Monte Carlo algorithms for simulating systems with adiabatic separation of electronic and nuclear degrees of freedom

Two Monte Carlo algorithms for the adiabatic sampling of nuclear and electronic degrees of freedom are introduced. In these algorithms the electronic degrees of freedom are subject to a secondary low-temperature thermostat in close analogy to the extended Lagrangian formalism used in molecular dynamics simulations. Numerical tests are carried out for two model systems of coupled harmonic oscillators, and for two more realistic systems: the water dimer and bulk liquid water. A statistical-mechanical discussion of the partition function for systems with adiabatic separation of electronic and nuclear degrees of freedom, but with finite electronic temperature, is presented. The theoretical analysis shows that the algorithms satisfy the adiabatic limit using suitable choices of the electronic temperature, T _elec, the number of electronic moves, R _elec, and the maximum step sizes used for displacements of nuclear coordinates. For quadratic coupling of the nuclear and electronic degrees of freedom, the electronic phase-space volume is independent of the nuclear coordinates. In this case, the sampling of the nuclear coordinate phase-space recovers the correct Born-Oppenheimer limit independent of T _elec, but each electronic degree of freedom contributes an offset of 0.5k _B T′_elec (with T _elec ^′−1=T ⁻¹+T _elec ⁻¹) to the average total energy. For nonquadratic coupling, satisfactory sampling of the nuclear coordinate phase-space requires a low T _elec to limit the ratio of the electronic phase-space volumes at T _elec and T′_elec to be close to unity. Received: 22 December 1998 / Accepted: 5 January 1999 / Published online: 21 June 1999     

Weighted HOMO-LUMO energy separation as an index of kinetic stability for fullerenes

A very simple but general index of kinetic stability, T, is proposed for π-electron systems, which is defined as a highest occupied molecular orbital (HOMO)- lowest unoccupied molecular orbital (LUMO) energy separation multiplied by the number of conjugated atoms. This new index can be justified by relating it to the approximate form of the superdelocalizability, an index of chemical reactivity defined by Fukui et al. It is best suited for predicting the kinetic stability of fullerenes. All isolable fullerene isomers have T values larger than 13. Received: 24 June 1998 / Accepted: 3 September 1998 / Published online: 17 December 1998     

Micropolarity of sodium bis(2-ethylhexyl) sulfosuccinate reverse micelles prepared in supercritical ethane and near-critical propane

The micropolarity of sodium bis(2-ethylhexyl) sulfosuccinate (AOT) reverse micelles prepared in supercritical ethane and near-critical propane has been determined in terms of a solvent polarity parameter, E _T(30) values, by using absorption probes, 1-ethyl-4-methoxycarbonyl pyridinium iodide and 2,6-diphenyl-4-(2,4,6-triphenylpyridinio)-phenolate as a functions of pressure and the molar ratio of water to AOT, W ₀, at a constant temperature of 310 K. The micropolarity comparable to that of ethanol was observed for reverse micelles containing water of W ₀ = 2. The micropolarity increased with the water content and became independent of pressure after the system changed to a one-phase reverse micelle solution. For a given W ₀ value, no difference in the micropolarity was noticed in the micelles prepared in ethane and propane. Phase behaviour investigations have revealed that complete dissolution of 50 mM AOT occurred at 20 MPa in supercritical ethane, while a much lower pressure of 1 MPa was required in near-critical propane. The amount of water solubilized in reverse micelles formed in supercritical ethane was relatively low, reaching a W ₀ value of 7 at 36 MPa. In contrast, the amount of water solubilized in near-critical propane reverse micelles was W ₀ = 11 at a much lower pressure of 6 MPa. A higher pressure was required to solubilize larger amount of water in reverse micelles prepared in both ethane and propane. Received: 9 October 1998 Accepted in revised form: 12 February 1999     

Correlated calculations of indirect nuclear spin-spin coupling constants using second-order polarization propagator approximations: SOPPA and SOPPA(CCSD)

