Select-divide-and-conquer method for large-scale configuration interaction

A select-divide-and-conquer variational method to approximate configuration interaction (CI) is presented. Given an orthonormal set made up of occupied orbitals (Hartree-Fock or similar) and suitable correlation orbitals (natural or localized orbitals), a large N-electron target space S is split into subspaces S0,S1,S2,...,SR. S0, of dimension d0, contains all configurations K with attributes (energy contributions, etc.) above thresholds T0={T0egy, T0etc.}; the CI coefficients in S0 remain always free to vary. S1 accommodates KS with attributes above T1≤T0. An eigenproblem of dimension d0+d1 for S0+S 1 is solved first, after which the last d1 rows and columns are contracted into a single row and column, thus freezing the last d1 CI coefficients hereinafter. The process is repeated with successive Sj(j≥2) chosen so that corresponding CI matrices fit random access memory (RAM). Davidson's eigensolver is used R times. The final energy eigenvalue (lowest or excited one) is always above the corresponding exact eigenvalue in S. Threshold values {Tj;j=0, 1, 2,...,R} regulate accuracy; for large-dimensional S, high accuracy requires S 0+S1 to be solved outside RAM. From there on, however, usually a few Davidson iterations in RAM are needed for each step, so that Hamiltonian matrix-element evaluation becomes rate determining. One μhartree accuracy is achieved for an eigenproblem of order 24 × 106, involving 1.2 × 1012 nonzero matrix elements, and 8.4×109 Slater determinants

Linear response functions for a vibrational configuration interaction state

Linear response functions are implemented for a vibrational configuration interaction state allowing accurate analytical calculations of pure vibrational contributions to dynamical polarizabilities. Sample calculations are presented for the pure vibrational contributions to the polarizabilities of water and formaldehyde. We discuss the convergence of the results with respect to various details of the vibrational wave function description as well as the potential and property surfaces. We also analyze the frequency dependence of the linear response function and the effect of accounting phenomenologically for the finite lifetime of the excited vibrational states. Finally, we compare the analytical response approach to a sum-over-states approach

Basis set superposition error-counterpoise corrected potential energy surfaces : application to hydrogen peroxide ... X (X=F-, Cl-, Br-, Li+, Na+) complexes

Møller-Plesset (MP2) and Becke-3-Lee-Yang-Parr (B3LYP) calculations have been used to compare the geometrical parameters, hydrogen-bonding properties, vibrational frequencies and relative energies for several X- and X+ hydrogen peroxide complexes. The geometries and interaction energies were corrected for the basis set superposition error (BSSE) in all the complexes (1-5), using the full counterpoise method, yielding small BSSE values for the 6-311 + G(3df,2p) basis set used. The interaction energies calculated ranged from medium to strong hydrogen-bonding systems (1-3) and strong electrostatic interactions (4 and 5). The molecular interactions have been characterized using the atoms in molecules theory (AIM), and by the analysis of the vibrational frequencies. The minima on the BSSE-counterpoise corrected potential-energy surface (PES) have been determined as described by S. Simón, M. Duran, and J. J. Dannenberg, and the results were compared with the uncorrected PES

Electron localization function at the correlated level

The electron localization function (ELF) has been proven so far a valuable tool to determine the location of electron pairs. Because of that, the ELF has been widely used to understand the nature of the chemical bonding and to discuss the mechanism of chemical reactions. Up to now, most applications of the ELF have been performed with monodeterminantal methods and only few attempts to calculate this function for correlated wave functions have been carried out. Here, a formulation of ELF valid for mono- and multiconfigurational wave functions is given and compared with previous recently reported approaches. The method described does not require the use of the homogeneous electron gas to define the ELF, at variance with the ELF definition given by Becke. The effect of the electron correlation in the ELF, introduced by means of configuration interaction with singles and doubles calculations, is discussed in the light of the results derived from a set of atomic and molecular systems

C-H···O H-bonded complexes: how does basis set superposition error change their potential-energy surfaces?

Geometries, vibrational frequencies, and interaction energies of the CNH⋯O3 and HCCH⋯O3 complexes are calculated in a counterpoise-corrected (CP-corrected) potential-energy surface (PES) that corrects for the basis set superposition error (BSSE). Ab initio calculations are performed at the Hartree-Fock (HF) and second-order Møller-Plesset (MP2) levels, using the 6-31G(d,p) and D95++(d,p) basis sets. Interaction energies are presented including corrections for zero-point vibrational energy (ZPVE) and thermal correction to enthalpy at 298 K. The CP-corrected and conventional PES are compared; the unconnected PES obtained using the larger basis set including diffuse functions exhibits a double well shape, whereas use of the 6-31G(d,p) basis set leads to a flat single-well profile. The CP-corrected PES has always a multiple-well shape. In particular, it is shown that the CP-corrected PES using the smaller basis set is qualitatively analogous to that obtained with the larger basis sets, so the CP method becomes useful to correctly describe large systems, where the use of small basis sets may be necessary

How does basis set superposition error change the potential surfaces for hydrogen-bonded dimers?

