced by the ECP’s are generally only a few percent. |
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J. Chem. Phys. 53, 2823 (1970); http://dx.doi.org/10.1063/1.1674408 (11 pages) | Cited 2517 times Online Publication Date: 18 September 2003
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The contraction of Gaussian basis functions for use in molecular calculations is investigated by considering the effects of contraction on the energies and one‐electron properties of the water and nitrogen molecules. The emphasis is on obtaining principles which can be used to predict optimal contraction schemes for other systems without the necessity of such exhaustive calculations. Using these principles, contractions are predicted for the first‐row atoms. |
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J. Chem. Phys. 54, 724 (1971); http://dx.doi.org/10.1063/1.1674902 (5 pages) | Cited 2471 times Online Publication Date: 10 September 2003
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An extended basis set of atomic functions expressed as fixed linear combinations of Gaussian functions is presented for hydrogen and the first‐row atoms carbon to fluorine. In this set, described as 4–31 G, each inner shell is represented by a single basis function taken as a sum of four Gaussians and each valence orbital is split into inner and outer parts described by three and one Gaussian function, respectively. The expansion coefficients and Gaussian exponents are determined by minimizing the total calculated energy of the atomic ground state. This basis set is then used in single‐determinant molecular‐orbital studies of a group of small polyatomic molecules. Optimization of valence‐shell scaling factors shows that considerable rescaling of atomic functions occurs in molecules, the largest effects being observed for hydrogen and carbon. However, the range of optimum scale factors for each atom is small enough to allow the selection of a standard molecular set. The use of this standard basis gives theoretical equilibrium geometries in reasonable agreement with experiment. |
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A Theory of Sensitized Luminescence in Solids J. Chem. Phys. 21, 836 (1953); http://dx.doi.org/10.1063/1.1699044 (15 pages) | Cited 2445 times Online Publication Date: 23 December 2004
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The term ``sensitized luminescence'' in crystalline phosphors refers to the phenomenon whereby an impurity (activator, or emitter) is enabled to luminesce upon the absorption of light in a different type of center (sensitizer, or absorber) and upon the subsequent radiationless transfer of energy from the sensitizer to the activator. The resonance theory of Förster, which involves only allowed transitions, is extended to include transfer by means of forbidden transitions which, it is concluded, are responsible for the transfer in all inorganic systems yet investigated. The transfer mechanisms of importance are, in order of decreasing strength, the overlapping of the electric dipole fields of the sensitizer and the activator, the overlapping of the dipole field of the sensitizer with the quadrupole field of the activator, and exchange effects. These mechanisms will give rise to ``sensitization'' of about 103−104, 102, and 30 lattice sites surrounding each sensitizer in typical systems. The dependence of transfer efficiency upon sensitizer and activator concentrations and on temperature are discussed. Application is made of the theory to experimental results on inorganic phosphors, and further experiments are suggested. |
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A unified formulation of the constant temperature molecular dynamics methods J. Chem. Phys. 81, 511 (1984); http://dx.doi.org/10.1063/1.447334 (9 pages) | Cited 2371 times
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Three recently proposed constant temperature molecular dynamics methods by: (i) Nosé (Mol. Phys., to be published); (ii) Hoover et al. [Phys. Rev. Lett. 48, 1818 (1982)], and Evans and Morriss [Chem. Phys. 77, 63 (1983)]; and (iii) Haile and Gupta [J. Chem. Phys. 79, 3067 (1983)] are examined analytically via calculating the equilibrium distribution functions and comparing them with that of the canonical ensemble. Except for effects due to momentum and angular momentum conservation, method (1) yields the rigorous canonical distribution in both momentum and coordinate space. Method (2) can be made rigorous in coordinate space, and can be derived from method (1) by imposing a specific constraint. Method (3) is not rigorous and gives a deviation of order N−1/2 from the canonical distribution (N the number of particles). The results for the constant temperature–constant pressure ensemble are similar to the canonical ensemble case. |
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Equation of State for Nonattracting Rigid Spheres J. Chem. Phys. 51, 635 (1969); http://dx.doi.org/10.1063/1.1672048 (2 pages) | Cited 2306 times Online Publication Date: 5 September 2003
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A new equation of state for rigid spheres has been developed from an analysis of the reduced virial series. Comparisons with existing equations show that the new formula possesses superior ability to describe rigid‐sphere behavior. |
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Spin Diffusion Measurements: Spin Echoes in the Presence of a Time‐Dependent Field Gradient J. Chem. Phys. 42, 288 (1965); http://dx.doi.org/10.1063/1.1695690 (5 pages) | Cited 2305 times Online Publication Date: 2 July 2004
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A derivation is given of the effect of a time‐dependent magnetic field gradient on the spin‐echo experiment, particularly in the presence of spin diffusion. There are several reasons for preferring certain kinds of time‐dependent magnetic field gradients to the more usual steady gradient. If the gradient is reduced during the rf pulses, H1 need not be particularly large; if the gradient is small at the time of the echo, the echo will be broad and its amplitude easy to measure. Both of these relaxations of restrictions on the measurement of diffusion coefficients by the spin‐echo technique serve to extend its range of applicability. Furthermore, a pulsed gradient can be recommended when it is critical to define the precise time period over which diffusion is being measured. The theoretical expression derived has been verified experimentally for several choices of time dependent magnetic field gradient. An apparatus is described suitable for the production of pulsed gradients with amplitudes as large as 100 G cm−1. The diffusion coefficient of dry glycerol at 26°±1°C has been found to be (2.5±0.2)×10−8 cm2 sec−1, a value smaller than can ordinarily be measured by the steady gradient method. |
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J. Chem. Phys. 53, 1126 (1970); http://dx.doi.org/10.1063/1.1674108 (5 pages) | Cited 2262 times Online Publication Date: 18 September 2003
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Raman spectra are reported from single crystals of graphite and other graphite materials. Single crystals of graphite show one single line at 1575 cm−1. For the other materials like stress‐annealed pyrolitic graphite, commercial graphites, activated charcoal, lampblack, and vitreous carbon another line is detected at 1355 cm−1. The Raman intensity of this band is inversely proportional to the crystallite size and is caused by a breakdown of the k‐selection rule. The intensity of this band allows an estimate of the crystallite size in the surface layer of any carbon sample. Two in‐plane force constants are calculated from the frequencies. |
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