We present correlated calculations of the indirect nuclear spin-spin coupling constants of HD, HF, H₂O, CH₄, C₂H₂, BH, AlH, CO and N₂ at the level of the second-order polarization propagator approximation (SOPPA) and the second-order polarization propagator approximation with coupled-cluster singles and doubles amplitudes – SOPPA(CCSD). Attention is given to the effect of the so-called W ₄ term, which has not been included in previous SOPPA spin-spin coupling constant studies of these molecules. Large sets of Gaussian basis functions, optimized for the calculation of indirect nuclear spin-spin coupling constants, were used instead of the in general rather small basis sets used in previous studies. We find that for nearly all couplings the SOPPA(CCSD) method performs better than SOPPA. Received: 6 July 1998 / Accepted: 8 September 1998 / Published online: 23 November 1998     

Energy decomposition in the topological theory of atoms in molecules and in the linear combination of atomic orbitals formalism: a note

 It is shown that the molecular energy calculated at the self-consistent-field level can be strictly expressed as a sum of one- and two-atom energy components in the framework of Bader's topological theory of atoms in molecules (AIM). The expressions of our recent “chemical energy component analysis” can be obtained from the AIM ones as some linear combination of atomic orbitals mappings of the integrations over the atomic basins. Received: 15 June 2000 / Accepted: 4 October 2000 / Published online: 19 January 2001     

Diatomic potential well depths from analyses of high-resolution electron energy spectra for autoionizing collision complexes

High-resolution energy spectra of electrons released in Penning ionization collisions of metastable rare gas atoms Rg*(ns) (Rg = He, Ne, Ar, Kr, Xe) with several open-shell and closed-shell atoms are analyzed to determine the well depth of the potential energy curve which describes the respective autoionizing collision complex. We thereby elucidate trends in the chemical interaction of Rg* with closed-shell target atoms A(ns ²) and establish a basis for detailed comparison with the respective interactions involving open-shell, ground state alkali atoms A(ns). From electron energy spectra due to␣associative ionization (RgH⁺ formation) in Rg* + H(1s) collisions, we determine binding energies for the RgH⁺(¹Σ) ground state potential (Rg = Ne, Ar, Kr, Xe) with uncertainties around 0.03 eV. Received: 30 June 1998 / Accepted: 5 August 1998 / Published online: 28 October 1998     

Obtaining self–consistent wave functions which satisfy the virial theorem

The virial theorem has played an important role in applying quantum mechanics to chemical problems. It has served as one criterion of a satisfactory wave function and its consequences on chemical bonding, molecular structure, and substituent effects have been analyzed extensively. A common method of gaining compliance with the virial theorem is to introduce a “scale” factor which adjusts all distances by a factor η. Optimizing the scale factor through the variational principle produces a wave function satisfying the virial theorem. In the present paper it is shown that when this “scaling” procedure is applied to self-consistent wave functions, the virial theorem can be satisfied, but self-consistency is lost. Scaling generally has a small effect on the total energy, but the effects on the energy components (T, V_ne, V_ee, V_nn) can be two to three orders of magnitude larger and in the range of tens to hundreds of kcal. Consequently, for applications where the energy components are useful, it is highly desirable to obtain wave functions which satisfy the virial theorem and are self-consistent. In the present paper, a simple, inexpensive extrapolation technique is reported which requires one integral evaluation and two SCF cycles to achieve convergence. Applications to atoms and small molecules are reported.     

Preparation and Crystal Structure of K2Ag12Te7

Summary.  Single crystals of K₂Ag₁₂Te₇ (a = 11.460(2), c = 4.660(1) ?; V = 530.01 ?³; space group: P6₃/m; Z = 1) were synthesized under hydrothermal conditions at 250°C in concentrated aqueous KOH solution from elementary silver and tellurium. The crystal structure is characterized by trigonal prismatic KTe₆ polyhedra, connected via two common faces to KTe₃ rods parallel to [001]. These rods are combined by two crystallographically independent Ag atoms, each coordinated to four Te and three Ag atoms (Ag–Te and Ag–Ag < 3.1 ?) to a framework of the formula (K₂Ag₁₂Te₆)^2 + and with channels parallel to the sixfold axis. These channels are statistically occupied by one further Te atom per unit cell, distributed over two independent positions. Received May 17, 2001. Accepted (revised) July 3, 2001     