We describe a simple method to automate the geometric optimization of molecular orbital calculations of supermolecules on potential surfaces that are corrected for basis set superposition error using the counterpoise (CP) method. This method is applied to the H-bonding complexes HF/HCN, HF/H2O, and HCCH/H2O using the 6-31G(d,p) and D95 + + (d,p) basis sets at both the Hartree-Fock and second-order Møller-Plesset levels. We report the interaction energies, geometries, and vibrational frequencies of these complexes on the CP-optimized surfaces; and compare them with similar values calculated using traditional methods, including the (more traditional) single point CP correction. Upon optimization on the CP-corrected surface, the interaction energies become more negative (before vibrational corrections) and the H-bonding stretching vibrations decrease in all cases. The extent of the effects vary from extremely small to quite large depending on the complex and the calculational method. The relative magnitudes of the vibrational corrections cannot be predicted from the H-bond stretching frequencies alone

The hardness profile as a tool to detect spurious stationary points in the potential energy surface

The energy and hardness profile for a series of inter and intramolecular conformational changes at several levels of calculation were computed. The hardness profiles were found to be calculated as the difference between the vertical ionization potential and electron affinity. The hardness profile shows the correct number of stationary points independently of the basis set and methodology used. It was found that the hardness profiles can be used to check the reliability of the energy profiles for those chemical system

Desenvolupament de mètodes de preconcentració emprant membranes líquides suportades i extracció en fase sòlida per a la determinació de l'herbicida glifosat i el seu metabòlit AMPA en aigües naturals

El glifosat, N-(fosfonometil) glicina, és un dels herbicides més utilitzats arreu del món a causa de la seva baixa toxicitat i al seu ampli espectre d'aplicació. A conseqüència del gran ús que se'n fa, és necessari monitoritzar aquest compost i el seu principal metabòlit, l'àcid aminometilfosfònic (AMPA), en el medi ambient. S'han descrit diversos mètodes instrumentals basats en cromatografia de gasos (GC) i de líquids (HPLC), sent aquesta darrera l'opció més favorable a causa del caràcter polar dels anàlits. Per assolir nivells de concentració baixos cal, però, la preconcentració dels anàlits. En aquest treball s'estudien diferents alternatives amb aquest objectiu. S'ha avaluat la tècnica de membrana líquida suportada (SLM) on la membrana consisteix en una dissolució orgànica, que conté un transportador (en el nostre cas, un bescanviador d'anions comercial, Aliquat 336), que impregna un suport polimèric microporós que se situa entre dues solucions aquoses: la de càrrega, que conté els anàlits inicialment, i la receptora, on es retenen els anàlits després del seu transport a través de la membrana. Les condicions d'extracció més adequades s'obtenen treballant en medi bàsic amb NaOH on els anàlits estan en forma aniònica i les majors recuperacions s'obtenen amb HCl 0,1 M o NaCl 0,5 M, la qual cosa indica que l'ió clorur és la força impulsora del transport. Un cop dissenyat el sistema, es duen a terme experiments de preconcentració amb dues geometries diferents: un sistema de membrana laminar (LSLM) on recircula la fase receptora i un sistema de fibra buida (HFSLM). Els millors resultats s'obtenen amb el mòdul de fibra buida, amb factors de concentració de 25 i 3 per a glifosat i AMPA, respectivament, fent recircular durant 24 hores 100 ml de solució de càrrega i 4 ml de solució receptora. També s'aplica una tècnica més selectiva, la cromatografia d'afinitat amb ió metàl·lic immobilitzat (IMAC), basada en la interacció entre els anàlits i un metall immobilitzat en una resina a través d'un grup funcional d'aquesta. En aquest estudi s'immobilitza pal·ladi al grup funcional 8-hidroxiquinoleïna de la resina amb matriu acrílica Spheron Oxine 1000 i s'avalua per a l'extracció i preconcentració de glifosat i AMPA. Per a ambdós anàlits l'adsorció és del 100 % i les recuperacions són superiors al 80 % i al 60 % per a glifosat i AMPA, respectivament, utilitzant HCl 0,1 M + NaCl 1 M com a eluent. Aquests resultats es comparen amb els obtinguts amb dues resines més, també carregades amb pal·ladi: Iontosorb Oxin 100, que té el mateix grup funcional però matriu de cel·lulosa, i Spheron Thiol 1000, on el grup funcional és un tiol i la matriu també és acrílica. Per al glifosat els resultats són similars amb totes les resines, però per a l'AMPA la resina Spheron Thiol és la única que proporciona recuperacions superiors al 93 %. Finalment, una altra opció estudiada és l'acoblament de dues columnes de cromatografia líquida (LC-LC). En l'estudi l'objectiu és millorar el mètode existent per a glifosat i AMPA en aigües naturals on el LOD era de 0,25 ug/l. El mètode consisteix en la derivatització precolumna amb el reactiu fluorescent FMOC i l'anàlisi amb l'acoblament LC-LC-fluorescència. Variant lleugerament les condicions de derivatització s'aconsegueix quantificar 0,1 ug/l de glifosat i AMPA. Es fortifiquen aigües naturals amb 0,1, 1 i 10 ug/l dels anàlits per validar el mètode. S'obtenen recuperacions d'entre el 85 % i el 100 %, amb desviacions estàndard relatives inferiors al 8 %. Aplicant una tècnica de preconcentració prèvia a la derivatització i anàlisi utilitzant una resina de bescanvi aniònic, Amberlite IRA-900, es millora la sensibilitat del mètode i s'assoleix un LOD per al glifosat de 0,02 ug/l.