Theoretical Study of the Interactions between Isolated <Emphasis Type="Italic">DNA</Emphasis> Bases and Various Groups IA and IIA Metal Ions by <Emphasis Type="Italic">Ab Initio</Emphasis> Calculations

Summary. Interactions of the DNA bases adenine (A), guanine (G), cytosine (C), and thymine (T) with various metal ions (M) of groups IA and IIA of the periodic table of the elements were studied at the HF, MP2, and DFT levels of theory. The structures and thermodynamic stabilities of these species were studied at the gas phase. The calculations uphold that there exist two active sites in G and one in A, C, and T. The calculations also show that the O² atom in T is a more active site for metal ion bindings than that in C. The stability energies for G … M complexes are larger than those for A … M complexes and the stability energies for T … M complexes are larger than those for C … M complexes. As z/r ratio for the metal ion increases, the interaction energy for the complex increases systematically. Thermodynamic quantities such as ΔH, ΔG, ΔS, and ln K were determined for each complexation reaction, [Base+M ⁿ⁺ →(Base … M) ⁿ⁺]. A, G, and C complexation reactions except for C … Rb⁺ are exothermic. The situation is quite different for T complexation reactions and all except for T … Be²⁺ and T … Mg²⁺ are endothermic.     

Contracted Gaussian-type basis functions revisited. III. Atoms K through Kr

Six minimal basis sets of contracted Gaussian-type functions (GTFs) are developed for the third-row atoms K through Kr. The smallest and largest sets for transition metal atoms are (3333/33/3) and (8433/84/8), respectively, where a slash distinguishes the s, p, and d symmetries and single-digit figures in the parentheses denote the numbers of primitive GTFs. The two largest sets, (7433/74/7) and (8433/84/8), surpass the (62111111/33111/311) set of Schaefer et al. in the associated total energies. Our (8433/84/8) set is also superior to their (842111/631/411) set. The quality of the present basis sets is tested by self-consistent field (SCF) and configuration interaction (CI) calculations on the Cu₂ molecule. As the accuracy of the basis set increases, SCF calculations show a decrease in the dissociation energy and an increase in the equilibrium internuclear distance. The same tendencies are found in the results of CI calculations with and without a Davidson correction. All the present basis sets are freely available at the internet address: http://202.35.198.41/∼htatewak/. Received: 17 June 1998 / Accepted: 4 August 1998 / Published online: 23 November 1998     

Theoretical Study of the Interactions between Isolated DNA Bases and Various Groups IA and IIA Metal Ions by Ab Initio Calculations

Interactions of the DNA bases adenine (A), guanine (G), cytosine (C), and thymine (T) with various metal ions (M) of groups IA and IIA of the periodic table of the elements were studied at the HF, MP2, and DFT levels of theory. The structures and thermodynamic stabilities of these species were studied at the gas phase. The calculations uphold that there exist two active sites in G and one in A, C, and T. The calculations also show that the O² atom in T is a more active site for metal ion bindings than that in C. The stability energies for G … M complexes are larger than those for A … M complexes and the stability energies for T … M complexes are larger than those for C … M complexes. As z/r ratio for the metal ion increases, the interaction energy for the complex increases systematically. Thermodynamic quantities such as ΔH, ΔG, ΔS, and ln K were determined for each complexation reaction, [Base+M ⁿ⁺ →(Base … M) ⁿ⁺]. A, G, and C complexation reactions except for C … Rb⁺ are exothermic. The situation is quite different for T complexation reactions and all except for T … Be²⁺ and T … Mg²⁺ are endothermic.     

Π delocalisation in 1,3-butadiene: a nonempirical molecular orbital study

A value of −0.33 eV or −7.6 kcal mol⁻¹ has been obtained for the vertical delocalisation energy of trans-1,3-butadiene from a nonempirical molecular orbital calculation on the π system. The result agrees well enough with ab initio calculations to suggest that a simplified approach need not be semiempirical. In a basis of orthogonalised atomic orbitals the central bond order is found to be 0.295 (Hückel value 0.447) for the delocalised structure and 0.125 for the localised (Hückel value zero). Core resonance integrals between neighbouring atoms, the analogues of Hückel's β, have theoretical values of −3.9 and −3.2 eV compared with −3.6 eV in benzene. Received: 11 May 1999 / Accepted: 22 July 1999 / Published online: 2 November 1999     

Infrared spectra of CO in absorption and evaluation of radial functions for potential energy and electric dipolar moment

From quantum-chemical calculations of rotational g factor and new experimental measurements of strengths of lines in infrared spectra of vibration–rotational bands v′–0 in absorption, with 1≤v′≤4, of ¹²C¹⁶O, and from analysis of 16,947 frequencies and wave numbers assigned to pure rotational and vibration–rotational transitions within electronic ground state X ¹Σ⁺, including new measurements of band 4–0 of ¹²C¹⁶O, we evaluate radial functions for potential energy and electric dipolar moment, the latter both in polynomial form and as a rational function that has qualitatively correct behaviour under limiting conditions. Received: 8 November 2001 / Accepted: 5 February 2002 / Published online: 14 August 2002     

A systematic theoretical investigation of the valence excited states of the diatomic molecules B2, C2, N2 and O2

A quantitative survey on the performance of multireference (MR), configuration interaction with all singles and doubles (CISD), MRCISD with the Davidson correction and MR-average quadratic coupled cluster (AQCC) methods for a wide range of excited states of the diatomic molecules B₂, C₂, N₂ and O₂ is presented. The spectroscopic constants r _e, ω_e, T _e and D _e for a total of 60 states have been evaluated and critically compared with available experimental data. Basis set extrapolations and size-extensivity corrections are essential for highly accurate results: MR-AQCC mean-errors of 0.001 ?, 10 cm⁻¹, 300 cm⁻¹ and 300 cm⁻¹ have been obtained for r _e, ω_e, T _e and D _e, respectively. Owing to the very systematic behavior of the results depending on the basis set and the choice of method, shortcomings of the calculations, such as Rydberg state coupling or insufficient configuration spaces, can be identified independently of experimental data. On the other hand, significant discrepancies with experiment for states which indicate no shortcomings whatsoever in the theoretical treatment suggest the re-evaluation of experimental results. The broad variety of states included in our survey and the uniform quality of the results indicate that the observed systematics is a general feature of the methods and, hence, is molecule-independent. Received: 12 June 2000 / Accepted: 1 September 2000 / Published online: 21 December 2000     

Core and valence regions of molecules

In real space, the partitioning of a molecule into valence and core regions is rooted in the picture of `valence electrons' in the field of `effective cores' consisting of nuclei partially shielded by inner-shell `core' electrons. The appropriate valence kinetic and potential energies, T ^v and V ^v, respectively, are obtained by subtracting the pertinent parts associated with the cores from the corresponding conventional total T and V energies but, far from T ^v+V ^v, the physically correct valence-region energy is . This result differs markedly from T ^v+V ^v because E ^v, T ^v and V ^v do not obey the virial theorem. Received: 21 August 1996 / Accepted: 14 November 1996     