Implementation and application of basis set superposition error-correction schemes to the theoretical modeling of weak intermolecular interactions

This thesis deals with the so-called Basis Set Superposition Error (BSSE) from both a methodological and a practical point of view. The purpose of the present thesis is twofold: (a) to contribute step ahead in the correct characterization of weakly bound complexes and, (b) to shed light the understanding of the actual implications of the basis set extension effects in the ab intio calculations and contribute to the BSSE debate. The existing BSSE-correction procedures are deeply analyzed, compared, validated and, if necessary, improved. A new interpretation of the counterpoise (CP) method is used in order to define counterpoise-corrected descriptions of the molecular complexes. This novel point of view allows for a study of the BSSE-effects not only in the interaction energy but also on the potential energy surface and, in general, in any property derived from the molecular energy and its derivatives A program has been developed for the calculation of CP-corrected geometry optimizations and vibrational frequencies, also using several counterpoise schemes for the case of molecular clusters. The method has also been implemented in Gaussian98 revA10 package. The Chemical Hamiltonian Approach (CHA) methodology has been also implemented at the RHF and UHF levels of theory for an arbitrary number interacting systems using an algorithm based on block-diagonal matrices. Along with the methodological development, the effects of the BSSE on the properties of molecular complexes have been discussed in detail. The CP and CHA methodologies are used for the determination of BSSE-corrected molecular complexes properties related to the Potential Energy Surfaces and molecular wavefunction, respectively. First, the behaviour of both BSSE-correction schemes are systematically compared at different levels of theory and basis sets for a number of hydrogen-bonded complexes. The Complete Basis Set (CBS) limit of both uncorrected and CP-corrected molecular properties like stabilization energies and intermolecular distances has also been determined, showing the capital importance of the BSSE correction. Several controversial topics of the BSSE correction are addressed as well. The application of the counterpoise method is applied to internal rotational barriers. The importance of the nuclear relaxation term is also pointed out. The viability of the CP method for dealing with charged complexes and the BSSE effects on the double-well PES blue-shifted hydrogen bonds is also studied in detail. In the case of the molecular clusters the effect of high-order BSSE effects introduced with the hierarchical counterpoise scheme is also determined. The effect of the BSSE on the electron density-related properties is also addressed. The first-order electron density obtained with the CHA/F and CHA/DFT methodologies was used to assess, both graphically and numerically, the redistribution of the charge density upon BSSE-correction. Several tools like the Atoms in Molecules topologycal analysis, density difference maps, Quantum Molecular Similarity, and Chemical Energy Component Analysis were used to deeply analyze, for the first time, the BSSE effects on the electron density of several hydrogen bonded complexes of increasing size. The indirect effect of the BSSE on intermolecular perturbation theory results is also pointed out It is shown that for a BSSE-free SAPT study of hydrogen fluoride clusters, the use of a counterpoise-corrected PES is essential in order to determine the proper molecular geometry to perform the SAPT analysis.