Theoretical study of the potential-energy surface of C2NP

 The B3LYP/6-311G(d) and CCSD(T)/6-311G(2df) (single-point) methods have been used to investigate the singlet potential energy surface of C₂NP, in which seven stationary isomers and seventeen interconversion transition states are involved. At the final CCSD(T)/6-311G(2df)//B3LYP6-311G(d) level with zero-point vibrational energy correction the lowest-lying isomer is a linear NCCP followed by two linear CNCP isomers at 23.9  and CCNP at 65.8 kcal mol⁻¹, respectively. The three isomers are kinetically very stable towards both isomerization and dissociation, and CCNP is even more kinetically stable than CNCP – by 14.3 kcal mol⁻¹ despite its high energy. Further comparative calculations were performed at the QCISD and QCISD(T) levels with the 6-311G(d) and 6-311G(2d) basis sets to obtain more reliable structures and spectroscopy for the three isomers. The calculated bond lengths, rotational constant, and dipole moment for NCCP were in close agreement with the experimentally determined values. Finally, similarities and discrepancies between the potential energy surface of C₂NP and those of the analogous species C₂N₂ and C₂P₂ were compared. The results presented in this paper might be helpful for future identification of the two still unknown yet kinetically very stable isomers CNCP and CCNP, both in the laboratory and in interstellar space. Received: 3 January 2001 / Accepted: 6 June 2001 / Published online: 30 October 2001     

The topology of catchment regions of potential energy hypersurfaces

A simple proof is presented for a fundamental topological property of catchment regions of potential energy hypersurfaces: each catchment region C(λ,i), representing a chemical species and its conformational range on the potential energy hypersurface, is simply k-connected for each dimension k=1,2,…3N−6−λ, where λ is the index of the catchment region. The consequences of this property on the structure of the fundamental group of reaction mechanisms (the one-dimensional homotopy group of reaction paths) is discussed. Received: 8 July 1998 / Accepted: 6 October 1998 / Published online: 23 February 1999     

Direct-space analysis of the Si–Si bonding pattern in the π-bonded chain reconstructed Si(111)(2 × 1) surface

Atomic and bond properties of silicon atoms in the buckled π-bonded chain reconstructed Si(111)(2 × 1) system were investigated by applying the quantum theory of atoms in molecules to a number of wavefunctions from periodic ab initio calculations using a slab model for the surface and geometries from experiment. Reconstruction involves much larger surface-cell charge distortions than in the unrelaxed surface and drastic changes in the atomic polarizations of the surface layer atoms. The effect of buckling is to largely differentiate the properties (charge, energy, volume, atomic polarizations) of the two unique atoms of each surface layer. The direction of electronic charge transfer in the topmost chain (from the “up” to the “down” atom) was found to be opposite to what was claimed previously. The π conjugation is not strictly localized along the topmost layer chains (where it is also largely incomplete), but rather it extends over a 2D array of bonds between the topmost and the lower surface layers. Received: 19 July 2000 / Accepted: 2 October 2000 / Published online: 23 January 2001     

Topological structures of tetrahedral (Td and T) fullerenes with hexagonal and triangular faces and their vibration and NMR spectra

On analyzing the topological structures of the three types of tetrahedral fullerenes (which consist only of triangles and hexagons), (1) C _n (T _d ,n=12h ²; h=1,2,…), (2) C _n (T _d ,n=4h ²;h=1,2,…), and (3) C _n (T,n=4(h ²+hk+k ²);h>k,h,k=1,2,…), we have obtained theoretically the Infrared and Raman active modes by means of the derived formulas for the decomposition of their nuclear motions into irreducible representations, and the ¹³C NMR spectra with natural abundance for ¹³C by using the distribution functions for all of the tetrahedral (T _d and T) fullerenes, respectively. Received: 25 May 1998 / Accepted: 30 July 1998 / Published online: 23 November 1998     

Expansion coefficients and moments of electron momentum densities for singly charged ions

Numerical Hartree–Fock calculations of the first three coefficients of the MacLaurin expansion and the leading coefficient of the large-p asymptotic expansion of the electron momentum densities Π(p) are reported for 54 singly charged atomic cations from He⁺ (atomic number Z = 2) to Cs⁺ (Z = 55) and 43 anions from H⁻ (Z = 1) to I⁻ (Z = 53) in their experimental ground states. We also report all the finite moments <p ^k > (−2≤k≤+4) of the momentum densities Π(p) for the above-mentioned 97 ionic species. The results are compared with the previous ones for neutral atoms [Koga and Thakkar (1996) J Phys B 29: 2973], and the dependence of the expansion coefficients and moments on nuclear charge is discussed among isoelectronic species. Received: 20 November 1998 / Accepted: 15 January 1999 / Published online: 7 June 1999